Sample records for explicit analytic results

  1. Analytical validation of an explicit finite element model of a rolling element bearing with a localised line spall

    NASA Astrophysics Data System (ADS)

    Singh, Sarabjeet; Howard, Carl Q.; Hansen, Colin H.; Köpke, Uwe G.

    2018-03-01

    In this paper, numerically modelled vibration response of a rolling element bearing with a localised outer raceway line spall is presented. The results were obtained from a finite element (FE) model of the defective bearing solved using an explicit dynamics FE software package, LS-DYNA. Time domain vibration signals of the bearing obtained directly from the FE modelling were processed further to estimate time-frequency and frequency domain results, such as spectrogram and power spectrum, using standard signal processing techniques pertinent to the vibration-based monitoring of rolling element bearings. A logical approach to analyses of the numerically modelled results was developed with an aim to presenting the analytical validation of the modelled results. While the time and frequency domain analyses of the results show that the FE model generates accurate bearing kinematics and defect frequencies, the time-frequency analysis highlights the simulation of distinct low- and high-frequency characteristic vibration signals associated with the unloading and reloading of the rolling elements as they move in and out of the defect, respectively. Favourable agreement of the numerical and analytical results demonstrates the validation of the results from the explicit FE modelling of the bearing.

  2. Adhesive-bonded double-lap joints. [analytical solutions for static load carrying capacity

    NASA Technical Reports Server (NTRS)

    Hart-Smith, L. J.

    1973-01-01

    Explicit analytical solutions are derived for the static load carrying capacity of double-lap adhesive-bonded joints. The analyses extend the elastic solution Volkersen and cover adhesive plasticity, adherend stiffness imbalance and thermal mismatch between the adherends. Both elastic-plastic and bi-elastic adhesive representations lead to the explicit result that the influence of the adhesive on the maximum potential bond strength is defined uniquely by the strain energy in shear per unit area of bond. Failures induced by peel stresses at the ends of the joint are examined. This failure mode is particularly important for composite adherends. The explicit solutions are sufficiently simple to be used for design purposes

  3. Adaptive steganography

    NASA Astrophysics Data System (ADS)

    Chandramouli, Rajarathnam; Li, Grace; Memon, Nasir D.

    2002-04-01

    Steganalysis techniques attempt to differentiate between stego-objects and cover-objects. In recent work we developed an explicit analytic upper bound for the steganographic capacity of LSB based steganographic techniques for a given false probability of detection. In this paper we look at adaptive steganographic techniques. Adaptive steganographic techniques take explicit steps to escape detection. We explore different techniques that can be used to adapt message embedding to the image content or to a known steganalysis technique. We investigate the advantages of adaptive steganography within an analytical framework. We also give experimental results with a state-of-the-art steganalysis technique demonstrating that adaptive embedding results in a significant number of bits embedded without detection.

  4. The Challenge of Understanding Process in Clinical Behavior Analysis: The Case of Functional Analytic Psychotherapy

    ERIC Educational Resources Information Center

    Follette, William C.; Bonow, Jordan T.

    2009-01-01

    Whether explicitly acknowledged or not, behavior-analytic principles are at the heart of most, if not all, empirically supported therapies. However, the change process in psychotherapy is only now being rigorously studied. Functional analytic psychotherapy (FAP; Kohlenberg & Tsai, 1991; Tsai et al., 2009) explicitly identifies behavioral-change…

  5. Soliton polarization rotation in fiber lasers

    NASA Astrophysics Data System (ADS)

    Afanasjev, V. V.

    1995-02-01

    I have found the approximate analytical solution in explicit form for a vector soliton with an arbitrary component ratio. My solution describes the dependence of soliton intensity on polarization angle and also nonlinear polarization rotation. The analytical results agree well with the numerical simulations.

  6. Revisiting analytical solutions for steady interface flow in subsea aquifers: Aquitard salinity effects

    NASA Astrophysics Data System (ADS)

    Werner, Adrian D.; Robinson, Neville I.

    2018-06-01

    Existing analytical solutions for the distribution of fresh groundwater in subsea aquifers presume that the overlying offshore aquitard, represented implicitly, contains seawater. Here, we consider the case where offshore fresh groundwater is the result of freshwater discharge from onshore aquifers, and neglect paleo-freshwater sources. A recent numerical modeling investigation, involving explicit simulation of the offshore aquitard, demonstrates that offshore aquitards more likely contain freshwater in areas of upward freshwater leakage to the sea. We integrate this finding into the existing analytical solutions by providing an alternative formulation for steady interface flow in subsea aquifers, whereby the salinity in the offshore aquitard can be chosen. The new solution, taking the aquitard salinity as that of freshwater, provides a closer match to numerical modeling results in which the aquitard is represented explicitly.

  7. The mere exposure effect and recognition depend on the way you look!

    PubMed

    Willems, Sylvie; Dedonder, Jonathan; Van der Linden, Martial

    2010-01-01

    In line with Whittlesea and Price (2001), we investigated whether the memory effect measured with an implicit memory paradigm (mere exposure effect) and an explicit recognition task depended on perceptual processing strategies, regardless of whether the task required intentional retrieval. We found that manipulation intended to prompt functional implicit-explicit dissociation no longer had a differential effect when we induced similar perceptual strategies in both tasks. Indeed, the results showed that prompting a nonanalytic strategy ensured performance above chance on both tasks. Conversely, inducing an analytic strategy drastically decreased both explicit and implicit performance. Furthermore, we noted that the nonanalytic strategy involved less extensive gaze scanning than the analytic strategy and that memory effects under this processing strategy were largely independent of gaze movement.

  8. Exact Local Correlations and Full Counting Statistics for Arbitrary States of the One-Dimensional Interacting Bose Gas

    NASA Astrophysics Data System (ADS)

    Bastianello, Alvise; Piroli, Lorenzo; Calabrese, Pasquale

    2018-05-01

    We derive exact analytic expressions for the n -body local correlations in the one-dimensional Bose gas with contact repulsive interactions (Lieb-Liniger model) in the thermodynamic limit. Our results are valid for arbitrary states of the model, including ground and thermal states, stationary states after a quantum quench, and nonequilibrium steady states arising in transport settings. Calculations for these states are explicitly presented and physical consequences are critically discussed. We also show that the n -body local correlations are directly related to the full counting statistics for the particle-number fluctuations in a short interval, for which we provide an explicit analytic result.

  9. Analytical Studies on the Synchronization of a Network of Linearly-Coupled Simple Chaotic Systems

    NASA Astrophysics Data System (ADS)

    Sivaganesh, G.; Arulgnanam, A.; Seethalakshmi, A. N.; Selvaraj, S.

    2018-05-01

    We present explicit generalized analytical solutions for a network of linearly-coupled simple chaotic systems. Analytical solutions are obtained for the normalized state equations of a network of linearly-coupled systems driven by a common chaotic drive system. Two parameter bifurcation diagrams revealing the various hidden synchronization regions, such as complete, phase and phase-lag synchronization are identified using the analytical results. The synchronization dynamics and their stability are studied using phase portraits and the master stability function, respectively. Further, experimental results for linearly-coupled simple chaotic systems are presented to confirm the analytical results. The synchronization dynamics of a network of chaotic systems studied analytically is reported for the first time.

  10. Implicit/explicit memory versus analytic/nonanalytic processing: rethinking the mere exposure effect.

    PubMed

    Whittlesea, B W; Price, J R

    2001-03-01

    In studies of the mere exposure effect, rapid presentation of items can increase liking without accurate recognition. The effect on liking has been explained as a misattribution of fluency caused by prior presentation. However, fluency is also a source of feelings of familiarity. It is, therefore, surprising that prior experience can enhance liking without also causing familiarity-based recognition. We suggest that when study opportunities are minimal and test items are perceptually similar, people adopt an analytic approach, attempting to recognize distinctive features. That strategy fails because rapid presentation prevents effective encoding of such features; it also prevents people from experiencing fluency and a consequent feeling of familiarity. We suggest that the liking-without-recognition effect results from using an effective (nonanalytic) strategy in judging pleasantness, but an ineffective (analytic) strategy in recognition. Explanations of the mere exposure effect based on a distinction between implicit and explicit memory are unnecessary.

  11. Meta-analytic evidence of low convergence between implicit and explicit measures of the needs for achievement, affiliation, and power

    PubMed Central

    Köllner, Martin G.; Schultheiss, Oliver C.

    2014-01-01

    The correlation between implicit and explicit motive measures and potential moderators of this relationship were examined meta-analytically, using Hunter and Schmidt's (2004) approach. Studies from a comprehensive search in PsycINFO, data sets of our research group, a literature list compiled by an expert, and the results of a request for gray literature were examined for relevance and coded. Analyses were based on 49 papers, 56 independent samples, 6151 subjects, and 167 correlations. The correlations (ρ) between implicit and explicit measures were 0.130 (CI: 0.077–0.183) for the overall relationship, 0.116 (CI: 0.050–0.182) for affiliation, 0.139 (CI: 0.080–0.198) for achievement, and 0.038 (CI: −0.055–0.131) for power. Participant age did not moderate the size of these relationships. However, a greater proportion of males in the samples and an earlier publication year were associated with larger effect sizes. PMID:25152741

  12. Explicit analytical expression for the condition number of polynomials in power form

    NASA Astrophysics Data System (ADS)

    Rack, Heinz-Joachim

    2017-07-01

    In his influential papers [1-3] W. Gautschi has defined and reshaped the condition number κ∞ of polynomials Pn of degree ≤ n which are represented in power form on a zero-symmetric interval [-ω, ω]. Basically, κ∞ is expressed as the product of two operator norms: an explicit factor times an implicit one (the l∞-norm of the coefficient vector of the n-th Chebyshev polynomial of the first kind relative to [-ω, ω]). We provide a new proof, economize the second factor and express it by an explicit analytical formula.

  13. Nonlinear core deflection in injection molding

    NASA Astrophysics Data System (ADS)

    Poungthong, P.; Giacomin, A. J.; Saengow, C.; Kolitawong, C.; Liao, H.-C.; Tseng, S.-C.

    2018-05-01

    Injection molding of thin slender parts is often complicated by core deflection. This deflection is caused by molten plastics race tracking through the slit between the core and the rigid cavity wall. The pressure of this liquid exerts a lateral force of the slender core causing the core to bend, and this bending is governed by a nonlinear fifth order ordinary differential equation for the deflection that is not directly in the position along the core. Here we subject this differential equation to 6 sets of boundary conditions, corresponding to 6 commercial core constraints. For each such set of boundary conditions, we develop an explicit approximate analytical solution, including both a linear term and a nonlinear term. By comparison with finite difference solutions, we find our new analytical solutions to be accurate. We then use these solutions to derive explicit analytical approximations for maximum deflections and for the core position of these maximum deflections. Our experiments on the base-gated free-tip boundary condition agree closely with our new explicit approximate analytical solution.

  14. Research in digital adaptive flight controllers

    NASA Technical Reports Server (NTRS)

    Kaufman, H.

    1976-01-01

    A design study of adaptive control logic suitable for implementation in modern airborne digital flight computers was conducted. Both explicit controllers which directly utilize parameter identification and implicit controllers which do not require identification were considered. Extensive analytical and simulation efforts resulted in the recommendation of two explicit digital adaptive flight controllers. Interface weighted least squares estimation procedures with control logic were developed using either optimal regulator theory or with control logic based upon single stage performance indices.

  15. Band-to-band tunneling distance analysis in the heterogate electron–hole bilayer tunnel field-effect transistor

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

    Padilla, J. L., E-mail: jose.padilladelatorre@epfl.ch; Departamento de Electrónica y Tecnología de los Computadores, Universidad de Granada, Avda. Fuentenueva s/n, 18071 Granada; Palomares, A.

    In this work, we analyze the behavior of the band-to-band tunneling distance between electron and hole subbands resulting from field-induced quantum confinement in the heterogate electron–hole bilayer tunnel field-effect transistor. We show that, analogously to the explicit formula for the tunneling distance that can be easily obtained in the semiclassical framework where the conduction and valence band edges are allowed states, an equivalent analytical expression can be derived in the presence of field-induced quantum confinement for describing the dependence of the tunneling distance on the body thickness and material properties of the channel. This explicit expression accounting for quantum confinementmore » holds valid provided that the potential wells for electrons and holes at the top and bottom of the channel can be approximated by triangular profiles. Analytical predictions are compared to simulation results showing very accurate agreement.« less

  16. Analytical energy gradients for explicitly correlated wave functions. I. Explicitly correlated second-order Møller-Plesset perturbation theory

    NASA Astrophysics Data System (ADS)

    Győrffy, Werner; Knizia, Gerald; Werner, Hans-Joachim

    2017-12-01

    We present the theory and algorithms for computing analytical energy gradients for explicitly correlated second-order Møller-Plesset perturbation theory (MP2-F12). The main difficulty in F12 gradient theory arises from the large number of two-electron integrals for which effective two-body density matrices and integral derivatives need to be calculated. For efficiency, the density fitting approximation is used for evaluating all two-electron integrals and their derivatives. The accuracies of various previously proposed MP2-F12 approximations [3C, 3C(HY1), 3*C(HY1), and 3*A] are demonstrated by computing equilibrium geometries for a set of molecules containing first- and second-row elements, using double-ζ to quintuple-ζ basis sets. Generally, the convergence of the bond lengths and angles with respect to the basis set size is strongly improved by the F12 treatment, and augmented triple-ζ basis sets are sufficient to closely approach the basis set limit. The results obtained with the different approximations differ only very slightly. This paper is the first step towards analytical gradients for coupled-cluster singles and doubles with perturbative treatment of triple excitations, which will be presented in the second part of this series.

  17. Solutions of conformal Israel-Stewart relativistic viscous fluid dynamics

    NASA Astrophysics Data System (ADS)

    Marrochio, Hugo; Noronha, Jorge; Denicol, Gabriel S.; Luzum, Matthew; Jeon, Sangyong; Gale, Charles

    2015-01-01

    We use symmetry arguments developed by Gubser to construct the first radially expanding explicit solutions of the Israel-Stewart formulation of hydrodynamics. Along with a general semi-analytical solution, an exact analytical solution is given which is valid in the cold plasma limit where viscous effects from shear viscosity and the relaxation time coefficient are important. The radially expanding solutions presented in this paper can be used as nontrivial checks of numerical algorithms employed in hydrodynamic simulations of the quark-gluon plasma formed in ultrarelativistic heavy ion collisions. We show this explicitly by comparing such analytic and semi-analytic solutions with the corresponding numerical solutions obtained using the music viscous hydrodynamics simulation code.

  18. Exact analytic solution for non-linear density fluctuation in a ΛCDM universe

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

    Yoo, Jaiyul; Gong, Jinn-Ouk, E-mail: jyoo@physik.uzh.ch, E-mail: jinn-ouk.gong@apctp.org

    We derive the exact third-order analytic solution of the matter density fluctuation in the proper-time hypersurface in a ΛCDM universe, accounting for the explicit time-dependence and clarifying the relation to the initial condition. Furthermore, we compare our analytic solution to the previous calculation in the comoving gauge, and to the standard Newtonian perturbation theory by providing Fourier kernels for the relativistic effects. Our results provide an essential ingredient for a complete description of galaxy bias in the relativistic context.

  19. Corruption of accuracy and efficiency of Markov chain Monte Carlo simulation by inaccurate numerical implementation of conceptual hydrologic models

    NASA Astrophysics Data System (ADS)

    Schoups, G.; Vrugt, J. A.; Fenicia, F.; van de Giesen, N. C.

    2010-10-01

    Conceptual rainfall-runoff models have traditionally been applied without paying much attention to numerical errors induced by temporal integration of water balance dynamics. Reliance on first-order, explicit, fixed-step integration methods leads to computationally cheap simulation models that are easy to implement. Computational speed is especially desirable for estimating parameter and predictive uncertainty using Markov chain Monte Carlo (MCMC) methods. Confirming earlier work of Kavetski et al. (2003), we show here that the computational speed of first-order, explicit, fixed-step integration methods comes at a cost: for a case study with a spatially lumped conceptual rainfall-runoff model, it introduces artificial bimodality in the marginal posterior parameter distributions, which is not present in numerically accurate implementations of the same model. The resulting effects on MCMC simulation include (1) inconsistent estimates of posterior parameter and predictive distributions, (2) poor performance and slow convergence of the MCMC algorithm, and (3) unreliable convergence diagnosis using the Gelman-Rubin statistic. We studied several alternative numerical implementations to remedy these problems, including various adaptive-step finite difference schemes and an operator splitting method. Our results show that adaptive-step, second-order methods, based on either explicit finite differencing or operator splitting with analytical integration, provide the best alternative for accurate and efficient MCMC simulation. Fixed-step or adaptive-step implicit methods may also be used for increased accuracy, but they cannot match the efficiency of adaptive-step explicit finite differencing or operator splitting. Of the latter two, explicit finite differencing is more generally applicable and is preferred if the individual hydrologic flux laws cannot be integrated analytically, as the splitting method then loses its advantage.

  20. Fluctuation theorem for the effusion of an ideal gas.

    PubMed

    Cleuren, B; Van den Broeck, C; Kawai, R

    2006-08-01

    The probability distribution of the entropy production for the effusion of an ideal gas between two compartments is calculated explicitly. The fluctuation theorem is verified. The analytic results are in good agreement with numerical data from hard disk molecular dynamics simulations.

  1. Correlations and analytical approaches to co-evolving voter models

    NASA Astrophysics Data System (ADS)

    Ji, M.; Xu, C.; Choi, C. W.; Hui, P. M.

    2013-11-01

    The difficulty in formulating analytical treatments in co-evolving networks is studied in light of the Vazquez-Eguíluz-San Miguel voter model (VM) and a modified VM (MVM) that introduces a random mutation of the opinion as a noise in the VM. The density of active links, which are links that connect the nodes of opposite opinions, is shown to be highly sensitive to both the degree k of a node and the active links n among the neighbors of a node. We test the validity in the formalism of analytical approaches and show explicitly that the assumptions behind the commonly used homogeneous pair approximation scheme in formulating a mean-field theory are the source of the theory's failure due to the strong correlations between k, n and n2. An improved approach that incorporates spatial correlation to the nearest-neighbors explicitly and a random approximation for the next-nearest neighbors is formulated for the VM and the MVM, and it gives better agreement with the simulation results. We introduce an empirical approach that quantifies the correlations more accurately and gives results in good agreement with the simulation results. The work clarifies why simply mean-field theory fails and sheds light on how to analyze the correlations in the dynamic equations that are often generated in co-evolving processes.

  2. Analytical Applications of Monte Carlo Techniques.

    ERIC Educational Resources Information Center

    Guell, Oscar A.; Holcombe, James A.

    1990-01-01

    Described are analytical applications of the theory of random processes, in particular solutions obtained by using statistical procedures known as Monte Carlo techniques. Supercomputer simulations, sampling, integration, ensemble, annealing, and explicit simulation are discussed. (CW)

  3. DEVELOPMENTS AT U.S. EPA IN ADDRESSING UNCERTAINTY IN RISK ASSESSMENT

    EPA Science Inventory

    An emerging trend in risk assessment is to be more explicit about uncertainties, both during the analytical procedures and in communicating results. In February 1 992, then-Deputy EPA Administrator Henry Habicht set out Agency goals in a memorandum stating that the Agency will "p...

  4. The Purpose of Analytical Models from the Perspective of a Data Provider.

    ERIC Educational Resources Information Center

    Sheehan, Bernard S.

    The purpose of analytical models is to reduce complex institutional management problems and situations to simpler proportions and compressed time frames so that human skills of decision makers can be brought to bear most effectively. Also, modeling cultivates the art of management by forcing explicit and analytical consideration of important…

  5. Setting Learning Analytics in Context: Overcoming the Barriers to Large-Scale Adoption

    ERIC Educational Resources Information Center

    Ferguson, Rebecca; Macfadyen, Leah P.; Clow, Doug; Tynan, Belinda; Alexander, Shirley; Dawson, Shane

    2014-01-01

    A core goal for most learning analytic projects is to move from small-scale research towards broader institutional implementation, but this introduces a new set of challenges because institutions are stable systems, resistant to change. To avoid failure and maximize success, implementation of learning analytics at scale requires explicit and…

  6. Explicit robust schemes for implementation of general principal value-based constitutive models

    NASA Technical Reports Server (NTRS)

    Arnold, S. M.; Saleeb, A. F.; Tan, H. Q.; Zhang, Y.

    1993-01-01

    The issue of developing effective and robust schemes to implement general hyperelastic constitutive models is addressed. To this end, special purpose functions are used to symbolically derive, evaluate, and automatically generate the associated FORTRAN code for the explicit forms of the corresponding stress function and material tangent stiffness tensors. These explicit forms are valid for the entire deformation range. The analytical form of these explicit expressions is given here for the case in which the strain-energy potential is taken as a nonseparable polynomial function of the principle stretches.

  7. Longitudinal dielectric function and dispersion relation of electrostatic waves in relativistic plasmas

    NASA Astrophysics Data System (ADS)

    Touil, B.; Bendib, A.; Bendib-Kalache, K.

    2017-02-01

    The longitudinal dielectric function is derived analytically from the relativistic Vlasov equation for arbitrary values of the relevant parameters z = m c 2 / T , where m is the rest electron mass, c is the speed of light, and T is the electron temperature in energy units. A new analytical approach based on the Legendre polynomial expansion and continued fractions was used. Analytical expression of the electron distribution function was derived. The real part of the dispersion relation and the damping rate of electron plasma waves are calculated both analytically and numerically in the whole range of the parameter z . The results obtained improve significantly the previous results reported in the literature. For practical purposes, explicit expressions of the real part of the dispersion relation and the damping rate in the range z > 30 and strongly relativistic regime are also proposed.

  8. Piecewise linear emulator of the nonlinear Schrödinger equation and the resulting analytic solutions for Bose-Einstein condensates.

    PubMed

    Theodorakis, Stavros

    2003-06-01

    We emulate the cubic term Psi(3) in the nonlinear Schrödinger equation by a piecewise linear term, thus reducing the problem to a set of uncoupled linear inhomogeneous differential equations. The resulting analytic expressions constitute an excellent approximation to the exact solutions, as is explicitly shown in the case of the kink, the vortex, and a delta function trap. Such a piecewise linear emulation can be used for any differential equation where the only nonlinearity is a Psi(3) one. In particular, it can be used for the nonlinear Schrödinger equation in the presence of harmonic traps, giving analytic Bose-Einstein condensate solutions that reproduce very accurately the numerically calculated ones in one, two, and three dimensions.

  9. Meromorphic solutions of recurrence relations and DRA method for multicomponent master integrals

    NASA Astrophysics Data System (ADS)

    Lee, Roman N.; Mingulov, Kirill T.

    2018-04-01

    We formulate a method to find the meromorphic solutions of higher-order recurrence relations in the form of the sum over poles with coefficients defined recursively. Several explicit examples of the application of this technique are given. The main advantage of the described approach is that the analytical properties of the solutions are very clear (the position of poles is explicit, the behavior at infinity can be easily determined). These are exactly the properties that are required for the application of the multiloop calculation method based on dimensional recurrence relations and analyticity (the DRA method).

  10. Analytic continuation of quantum Monte Carlo data by stochastic analytical inference.

    PubMed

    Fuchs, Sebastian; Pruschke, Thomas; Jarrell, Mark

    2010-05-01

    We present an algorithm for the analytic continuation of imaginary-time quantum Monte Carlo data which is strictly based on principles of Bayesian statistical inference. Within this framework we are able to obtain an explicit expression for the calculation of a weighted average over possible energy spectra, which can be evaluated by standard Monte Carlo simulations, yielding as by-product also the distribution function as function of the regularization parameter. Our algorithm thus avoids the usual ad hoc assumptions introduced in similar algorithms to fix the regularization parameter. We apply the algorithm to imaginary-time quantum Monte Carlo data and compare the resulting energy spectra with those from a standard maximum-entropy calculation.

  11. An explicit analytical solution for sound propagation in a three-dimensional penetrable wedge with small apex angle.

    PubMed

    Petrov, Pavel S; Sturm, Frédéric

    2016-03-01

    A problem of sound propagation in a shallow-water waveguide with a weakly sloping penetrable bottom is considered. The adiabatic mode parabolic equations are used to approximate the solution of the three-dimensional (3D) Helmholtz equation by modal decomposition of the acoustic pressure field. The mode amplitudes satisfy parabolic equations that admit analytical solutions in the special case of the 3D wedge. Using the analytical formula for modal amplitudes, an explicit and remarkably simple expression for the acoustic pressure in the wedge is obtained. The proposed solution is validated by the comparison with a solution of the 3D penetrable wedge problem obtained using a fully 3D parabolic equation that includes a leading-order cross term correction.

  12. Analytical Approach to (2+1)-Dimensional Boussinesq Equation and (3+1)-Dimensional Kadomtsev-Petviashvili Equation

    NASA Astrophysics Data System (ADS)

    Sarıaydın, Selin; Yıldırım, Ahmet

    2010-05-01

    In this paper, we studied the solitary wave solutions of the (2+1)-dimensional Boussinesq equation utt -uxx-uyy-(u2)xx-uxxxx = 0 and the (3+1)-dimensional Kadomtsev-Petviashvili (KP) equation uxt -6ux 2 +6uuxx -uxxxx -uyy -uzz = 0. By using this method, an explicit numerical solution is calculated in the form of a convergent power series with easily computable components. To illustrate the application of this method numerical results are derived by using the calculated components of the homotopy perturbation series. The numerical solutions are compared with the known analytical solutions. Results derived from our method are shown graphically.

  13. Analytic descriptions of cylindrical electromagnetic waves in a nonlinear medium

    PubMed Central

    Xiong, Hao; Si, Liu-Gang; Yang, Xiaoxue; Wu, Ying

    2015-01-01

    A simple but highly efficient approach for dealing with the problem of cylindrical electromagnetic waves propagation in a nonlinear medium is proposed based on an exact solution proposed recently. We derive an analytical explicit formula, which exhibiting rich interesting nonlinear effects, to describe the propagation of any amount of cylindrical electromagnetic waves in a nonlinear medium. The results obtained by using the present method are accurately concordant with the results of using traditional coupled-wave equations. As an example of application, we discuss how a third wave affects the sum- and difference-frequency generation of two waves propagation in the nonlinear medium. PMID:26073066

  14. An explicit closed-form analytical solution for European options under the CGMY model

    NASA Astrophysics Data System (ADS)

    Chen, Wenting; Du, Meiyu; Xu, Xiang

    2017-01-01

    In this paper, we consider the analytical pricing of European path-independent options under the CGMY model, which is a particular type of pure jump Le´vy process, and agrees well with many observed properties of the real market data by allowing the diffusions and jumps to have both finite and infinite activity and variation. It is shown that, under this model, the option price is governed by a fractional partial differential equation (FPDE) with both the left-side and right-side spatial-fractional derivatives. In comparison to derivatives of integer order, fractional derivatives at a point not only involve properties of the function at that particular point, but also the information of the function in a certain subset of the entire domain of definition. This ;globalness; of the fractional derivatives has added an additional degree of difficulty when either analytical methods or numerical solutions are attempted. Albeit difficult, we still have managed to derive an explicit closed-form analytical solution for European options under the CGMY model. Based on our solution, the asymptotic behaviors of the option price and the put-call parity under the CGMY model are further discussed. Practically, a reliable numerical evaluation technique for the current formula is proposed. With the numerical results, some analyses of impacts of four key parameters of the CGMY model on European option prices are also provided.

  15. Spatially-explicit models of global tree density.

    PubMed

    Glick, Henry B; Bettigole, Charlie; Maynard, Daniel S; Covey, Kristofer R; Smith, Jeffrey R; Crowther, Thomas W

    2016-08-16

    Remote sensing and geographic analysis of woody vegetation provide means of evaluating the distribution of natural resources, patterns of biodiversity and ecosystem structure, and socio-economic drivers of resource utilization. While these methods bring geographic datasets with global coverage into our day-to-day analytic spheres, many of the studies that rely on these strategies do not capitalize on the extensive collection of existing field data. We present the methods and maps associated with the first spatially-explicit models of global tree density, which relied on over 420,000 forest inventory field plots from around the world. This research is the result of a collaborative effort engaging over 20 scientists and institutions, and capitalizes on an array of analytical strategies. Our spatial data products offer precise estimates of the number of trees at global and biome scales, but should not be used for local-level estimation. At larger scales, these datasets can contribute valuable insight into resource management, ecological modelling efforts, and the quantification of ecosystem services.

  16. High-order tail in Schwarzschild spacetime

    NASA Astrophysics Data System (ADS)

    Casals, Marc; Ottewill, Adrian

    2015-12-01

    We present an analysis of the behavior at late times of linear field perturbations of a Schwarzschild black hole spacetime. In particular, we give explicit analytic expressions for the field perturbations (for a specific ℓ-multipole) of general spin up to the first four orders at late times. These expressions are valid at arbitrary radius and include, apart from the well-known power-law tail decay at leading order (˜t-2 ℓ-3), a new logarithmic behavior at third leading order (˜t-2 ℓ-5ln t ). We obtain these late-time results by developing an analytical formalism initially formulated by Mano, Suzuki and Takasugi (MST) [Prog. Theor. Phys. 95, 1079 (1996); 96, 549 (1996)] formalism and by expanding the various MST Fourier-mode quantities for small frequency. While we give explicit expansions up to the first four leading orders (for small frequency for the Fourier modes, for late time for the field perturbation), we give a prescription for obtaining expressions to arbitrary order within a "perturbative regime."

  17. Symmetry boost of the fidelity of Shor factoring

    NASA Astrophysics Data System (ADS)

    Nam, Y. S.; Blümel, R.

    2018-05-01

    In Shor's algorithm quantum subroutines occur with the structure F U F-1 , where F is a unitary transform and U is performing a quantum computation. Examples are quantum adders and subunits of quantum modulo adders. In this paper we show, both analytically and numerically, that if, in analogy to spin echoes, F and F-1 can be implemented symmetrically when executing Shor's algorithm on actual, imperfect quantum hardware, such that F and F-1 have the same hardware errors, a symmetry boost in the fidelity of the combined F U F-1 quantum operation results when compared to the case in which the errors in F and F-1 are independently random. Running the complete gate-by-gate implemented Shor algorithm, we show that the symmetry-induced fidelity boost can be as large as a factor 4. While most of our analytical and numerical results concern the case of over- and under-rotation of controlled rotation gates, in the numerically accessible case of Shor's algorithm with a small number of qubits, we show explicitly that the symmetry boost is robust with respect to more general types of errors. While, expectedly, additional error types reduce the symmetry boost, we show explicitly, by implementing general off-diagonal SU (N ) errors (N =2 ,4 ,8 ), that the boost factor scales like a Lorentzian in δ /σ , where σ and δ are the error strengths of the diagonal over- and underrotation errors and the off-diagonal SU (N ) errors, respectively. The Lorentzian shape also shows that, while the boost factor may become small with increasing δ , it declines slowly (essentially like a power law) and is never completely erased. We also investigate the effect of diagonal nonunitary errors, which, in analogy to unitary errors, reduce but never erase the symmetry boost. Going beyond the case of small quantum processors, we present analytical scaling results that show that the symmetry boost persists in the practically interesting case of a large number of qubits. We illustrate this result explicitly for the case of Shor factoring of the semiprime RSA-1024, where, analytically, focusing on over- and underrotation errors, we obtain a boost factor of about 10. In addition, we provide a proof of the fidelity product formula, including its range of applicability.

  18. Symmetry Reductions and Group-Invariant Radial Solutions to the n-Dimensional Wave Equation

    NASA Astrophysics Data System (ADS)

    Feng, Wei; Zhao, Songlin

    2018-01-01

    In this paper, we derive explicit group-invariant radial solutions to a class of wave equation via symmetry group method. The optimal systems of one-dimensional subalgebras for the corresponding radial wave equation are presented in terms of the known point symmetries. The reductions of the radial wave equation into second-order ordinary differential equations (ODEs) with respect to each symmetry in the optimal systems are shown. Then we solve the corresponding reduced ODEs explicitly in order to write out the group-invariant radial solutions for the wave equation. Finally, several analytical behaviours and smoothness of the resulting solutions are discussed.

  19. Self-sustained peristaltic waves: Explicit asymptotic solutions

    NASA Astrophysics Data System (ADS)

    Dudchenko, O. A.; Guria, G. Th.

    2012-02-01

    A simple nonlinear model for the coupled problem of fluid flow and contractile wall deformation is proposed to describe peristalsis. In the context of the model the ability of a transporting system to perform autonomous peristaltic pumping is interpreted as the ability to propagate sustained waves of wall deformation. Piecewise-linear approximations of nonlinear functions are used to analytically demonstrate the existence of traveling-wave solutions. Explicit formulas are derived which relate the speed of self-sustained peristaltic waves to the rheological properties of the transporting vessel and the transported fluid. The results may contribute to the development of diagnostic and therapeutic procedures for cases of peristaltic motility disorders.

  20. Decision support systems in health economics.

    PubMed

    Quaglini, S; Dazzi, L; Stefanelli, M; Barosi, G; Marchetti, M

    1999-08-01

    This article describes a system addressed to different health care professionals for building, using, and sharing decision support systems for resource allocation. The system deals with selected areas, namely the choice of diagnostic tests, the therapy planning, and the instrumentation purchase. Decision support is based on decision-analytic models, incorporating an explicit knowledge representation of both the medical domain knowledge and the economic evaluation theory. Application models are built on top of meta-models, that are used as guidelines for making explicit both the cost and effectiveness components. This approach improves the transparency and soundness of the collaborative decision-making process and facilitates the result interpretation.

  1. Multidimensional assessment of awareness in early-stage dementia: a cluster analytic approach.

    PubMed

    Clare, Linda; Whitaker, Christopher J; Nelis, Sharon M; Martyr, Anthony; Markova, Ivana S; Roth, Ilona; Woods, Robert T; Morris, Robin G

    2011-01-01

    Research on awareness in dementia has yielded variable and inconsistent associations between awareness and other factors. This study examined awareness using a multidimensional approach and applied cluster analytic techniques to identify associations between the level of awareness and other variables. Participants were 101 individuals with early-stage dementia (PwD) and their carers. Explicit awareness was assessed at 3 levels: performance monitoring in relation to memory, evaluative judgement in relation to memory, everyday activities and socio-emotional functioning, and metacognitive reflection in relation to the experience and impact of the condition. Implicit awareness was assessed with an emotional Stroop task. Different measures of explicit awareness scores were related only to a limited extent. Cluster analysis yielded 3 groups with differing degrees of explicit awareness. These groups showed no differences in implicit awareness. Lower explicit awareness was associated with greater age, lower MMSE scores, poorer recall and naming scores, lower anxiety and greater carer stress. Multidimensional assessment offers a more robust approach to classifying PwD according to level of awareness and hence to examining correlates and predictors of awareness. Copyright © 2011 S. Karger AG, Basel.

  2. Revisiting the positive DC corona discharge theory: Beyond Peek's and Townsend's law

    NASA Astrophysics Data System (ADS)

    Monrolin, Nicolas; Praud, Olivier; Plouraboué, Franck

    2018-06-01

    The classical positive Corona Discharge theory in a cylindrical axisymmetric configuration is revisited in order to find analytically the influence of gas properties and thermodynamic conditions on the corona current. The matched asymptotic expansion of Durbin and Turyn [J. Phys. D: Appl. Phys. 20, 1490-1495 (1987)] of a simplified but self-consistent problem is performed and explicit analytical solutions are derived. The mathematical derivation enables us to express a new positive DC corona current-voltage characteristic, choosing either a dimensionless or dimensional formulation. In dimensional variables, the current voltage law and the corona inception voltage explicitly depend on the electrode size and physical gas properties such as ionization and photoionization parameters. The analytical predictions are successfully confronted with experiments and Peek's and Townsend's laws. An analytical expression of the corona inception voltage φ o n is proposed, which depends on the known values of physical parameters without adjustable parameters. As a proof of consistency, the classical Townsend current-voltage law I = C φ ( φ - φ o n ) is retrieved by linearizing the non-dimensional analytical solution. A brief parametric study showcases the interest in this analytical current model, especially for exploring small corona wires or considering various thermodynamic conditions.

  3. Adding uncertainty to forest inventory plot locations: effects on analyses using geospatial data

    Treesearch

    Alexia A. Sabor; Volker C. Radeloff; Ronald E. McRoberts; Murray Clayton; Susan I. Stewart

    2007-01-01

    The Forest Inventory and Analysis (FIA) program of the USDA Forest Service alters plot locations before releasing data to the public to ensure landowner confidentiality and sample integrity, but using data with altered plot locations in conjunction with other spatially explicit data layers produces analytical results with unknown amounts of error. We calculated the...

  4. The Dispersion Relation for the 1/sinh(exp 2) Potential in the Classical Limit

    NASA Technical Reports Server (NTRS)

    Campbell, Joel

    2009-01-01

    The dispersion relation for the inverse hyperbolic potential is calculated in the classical limit. This is shown for both the low amplitude phonon branch and the high amplitude soliton branch. It is shown these results qualitatively follow that previously found for the inverse squared potential where explicit analytic solutions are known.

  5. Analytical drafting curves provide exact equations for plotted data

    NASA Technical Reports Server (NTRS)

    Stewart, R. B.

    1967-01-01

    Analytical drafting curves provide explicit mathematical expressions for any numerical data that appears in the form of graphical plots. The curves each have a reference coordinate axis system indicated on the curve as well as the mathematical equation from which the curve was generated.

  6. Temporal fluctuations after a quantum quench: Many-particle dephasing

    NASA Astrophysics Data System (ADS)

    Marquardt, Florian; Kiendl, Thomas

    After a quantum quench, the expectation values of observables continue to fluctuate in time. In the thermodynamic limit, one expects such fluctuations to decrease to zero, in order for standard statistical physics to hold. However, it is a challenge to determine analytically how the fluctuations decay as a function of system size. So far, there have been analytical predictions for integrable models (which are, naturally, somewhat special), analytical bounds for arbitrary systems, and numerical results for moderate-size systems. We have discovered a dynamical regime where the decrease of fluctuations is driven by many-particle dephasing, instead of a redistribution of occupation numbers. On the basis of this insight, we are able to provide exact analytical expressions for a model with weak integrability breaking (transverse Ising chain with additional terms). These predictions explicitly show how fluctuations are exponentially suppressed with system size.

  7. Quantum decay model with exact explicit analytical solution

    NASA Astrophysics Data System (ADS)

    Marchewka, Avi; Granot, Er'El

    2009-01-01

    A simple decay model is introduced. The model comprises a point potential well, which experiences an abrupt change. Due to the temporal variation, the initial quantum state can either escape from the well or stay localized as a new bound state. The model allows for an exact analytical solution while having the necessary features of a decay process. The results show that the decay is never exponential, as classical dynamics predicts. Moreover, at short times the decay has a fractional power law, which differs from perturbation quantum method predictions. At long times the decay includes oscillations with an envelope that decays algebraically. This is a model where the final state can be either continuous or localized, and that has an exact analytical solution.

  8. The Analytic Hierarchy Process and Participatory Decisionmaking

    Treesearch

    Daniel L. Schmoldt; Daniel L. Peterson; Robert L. Smith

    1995-01-01

    Managing natural resource lands requires social, as well as biophysical, considerations. Unfortunately, it is extremely difficult to accurately assess and quantify changing social preferences, and to aggregate conflicting opinions held by diverse social groups. The Analytic Hierarchy Process (AHP) provides a systematic, explicit, rigorous, and robust mechanism for...

  9. Non-linear analytic and coanalytic problems ( L_p-theory, Clifford analysis, examples)

    NASA Astrophysics Data System (ADS)

    Dubinskii, Yu A.; Osipenko, A. S.

    2000-02-01

    Two kinds of new mathematical model of variational type are put forward: non-linear analytic and coanalytic problems. The formulation of these non-linear boundary-value problems is based on a decomposition of the complete scale of Sobolev spaces into the "orthogonal" sum of analytic and coanalytic subspaces. A similar decomposition is considered in the framework of Clifford analysis. Explicit examples are presented.

  10. The assessment of mangrove biomass and carbon in West Africa: a spatially explicit analytical framework

    Treesearch

    Wenwu Tang; Wenpeng Feng; Meijuan Jia; Jiyang Shi; Huifang Zuo; Carl C. Trettin

    2015-01-01

    Mangrove forests are highly productive and have large carbon sinks while also providing numerous goods and ecosystem services. However, effective management and conservation of the mangrove forests are often dependent on spatially explicit assessments of the resource. Given the remote and highly dispersed nature of mangroves, estimation of biomass and carbon...

  11. Vocation in theology-based nursing theories.

    PubMed

    Lundmark, Mikael

    2007-11-01

    By using the concepts of intrinsicality/extrinsicality as analytic tools, the theology-based nursing theories of Ann Bradshaw and Katie Eriksson are analyzed regarding their explicit and/or implicit understanding of vocation as a motivational factor for nursing. The results show that both theories view intrinsic values as guarantees against reducing nursing practice to mechanistic applications of techniques and as being a way of reinforcing a high ethical standard. The theories explicitly (Bradshaw) or implicitly (Eriksson) advocate a vocational understanding of nursing as being essential for nursing theories. Eriksson's theory has a potential for conceptualizing an understanding of extrinsic and intrinsic motivational factors for nursing but one weakness in the theory could be the risk of slipping over to moral judgments where intrinsic factors are valued as being superior to extrinsic. Bradshaw's theory is more complex and explicit in understanding the concept of vocation and is theologically more plausible, although also more confessional.

  12. Analytical saturated domain orientation textures and electromechanical properties of ferroelectric ceramics due to electric/mechanical poling

    NASA Astrophysics Data System (ADS)

    Li, F. X.; Rajapakse, R. K. N. D.

    2007-03-01

    Saturated domain orientation textures of three types of pseudocubic (tetragonal, rhombohedral, and orthorhombic) ferroelectric ceramics after complete electric and uniaxial tension (compression) poling is studied analytically in this paper. A one-dimensional orientation distribution function (ODF) of the domain polar vectors is explicitly derived from the uniform inverse pole figures of the poling field axes on a stereographic projection with respect to the fixed crystallite coordinates. The analytical ODF is used to obtain the analytical solutions of saturated polarization and strain after electric/mechanical poling. Based on the closed form solution of the saturated domain orientation textures, the resultant intrinsic electromechanical properties of ferroelectric ceramics, which depend only on the ODF and properties of the corresponding single crystals, are obtained. The results show how the macroscopic symmetries of ferroelectric crystals change from 4mm (tetragonal), 3m (rhombohedral), and mm2 (orthorhombic) single crystals to a ∞mm (transversely isotropic) completely poled ceramic.

  13. Effective diffusion of confined active Brownian swimmers.

    PubMed

    Sandoval, Mario; Dagdug, Leornardo

    2014-12-01

    We theoretically find the effect of confinement and thermal fluctuations on the diffusivity of a spherical active swimmer moving inside a two-dimensional narrow cavity of general shape. The explicit formulas for the effective diffusion coefficient of a swimmer moving inside two particular cavities are presented. We also compare our analytical results with Brownian dynamics simulations and we obtain excellent agreement.

  14. Brillouin precursors in Debye media

    NASA Astrophysics Data System (ADS)

    Macke, Bruno; Ségard, Bernard

    2015-05-01

    We theoretically study the formation of Brillouin precursors in Debye media. We point out that the precursors are visible only at propagation distances such that the impulse response of the medium is essentially determined by the frequency dependence of its absorption and is practically Gaussian. By simple convolution, we then obtain explicit analytical expressions of the transmitted waves generated by reference incident waves, distinguishing precursor and main signal by a simple examination of the long-time behavior of the overall signal. These expressions are in good agreement with the signals obtained in numerical or real experiments performed on water in the radio-frequency domain and explain in particular some observed shapes of the precursor. Results are obtained for other remarkable incident waves. In addition, we show quite generally that the shape of the Brillouin precursor appearing alone at sufficiently large propagation distance and the law giving its amplitude as a function of this distance do not depend on the precise form of the incident wave but only on its integral properties. The incidence of a static conductivity of the medium is also examined and explicit analytical results are again given in the limit of weak and strong conductivities.

  15. Putting an Ethical Lens on Learning Analytics

    ERIC Educational Resources Information Center

    West, Deborah; Huijser, Henk; Heath, David

    2016-01-01

    As learning analytics activity has increased, a variety of ethical implications and considerations have emerged, though a significant research gap remains in explicitly investigating the views of key stakeholders, such as academic staff. This paper draws on ethics-related findings from an Australian study featuring two surveys, one of…

  16. Quantum cluster theory for the polarizable continuum model. I. The CCSD level with analytical first and second derivatives.

    PubMed

    Cammi, R

    2009-10-28

    We present a general formulation of the coupled-cluster (CC) theory for a molecular solute described within the framework of the polarizable continuum model (PCM). The PCM-CC theory is derived in its complete form, called PTDE scheme, in which the correlated electronic density is used to have a self-consistent reaction field, and in an approximate form, called PTE scheme, in which the PCM-CC equations are solved assuming the fixed Hartree-Fock solvent reaction field. Explicit forms for the PCM-CC-PTDE equations are derived at the single and double (CCSD) excitation level of the cluster operator. At the same level, explicit equations for the analytical first derivatives of the PCM basic energy functional are presented, and analytical second derivatives are also discussed. The corresponding PCM-CCSD-PTE equations are given as a special case of the full theory.

  17. A theoretical framework for modeling dilution enhancement of non-reactive solutes in heterogeneous porous media.

    PubMed

    de Barros, F P J; Fiori, A; Boso, F; Bellin, A

    2015-01-01

    Spatial heterogeneity of the hydraulic properties of geological porous formations leads to erratically shaped solute clouds, thus increasing the edge area of the solute body and augmenting the dilution rate. In this study, we provide a theoretical framework to quantify dilution of a non-reactive solute within a steady state flow as affected by the spatial variability of the hydraulic conductivity. Embracing the Lagrangian concentration framework, we obtain explicit semi-analytical expressions for the dilution index as a function of the structural parameters of the random hydraulic conductivity field, under the assumptions of uniform-in-the-average flow, small injection source and weak-to-mild heterogeneity. Results show how the dilution enhancement of the solute cloud is strongly dependent on both the statistical anisotropy ratio and the heterogeneity level of the porous medium. The explicit semi-analytical solution also captures the temporal evolution of the dilution rate; for the early- and late-time limits, the proposed solution recovers previous results from the literature, while at intermediate times it reflects the increasing interplay between large-scale advection and local-scale dispersion. The performance of the theoretical framework is verified with high resolution numerical results and successfully tested against the Cape Cod field data. Copyright © 2015 Elsevier B.V. All rights reserved.

  18. Age Differences and Cognitive Aptitudes for Implicit and Explicit Learning in Ultimate Second Language Attainment

    ERIC Educational Resources Information Center

    Granena, Gisela

    2012-01-01

    Very high-level, functional ability in foreign languages is increasingly important in many walks of life. It is also very rare, and likely requires an early start and/or a special aptitude. This study investigated the extent to which aptitude for explicit learning, defined as "analytic ability" and aptitude for implicit learning, defined…

  19. The Effectiveness of Guided Induction versus Deductive Instruction on the Development of Complex Spanish "Gustar" Structures: An Analysis of Learning Outcomes and Processes

    ERIC Educational Resources Information Center

    Cerezo, Luis; Caras, Allison; Leow, Ronald P.

    2016-01-01

    Meta-analytic research suggests an edge of explicit over implicit instruction for the development of complex L2 grammatical structures, but the jury is still out as to which type of explicit instruction--"deductive" or "inductive," where rules are respectively provided or elicited--proves more effective. Avoiding this…

  20. Gravity discharge vessel revisited: An explicit Lambert W function solution

    NASA Astrophysics Data System (ADS)

    Digilov, Rafael M.

    2017-07-01

    Based on the generalized Poiseuille equation modified by a kinetic energy correction, an explicit solution for the time evolution of a liquid column draining under gravity through an exit capillary tube is derived in terms of the Lambert W function. In contrast to the conventional exponential behavior, as implied by the Poiseuille law, a new analytical solution gives a full account for the volumetric flow rate of a fluid through a capillary of any length and improves the precision of viscosity determination. The theoretical consideration may be of interest to students as an example of how implicit equations in the field of physics can be solved analytically using the Lambert function.

  1. An analytical fuzzy-based approach to ?-gain optimal control of input-affine nonlinear systems using Newton-type algorithm

    NASA Astrophysics Data System (ADS)

    Milic, Vladimir; Kasac, Josip; Novakovic, Branko

    2015-10-01

    This paper is concerned with ?-gain optimisation of input-affine nonlinear systems controlled by analytic fuzzy logic system. Unlike the conventional fuzzy-based strategies, the non-conventional analytic fuzzy control method does not require an explicit fuzzy rule base. As the first contribution of this paper, we prove, by using the Stone-Weierstrass theorem, that the proposed fuzzy system without rule base is universal approximator. The second contribution of this paper is an algorithm for solving a finite-horizon minimax problem for ?-gain optimisation. The proposed algorithm consists of recursive chain rule for first- and second-order derivatives, Newton's method, multi-step Adams method and automatic differentiation. Finally, the results of this paper are evaluated on a second-order nonlinear system.

  2. Analytical transport network theory to guide the design of 3-D microstructural networks in energy materials: Part 1. Flow without reactions

    NASA Astrophysics Data System (ADS)

    Cocco, Alex P.; Nakajo, Arata; Chiu, Wilson K. S.

    2017-12-01

    We present a fully analytical, heuristic model - the "Analytical Transport Network Model" - for steady-state, diffusive, potential flow through a 3-D network. Employing a combination of graph theory, linear algebra, and geometry, the model explicitly relates a microstructural network's topology and the morphology of its channels to an effective material transport coefficient (a general term meant to encompass, e.g., conductivity or diffusion coefficient). The model's transport coefficient predictions agree well with those from electrochemical fin (ECF) theory and finite element analysis (FEA), but are computed 0.5-1.5 and 5-6 orders of magnitude faster, respectively. In addition, the theory explicitly relates a number of morphological and topological parameters directly to the transport coefficient, whereby the distributions that characterize the structure are readily available for further analysis. Furthermore, ATN's explicit development provides insight into the nature of the tortuosity factor and offers the potential to apply theory from network science and to consider the optimization of a network's effective resistance in a mathematically rigorous manner. The ATN model's speed and relative ease-of-use offer the potential to aid in accelerating the design (with respect to transport), and thus reducing the cost, of energy materials.

  3. Analytical description of the transverse Anderson localization of light

    NASA Astrophysics Data System (ADS)

    Schirmacher, Walter; Leonetti, Marco; Ruocco, Giancarlo

    2017-04-01

    We develop an analytical theory for describing the transverse localization properties of light beams in optical fibers with lateral disorder. This theory, which starts from the widely used paraxial approximation for the Helmholtz equation of the electric field, is a combination of an effective-medium theory for transverse disorder with the self-consistent localization theory of Vollhardt and Wölfle. We obtain explicit expressions for the dependence of the transverse localization length on the direction along the fiber. These results are in agreement with simulational data published recently by Karbasi et al. In particular we explain the focussing mechanism leading to the establishment of narrow transparent channels along the sample.

  4. Effects of divided attention and speeded responding on implicit and explicit retrieval of artificial grammar knowledge.

    PubMed

    Helman, Shaun; Berry, Dianne C

    2003-07-01

    The artificial grammar (AG) learning literature (see, e.g., Mathews et al., 1989; Reber, 1967) has relied heavily on a single measure of implicitly acquired knowledge. Recent work comparing this measure (string classification) with a more indirect measure in which participants make liking ratings of novel stimuli (e.g., Manza & Bornstein, 1995; Newell & Bright, 2001) has shown that string classification (which we argue can be thought of as an explicit, rather than an implicit, measure of memory) gives rise to more explicit knowledge of the grammatical structure in learning strings and is more resilient to changes in surface features and processing between encoding and retrieval. We report data from two experiments that extend these findings. In Experiment 1, we showed that a divided attention manipulation (at retrieval) interfered with explicit retrieval of AG knowledge but did not interfere with implicit retrieval. In Experiment 2, we showed that forcing participants to respond within a very tight deadline resulted in the same asymmetric interference pattern between the tasks. In both experiments, we also showed that the type of information being retrieved influenced whether interference was observed. The results are discussed in terms of the relatively automatic nature of implicit retrieval and also with respect to the differences between analytic and nonanalytic processing (Whittlesea & Price, 2001).

  5. Performance Analysis of Blind Subspace-Based Signature Estimation Algorithms for DS-CDMA Systems with Unknown Correlated Noise

    NASA Astrophysics Data System (ADS)

    Zarifi, Keyvan; Gershman, Alex B.

    2006-12-01

    We analyze the performance of two popular blind subspace-based signature waveform estimation techniques proposed by Wang and Poor and Buzzi and Poor for direct-sequence code division multiple-access (DS-CDMA) systems with unknown correlated noise. Using the first-order perturbation theory, analytical expressions for the mean-square error (MSE) of these algorithms are derived. We also obtain simple high SNR approximations of the MSE expressions which explicitly clarify how the performance of these techniques depends on the environmental parameters and how it is related to that of the conventional techniques that are based on the standard white noise assumption. Numerical examples further verify the consistency of the obtained analytical results with simulation results.

  6. Exact Solution of a Strongly Coupled Gauge Theory in 0 +1 Dimensions

    NASA Astrophysics Data System (ADS)

    Krishnan, Chethan; Kumar, K. V. Pavan

    2018-05-01

    Gauged tensor models are a class of strongly coupled quantum mechanical theories. We present the exact analytic solution of a specific example of such a theory: namely, the smallest colored tensor model due to Gurau and Witten that exhibits nonlinearities. We find explicit analytic expressions for the eigenvalues and eigenstates, and the former agree precisely with previous numerical results on (a subset of) eigenvalues of the ungauged theory. The physics of the spectrum, despite the smallness of N , exhibits rudimentary signatures of chaos. This Letter is a summary of our main results: the technical details will appear in companion paper [C. Krishnan and K. V. Pavan Kumar, Complete solution of a gauged tensor model, arXiv:1804.10103].

  7. Explicit Low-Thrust Guidance for Reference Orbit Targeting

    NASA Technical Reports Server (NTRS)

    Lam, Try; Udwadia, Firdaus E.

    2013-01-01

    The problem of a low-thrust spacecraft controlled to a reference orbit is addressed in this paper. A simple and explicit low-thrust guidance scheme with constrained thrust magnitude is developed by combining the fundamental equations of motion for constrained systems from analytical dynamics with a Lyapunov-based method. Examples are given for a spacecraft controlled to a reference trajectory in the circular restricted three body problem.

  8. Explicit Computations of Instantons and Large Deviations in Beta-Plane Turbulence

    NASA Astrophysics Data System (ADS)

    Laurie, J.; Bouchet, F.; Zaboronski, O.

    2012-12-01

    We use a path integral formalism and instanton theory in order to make explicit analytical predictions about large deviations and rare events in beta-plane turbulence. The path integral formalism is a concise way to get large deviation results in dynamical systems forced by random noise. In the most simple cases, it leads to the same results as the Freidlin-Wentzell theory, but it has a wider range of applicability. This approach is however usually extremely limited, due to the complexity of the theoretical problems. As a consequence it provides explicit results in a fairly limited number of models, often extremely simple ones with only a few degrees of freedom. Few exception exist outside the realm of equilibrium statistical physics. We will show that the barotropic model of beta-plane turbulence is one of these non-equilibrium exceptions. We describe sets of explicit solutions to the instanton equation, and precise derivations of the action functional (or large deviation rate function). The reason why such exact computations are possible is related to the existence of hidden symmetries and conservation laws for the instanton dynamics. We outline several applications of this apporach. For instance, we compute explicitly the very low probability to observe flows with an energy much larger or smaller than the typical one. Moreover, we consider regimes for which the system has multiple attractors (corresponding to different numbers of alternating jets), and discuss the computation of transition probabilities between two such attractors. These extremely rare events are of the utmost importance as the dynamics undergo qualitative macroscopic changes during such transitions.

  9. A hybridized method for computing high-Reynolds-number hypersonic flow about blunt bodies

    NASA Technical Reports Server (NTRS)

    Weilmuenster, K. J.; Hamilton, H. H., II

    1979-01-01

    A hybridized method for computing the flow about blunt bodies is presented. In this method the flow field is split into its viscid and inviscid parts. The forebody flow field about a parabolic body is computed. For the viscous solution, the Navier-Stokes equations are solved on orthogonal parabolic coordinates using explicit finite differencing. The inviscid flow is determined by using a Moretti type scheme in which the Euler equations are solved, using explicit finite differences, on a nonorthogonal coordinate system which uses the bow shock as an outer boundary. The two solutions are coupled along a common data line and are marched together in time until a converged solution is obtained. Computed results, when compared with experimental and analytical results, indicate the method works well over a wide range of Reynolds numbers and Mach numbers.

  10. Special solutions to Chazy equation

    NASA Astrophysics Data System (ADS)

    Varin, V. P.

    2017-02-01

    We consider the classical Chazy equation, which is known to be integrable in hypergeometric functions. But this solution has remained purely existential and was never used numerically. We give explicit formulas for hypergeometric solutions in terms of initial data. A special solution was found in the upper half plane H with the same tessellation of H as that of the modular group. This allowed us to derive some new identities for the Eisenstein series. We constructed a special solution in the unit disk and gave an explicit description of singularities on its natural boundary. A global solution to Chazy equation in elliptic and theta functions was found that allows parametrization of an arbitrary solution to Chazy equation. The results have applications to analytic number theory.

  11. Nonlinear truncation error analysis of finite difference schemes for the Euler equations

    NASA Technical Reports Server (NTRS)

    Klopfer, G. H.; Mcrae, D. S.

    1983-01-01

    It is pointed out that, in general, dissipative finite difference integration schemes have been found to be quite robust when applied to the Euler equations of gas dynamics. The present investigation considers a modified equation analysis of both implicit and explicit finite difference techniques as applied to the Euler equations. The analysis is used to identify those error terms which contribute most to the observed solution errors. A technique for analytically removing the dominant error terms is demonstrated, resulting in a greatly improved solution for the explicit Lax-Wendroff schemes. It is shown that the nonlinear truncation errors are quite large and distributed quite differently for each of the three conservation equations as applied to a one-dimensional shock tube problem.

  12. Delivering Faster Congestion Feedback with the Mark-Front Strategy

    NASA Technical Reports Server (NTRS)

    Liu, Chunlei; Jain, Raj

    2001-01-01

    Computer networks use congestion feedback from the routers and destinations to control the transmission load. Delivering timely congestion feedback is essential to the performance of networks. Reaction to the congestion can be more effective if faster feedback is provided. Current TCP/IP networks use timeout, duplicate Acknowledgement Packets (ACKs) and explicit congestion notification (ECN) to deliver the congestion feedback, each provides a faster feedback than the previous method. In this paper, we propose a markfront strategy that delivers an even faster congestion feedback. With analytical and simulation results, we show that mark-front strategy reduces buffer size requirement, improves link efficiency and provides better fairness among users. Keywords: Explicit Congestion Notification, mark-front, congestion control, buffer size requirement, fairness.

  13. An analytical approach to the CMB polarization in a spatially closed background

    NASA Astrophysics Data System (ADS)

    Niazy, Pedram; Abbassi, Amir H.

    2018-03-01

    The scalar mode polarization of the cosmic microwave background is derived in a spatially closed universe from the Boltzmann equation using the line of sight integral method. The EE and TE multipole coefficients have been extracted analytically by considering some tolerable approximations such as considering the evolution of perturbation hydrodynamically and sudden transition from opacity to transparency at the time of last scattering. As the major advantage of analytic expressions, CEE,ℓS and CTE,ℓ explicitly show the dependencies on baryon density ΩB, matter density ΩM, curvature ΩK, primordial spectral index ns, primordial power spectrum amplitude As, Optical depth τreion, recombination width σt and recombination time tL. Using a realistic set of cosmological parameters taken from a fit to data from Planck, the closed universe EE and TE power spectrums in the scalar mode are compared with numerical results from the CAMB code and also latest observational data. The analytic results agree with the numerical ones on the big and moderate scales. The peak positions are in good agreement with the numerical result on these scales while the peak heights agree with that to within 20% due to the approximations have been considered for these derivations. Also, several interesting properties of CMB polarization are revealed by the analytic spectra.

  14. Spiral trajectory design: a flexible numerical algorithm and base analytical equations.

    PubMed

    Pipe, James G; Zwart, Nicholas R

    2014-01-01

    Spiral-based trajectories for magnetic resonance imaging can be advantageous, but are often cumbersome to design or create. This work presents a flexible numerical algorithm for designing trajectories based on explicit definition of radial undersampling, and also gives several analytical expressions for charactering the base (critically sampled) class of these trajectories. Expressions for the gradient waveform, based on slew and amplitude limits, are developed such that a desired pitch in the spiral k-space trajectory is followed. The source code for this algorithm, written in C, is publicly available. Analytical expressions approximating the spiral trajectory (ignoring the radial component) are given to characterize measurement time, gradient heating, maximum gradient amplitude, and off-resonance phase for slew-limited and gradient amplitude-limited cases. Several numerically calculated trajectories are illustrated, and base Archimedean spirals are compared with analytically obtained results. Several different waveforms illustrate that the desired slew and amplitude limits are reached, as are the desired undersampling patterns, using the numerical method. For base Archimedean spirals, the results of the numerical and analytical approaches are in good agreement. A versatile numerical algorithm was developed, and was written in publicly available code. Approximate analytical formulas are given that help characterize spiral trajectories. Copyright © 2013 Wiley Periodicals, Inc.

  15. Characterizing Aeroelastic Systems Using Eigenanalysis, Explicitly Retaining The Aerodynamic Degrees of Freedom

    NASA Technical Reports Server (NTRS)

    Heeg, Jennifer; Dowell, Earl H.

    2001-01-01

    Discrete time aeroelastic models with explicitly retained aerodynamic modes have been generated employing a time marching vortex lattice aerodynamic model. This paper presents analytical results from eigenanalysis of these models. The potential of these models to calculate the behavior of modes that represent damped system motion (noncritical modes) in addition to the simple harmonic modes is explored. A typical section with only structural freedom in pitch is examined. The eigenvalues are examined and compared to experimental data. Issues regarding the convergence of the solution with regard to refining the aerodynamic discretization are investigated. Eigenvector behavior is examined; the eigenvector associated with a particular eigenvalue can be viewed as the set of modal participation factors for that particular mode. For the present formulation of the equations of motion, the vorticity for each aerodynamic element appears explicitly as an element of each eigenvector in addition to the structural dynamic generalized coordinates. Thus, modal participation of the aerodynamic degrees of freedom can be assessed in M addition to participation of structural degrees of freedom.

  16. Closed-form analytical solutions of high-temperature heat pipe startup and frozen startup limitation

    NASA Technical Reports Server (NTRS)

    Cao, Y.; Faghri, A.

    1992-01-01

    Previous numerical and experimental studies indicate that the high-temperature heat pipe startup process is characterized by a moving hot zone with relatively sharp fronts. Based on the above observation, a flat-front model for an approximate analytical solution is proposed. A closed-form solution related to the temperature distribution in the hot zone and the hot zone length as a function of time are obtained. The analytical results agree well with the corresponding experimental data, and provide a quick prediction method for the heat pipe startup performance. Finally, a heat pipe limitation related to the frozen startup process is identified, and an explicit criterion for the high-temperature heat pipe startup is derived. The frozen startup limit identified in this paper provides a fundamental guidance for high-temperature heat pipe design.

  17. Airside HVAC BESTEST: HVAC Air-Distribution System Model Test Cases for ASHRAE Standard 140

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

    Judkoff, Ronald; Neymark, Joel; Kennedy, Mike D.

    This paper summarizes recent work to develop new airside HVAC equipment model analytical verification test cases for ANSI/ASHRAE Standard 140, Standard Method of Test for the Evaluation of Building Energy Analysis Computer Programs. The analytical verification test method allows comparison of simulation results from a wide variety of building energy simulation programs with quasi-analytical solutions, further described below. Standard 140 is widely cited for evaluating software for use with performance-path energy efficiency analysis, in conjunction with well-known energy-efficiency standards including ASHRAE Standard 90.1, the International Energy Conservation Code, and other international standards. Airside HVAC Equipment is a common area ofmore » modelling not previously explicitly tested by Standard 140. Integration of the completed test suite into Standard 140 is in progress.« less

  18. Soft black hole absorption rates as conservation laws

    DOE PAGES

    Avery, Steven G.; Schwab, Burkhard U. W.

    2017-04-10

    The absorption rate of low-energy, or soft, electromagnetic radiation by spherically symmetric black holes in arbitrary dimensions is shown to be fixed by conservation of energy and large gauge transformations. Here, we interpret this result as the explicit realization of the Hawking-Perry-Strominger Ward identity for large gauge transformations in the background of a non-evaporating black hole. Along the way we rederive and extend our previous analytic results regarding the absorption rate for the minimal scalar and the photon.

  19. Soft black hole absorption rates as conservation laws

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

    Avery, Steven G.; Schwab, Burkhard U. W.

    The absorption rate of low-energy, or soft, electromagnetic radiation by spherically symmetric black holes in arbitrary dimensions is shown to be fixed by conservation of energy and large gauge transformations. Here, we interpret this result as the explicit realization of the Hawking-Perry-Strominger Ward identity for large gauge transformations in the background of a non-evaporating black hole. Along the way we rederive and extend our previous analytic results regarding the absorption rate for the minimal scalar and the photon.

  20. The Simpson's paradox unraveled

    PubMed Central

    Hernán, Miguel A; Clayton, David; Keiding, Niels

    2011-01-01

    Background In a famous article, Simpson described a hypothetical data example that led to apparently paradoxical results. Methods We make the causal structure of Simpson's example explicit. Results We show how the paradox disappears when the statistical analysis is appropriately guided by subject-matter knowledge. We also review previous explanations of Simpson's paradox that attributed it to two distinct phenomena: confounding and non-collapsibility. Conclusion Analytical errors may occur when the problem is stripped of its causal context and analyzed merely in statistical terms. PMID:21454324

  1. Nonadiabatic dynamics of electron transfer in solution: Explicit and implicit solvent treatments that include multiple relaxation time scales

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

    Schwerdtfeger, Christine A.; Soudackov, Alexander V.; Hammes-Schiffer, Sharon, E-mail: shs3@illinois.edu

    2014-01-21

    The development of efficient theoretical methods for describing electron transfer (ET) reactions in condensed phases is important for a variety of chemical and biological applications. Previously, dynamical dielectric continuum theory was used to derive Langevin equations for a single collective solvent coordinate describing ET in a polar solvent. In this theory, the parameters are directly related to the physical properties of the system and can be determined from experimental data or explicit molecular dynamics simulations. Herein, we combine these Langevin equations with surface hopping nonadiabatic dynamics methods to calculate the rate constants for thermal ET reactions in polar solvents formore » a wide range of electronic couplings and reaction free energies. Comparison of explicit and implicit solvent calculations illustrates that the mapping from explicit to implicit solvent models is valid even for solvents exhibiting complex relaxation behavior with multiple relaxation time scales and a short-time inertial response. The rate constants calculated for implicit solvent models with a single solvent relaxation time scale corresponding to water, acetonitrile, and methanol agree well with analytical theories in the Golden rule and solvent-controlled regimes, as well as in the intermediate regime. The implicit solvent models with two relaxation time scales are in qualitative agreement with the analytical theories but quantitatively overestimate the rate constants compared to these theories. Analysis of these simulations elucidates the importance of multiple relaxation time scales and the inertial component of the solvent response, as well as potential shortcomings of the analytical theories based on single time scale solvent relaxation models. This implicit solvent approach will enable the simulation of a wide range of ET reactions via the stochastic dynamics of a single collective solvent coordinate with parameters that are relevant to experimentally accessible systems.« less

  2. Does attitude acquisition in evaluative conditioning without explicit CS-US memory reflect implicit misattribution of affect?

    PubMed

    Mierop, Adrien; Hütter, Mandy; Stahl, Christoph; Corneille, Olivier

    2018-02-05

    Research that dissociates different types of processes within a given task using a processing tree approach suggests that attitudes may be acquired through evaluative conditioning in the absence of explicit encoding of CS-US pairings in memory. This research distinguishes explicit memory for the CS-US pairings from CS-liking acquired without encoding of CS-US pairs in explicit memory. It has been suggested that the latter effect may be due to an implicit misattribution process that is assumed to operate when US evocativeness is low. In the present research, the latter assumption was supported neither by two high-powered experiments nor by complementary meta-analytic evidence, whereas evocativeness exerted an influence on explicit memory. This pattern of findings is inconsistent with the view that CS-liking acquired without encoding of CS-US pairs in explicit memory reflects an implicit misattribution process at learning. Hence, the underlying learning process is awaiting further empirical scrutiny.

  3. Identifying the nonlinear mechanical behaviour of micro-speakers from their quasi-linear electrical response

    NASA Astrophysics Data System (ADS)

    Zilletti, Michele; Marker, Arthur; Elliott, Stephen John; Holland, Keith

    2017-05-01

    In this study model identification of the nonlinear dynamics of a micro-speaker is carried out by purely electrical measurements, avoiding any explicit vibration measurements. It is shown that a dynamic model of the micro-speaker, which takes into account the nonlinear damping characteristic of the device, can be identified by measuring the response between the voltage input and the current flowing into the coil. An analytical formulation of the quasi-linear model of the micro-speaker is first derived and an optimisation method is then used to identify a polynomial function which describes the mechanical damping behaviour of the micro-speaker. The analytical results of the quasi-linear model are compared with numerical results. This study potentially opens up the possibility of efficiently implementing nonlinear echo cancellers.

  4. A note on singularities of the 3-D Euler equation

    NASA Technical Reports Server (NTRS)

    Tanveer, S.

    1994-01-01

    In this paper, we consider analytic initial conditions with finite energy, whose complex spatial continuation is a superposition of a smooth background flow and a singular field. Through explicit calculation in the complex plane, we show that under some assumptions, the solution to the 3-D Euler equation ceases to be analytic in the real domain in finite time.

  5. Analytic integration of real-virtual counterterms in NNLO jet cross sections I

    NASA Astrophysics Data System (ADS)

    Aglietti, Ugo; Del Duca, Vittorio; Duhr, Claude; Somogyi, Gábor; Trócsányi, Zoltán

    2008-09-01

    We present analytic evaluations of some integrals needed to give explicitly the integrated real-virtual counterterms, based on a recently proposed subtraction scheme for next-to-next-to-leading order (NNLO) jet cross sections. After an algebraic reduction of the integrals, integration-by-parts identities are used for the reduction to master integrals and for the computation of the master integrals themselves by means of differential equations. The results are written in terms of one- and two-dimensional harmonic polylogarithms, once an extension of the standard basis is made. We expect that the techniques described here will be useful in computing other integrals emerging in calculations in perturbative quantum field theories.

  6. Explicit solutions for exit-only radioactive decay chains

    NASA Astrophysics Data System (ADS)

    Yuan, Ding; Kernan, Warnick

    2007-05-01

    In this study, we extended Bateman's [Proc. Cambridge Philos. Soc. 15, 423 (1910)] original work for solving radioactive decay chains and explicitly derived analytic solutions for generic exit-only radioactive decay problems under given initial conditions. Instead of using the conventional Laplace transform for solving Bateman's equations, we used a much simpler algebraic approach. Finally, we discuss methods of breaking down certain classes of large decay chains into collections of simpler chains for easy handling.

  7. On the effect of the degeneracy among dark energy parameters

    NASA Astrophysics Data System (ADS)

    Gong, Yungui; Gao, Qing

    2014-01-01

    The dynamics of scalar fields as dark energy is well approximated by some general relations between the equation of state parameter and the fractional energy density . Based on the approximation, for slowly rolling scalar fields, we derived the analytical expressions of which reduce to the popular Chevallier-Polarski-Linder parametrization with an explicit degeneracy relation between and . The models approximate the dynamics of scalar fields well and help eliminate the degeneracies among , , and . With the explicit degeneracy relations, we test their effects on the constraints of the cosmological parameters. We find that: (1) The analytical relations between and for the two models are consistent with observational data. (2) The degeneracies have little effect on . (3) The error of was reduced about 30 % with the degeneracy relations.

  8. Stochastic modelling of the hydrologic operation of rainwater harvesting systems

    NASA Astrophysics Data System (ADS)

    Guo, Rui; Guo, Yiping

    2018-07-01

    Rainwater harvesting (RWH) systems are an effective low impact development practice that provides both water supply and runoff reduction benefits. A stochastic modelling approach is proposed in this paper to quantify the water supply reliability and stormwater capture efficiency of RWH systems. The input rainfall series is represented as a marked Poisson process and two typical water use patterns are analytically described. The stochastic mass balance equation is solved analytically, and based on this, explicit expressions relating system performance to system characteristics are derived. The performances of a wide variety of RWH systems located in five representative climatic regions of the United States are examined using the newly derived analytical equations. Close agreements between analytical and continuous simulation results are shown for all the compared cases. In addition, an analytical equation is obtained expressing the required storage size as a function of the desired water supply reliability, average water use rate, as well as rainfall and catchment characteristics. The equations developed herein constitute a convenient and effective tool for sizing RWH systems and evaluating their performances.

  9. Closed form solution for a double quantum well using Gröbner basis

    NASA Astrophysics Data System (ADS)

    Acus, A.; Dargys, A.

    2011-07-01

    Analytical expressions for the spectrum, eigenfunctions and dipole matrix elements of a square double quantum well (DQW) are presented for a general case when the potential in different regions of the DQW has different heights and the effective masses are different. This was achieved by using a Gröbner basis algorithm that allowed us to disentangle the resulting coupled polynomials without explicitly solving the transcendental eigenvalue equation.

  10. Triple collinear emissions in parton showers

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

    Höche, Stefan; Prestel, Stefan

    2017-10-01

    A framework to include triple collinear splitting functions into parton showers is presented, and the implementation of flavor-changing NLO splitting kernels is discussed as a first application. The correspondence between the Monte-Carlo integration and the analytic computation of NLO DGLAP evolution kernels is made explicit for both timelike and spacelike parton evolution. Numerical simulation results are obtained with two independent implementations of the new algorithm, using the two independent event generation frameworks Pythia and Sherpa.

  11. Novel quadrilateral elements based on explicit Hermite polynomials for bending of Kirchhoff-Love plates

    NASA Astrophysics Data System (ADS)

    Beheshti, Alireza

    2018-03-01

    The contribution addresses the finite element analysis of bending of plates given the Kirchhoff-Love model. To analyze the static deformation of plates with different loadings and geometries, the principle of virtual work is used to extract the weak form. Following deriving the strain field, stresses and resultants may be obtained. For constructing four-node quadrilateral plate elements, the Hermite polynomials defined with respect to the variables in the parent space are applied explicitly. Based on the approximated field of displacement, the stiffness matrix and the load vector in the finite element method are obtained. To demonstrate the performance of the subparametric 4-node plate elements, some known, classical examples in structural mechanics are solved and there are comparisons with the analytical solutions available in the literature.

  12. The full spectrum of AdS5/CFT4 I: representation theory and one-loop Q-system

    NASA Astrophysics Data System (ADS)

    Marboe, Christian; Volin, Dmytro

    2018-04-01

    With the formulation of the quantum spectral curve for the AdS5/CFT4 integrable system, it became potentially possible to compute its full spectrum with high efficiency. This is the first paper in a series devoted to the explicit design of such computations, with no restrictions to particular subsectors being imposed. We revisit the representation theoretical classification of possible states in the spectrum and map the symmetry multiplets to solutions of the quantum spectral curve at zero coupling. To this end it is practical to introduce a generalisation of Young diagrams to the case of non-compact representations and define algebraic Q-systems directly on these diagrams. Furthermore, we propose an algorithm to explicitly solve such Q-systems that circumvents the traditional usage of Bethe equations and simplifies the computation effort. For example, our algorithm quickly obtains explicit analytic results for all 495 multiplets that accommodate single-trace operators in N=4 SYM with classical conformal dimension up to \\frac{13}{2} . We plan to use these results as the seed for solving the quantum spectral curve perturbatively to high loop orders in the next paper of the series.

  13. Molecular motion in cell membranes: Analytic study of fence-hindered random walks

    NASA Astrophysics Data System (ADS)

    Kenkre, V. M.; Giuggioli, L.; Kalay, Z.

    2008-05-01

    A theoretical calculation is presented to describe the confined motion of transmembrane molecules in cell membranes. The study is analytic, based on Master equations for the probability of the molecules moving as random walkers, and leads to explicit usable solutions including expressions for the molecular mean square displacement and effective diffusion constants. One outcome is a detailed understanding of the dependence of the time variation of the mean square displacement on the initial placement of the molecule within the confined region. How to use the calculations is illustrated by extracting (confinement) compartment sizes from experimentally reported published observations from single particle tracking experiments on the diffusion of gold-tagged G -protein coupled μ -opioid receptors in the normal rat kidney cell membrane, and by further comparing the analytical results to observations on the diffusion of phospholipids, also in normal rat kidney cells.

  14. Analytical expressions for the closure probability of a stiff wormlike chain for finite capture radius.

    PubMed

    Guérin, T

    2017-08-01

    Estimating the probability that two monomers of the same polymer chain are close together is a key ingredient to characterize intramolecular reactions and polymer looping. In the case of stiff wormlike polymers (rigid fluctuating elastic rods), for which end-to-end encounters are rare events, we derive an explicit analytical formula for the probability η(r_{c}) that the distance between the chain extremities is smaller than some capture radius r_{c}. The formula is asymptotically exact in the limit of stiff chains, and it leads to the identification of two distinct scaling regimes for the closure factor, originating from a strong variation of the fluctuations of the chain orientation at closure. Our theory is compatible with existing analytical results from the literature that cover the cases of a vanishing capture radius and of nearly fully extended chains.

  15. Viscous damping and spring force in periodic perforated planar microstructures when the Reynolds’ equation cannot be applied

    PubMed Central

    Homentcovschi, Dorel; Miles, Ronald N.

    2010-01-01

    A model of squeeze-film behavior is developed based on Stokes’ equations for viscous, compressible isothermal flows. The flow domain is an axisymmetrical, unit cell approximation of a planar, periodic, perforated microstructure. The model is developed for cases when the lubrication approximation cannot be applied. The complex force generated by vibrations of the diaphragm driving the flow has two components: the damping force and the spring force. While for large frequencies the spring force dominates, at low (acoustical) frequencies the damping force is the most important part. The analytical approach developed here yields an explicit formula for both forces. In addition, using a finite element software package, the damping force is also obtained numerically. A comparison is made between the analytic result, numerical solution, and some experimental data found in the literature, which validates the analytic formula and provides compelling arguments about its value in designing microelectomechanical devices. PMID:20329828

  16. Upon the Shoulders of Giants: Open-Source Hardware and Software in Analytical Chemistry.

    PubMed

    Dryden, Michael D M; Fobel, Ryan; Fobel, Christian; Wheeler, Aaron R

    2017-04-18

    Isaac Newton famously observed that "if I have seen further it is by standing on the shoulders of giants." We propose that this sentiment is a powerful motivation for the "open-source" movement in scientific research, in which creators provide everything needed to replicate a given project online, as well as providing explicit permission for users to use, improve, and share it with others. Here, we write to introduce analytical chemists who are new to the open-source movement to best practices and concepts in this area and to survey the state of open-source research in analytical chemistry. We conclude by considering two examples of open-source projects from our own research group, with the hope that a description of the process, motivations, and results will provide a convincing argument about the benefits that this movement brings to both creators and users.

  17. Event-by-Event Simulations of Early Gluon Fields in High Energy Nuclear Collisions

    NASA Astrophysics Data System (ADS)

    Nickel, Matthew; Rose, Steven; Fries, Rainer

    2017-09-01

    Collisions of heavy ions are carried out at ultra relativistic speeds at the Relativistic Heavy Ion Collider and the Large Hadron Collider to create Quark Gluon Plasma. The earliest stages of such collisions are dominated by the dynamics of classical gluon fields. The McLerran-Venugopalan (MV) model of color glass condensate provides a model for this process. Previous research has provided an analytic solution for event averaged observables in the MV model. Using the High Performance Research Computing Center (HPRC) at Texas A&M, we have developed a C++ code to explicitly calculate the initial gluon fields and energy momentum tensor event by event using the analytic recursive solution. The code has been tested against previously known analytic results up to fourth order. We have also have been able to test the convergence of the recursive solution at high orders in time and studied the time evolution of color glass condensate.

  18. Familiarity Vs Trust: A Comparative Study of Domain Scientists' Trust in Visual Analytics and Conventional Analysis Methods.

    PubMed

    Dasgupta, Aritra; Lee, Joon-Yong; Wilson, Ryan; Lafrance, Robert A; Cramer, Nick; Cook, Kristin; Payne, Samuel

    2017-01-01

    Combining interactive visualization with automated analytical methods like statistics and data mining facilitates data-driven discovery. These visual analytic methods are beginning to be instantiated within mixed-initiative systems, where humans and machines collaboratively influence evidence-gathering and decision-making. But an open research question is that, when domain experts analyze their data, can they completely trust the outputs and operations on the machine-side? Visualization potentially leads to a transparent analysis process, but do domain experts always trust what they see? To address these questions, we present results from the design and evaluation of a mixed-initiative, visual analytics system for biologists, focusing on analyzing the relationships between familiarity of an analysis medium and domain experts' trust. We propose a trust-augmented design of the visual analytics system, that explicitly takes into account domain-specific tasks, conventions, and preferences. For evaluating the system, we present the results of a controlled user study with 34 biologists where we compare the variation of the level of trust across conventional and visual analytic mediums and explore the influence of familiarity and task complexity on trust. We find that despite being unfamiliar with a visual analytic medium, scientists seem to have an average level of trust that is comparable with the same in conventional analysis medium. In fact, for complex sense-making tasks, we find that the visual analytic system is able to inspire greater trust than other mediums. We summarize the implications of our findings with directions for future research on trustworthiness of visual analytic systems.

  19. An analytical formulation of two‐dimensional groundwater dispersion induced by surficial recharge variability

    USGS Publications Warehouse

    Swain, Eric D.; Chin, David A.

    2003-01-01

    A predominant cause of dispersion in groundwater is advective mixing due to variability in seepage rates. Hydraulic conductivity variations have been extensively researched as a cause of this seepage variability. In this paper the effect of variations in surface recharge to a shallow surficial aquifer is investigated as an important additional effect. An analytical formulation has been developed that relates aquifer parameters and the statistics of recharge variability to increases in the dispersivity. This is accomplished by solving Fourier transforms of the small perturbation forms of the groundwater flow equations. Two field studies are presented in this paper to determine the statistics of recharge variability for input to the analytical formulation. A time series of water levels at a continuous groundwater recorder is used to investigate the temporal statistics of hydraulic head caused by recharge, and a series of infiltrometer measurements are used to define the spatial variability in the recharge parameters. With these field statistics representing head fluctuations due to recharge, the analytical formulation can be used to compute the dispersivity without an explicit representation of the recharge boundary. Results from a series of numerical experiments are used to define the limits of this analytical formulation and to provide some comparison. A sophisticated model has been developed using a particle‐tracking algorithm (modified to account for temporal variations) to estimate groundwater dispersion. Dispersivity increases of 9 percent are indicated by the analytical formulation for the aquifer at the field site. A comparison with numerical model results indicates that the analytical results are reasonable for shallow surficial aquifers in which two‐dimensional flow can be assumed.

  20. Explicit correlation treatment of the six-dimensional potential energy surface and predicted infrared spectra for OCS-H2

    NASA Astrophysics Data System (ADS)

    Liu, Jing-Min; Zhai, Yu; Li, Hui

    2017-07-01

    An effective six-dimensional ab initio potential energy surface (PES) for H2-OCS which explicitly includes the intramolecular stretch normal modes of carbonyl sulfide (OCS) is presented. The electronic structure computations are carried out using the explicitly correlated coupled cluster [CCSD(T)-F12] method with the augmented correlation-consistent aug-cc-pVTZ basis set, and the accuracy is critically tested by performing a series of benchmark calculations. Analytic four-dimensional PESs are obtained by least-squares fitting vibrationally averaged interaction energies to the Morse/long-range potential model. These fits to 13 485 points have a root-mean-square deviation (RMSD) of 0.16 cm-1. The combined radial discrete variable representation/angular finite basis representation method and the Lanczos algorithm were employed to evaluate the rovibrational energy levels for five isotopic species of the OCS-hydrogen complexes. The predicted transition frequencies and intensities based on the resulting vibrationally averaged PESs are in good agreement with the available experimental values, whose RMSDs are smaller than 0.004 cm-1 for five different species of OCS-hydrogen complexes. The calculated infrared band origin shifts for all five species of OCS-hydrogen complexes are only 0.03 cm-1 smaller than the corresponding experimental values. These validate the high quality of our PESs which can be used for modeling OCS doped in hydrogen clusters to further study quantum solution and microscopic superfluidity. In addition, the analytic coordinate transformation functions between isotopologues are also derived due to the center of mass shifting of different isotope substitutes.

  1. Exact results in the large system size limit for the dynamics of the chemical master equation, a one dimensional chain of equations.

    PubMed

    Martirosyan, A; Saakian, David B

    2011-08-01

    We apply the Hamilton-Jacobi equation (HJE) formalism to solve the dynamics of the chemical master equation (CME). We found exact analytical expressions (in large system-size limit) for the probability distribution, including explicit expression for the dynamics of variance of distribution. We also give the solution for some simple cases of the model with time-dependent rates. We derived the results of the Van Kampen method from the HJE approach using a special ansatz. Using the Van Kampen method, we give a system of ordinary differential equations (ODEs) to define the variance in a two-dimensional case. We performed numerics for the CME with stationary noise. We give analytical criteria for the disappearance of bistability in the case of stationary noise in one-dimensional CMEs.

  2. What is the right formalism to search for resonances?

    NASA Astrophysics Data System (ADS)

    Mikhasenko, M.; Pilloni, A.; Nys, J.; Albaladejo, M.; Fernández-Ramírez, C.; Jackura, A.; Mathieu, V.; Sherrill, N.; Skwarnicki, T.; Szczepaniak, A. P.

    2018-03-01

    Hadron decay chains constitute one of the main sources of information on the QCD spectrum. We discuss the differences between several partial wave analysis formalisms used in the literature to build the amplitudes. We match the helicity amplitudes to the covariant tensor basis. Hereby, we pay attention to the analytical properties of the amplitudes and separate singularities of kinematical and dynamical nature. We study the analytical properties of the spin-orbit (LS) formalism, and some of the covariant tensor approaches. In particular, we explicitly build the amplitudes for the B→ ψ π K and B→ \\bar{D}π π decays, and show that the energy dependence of the covariant approach is model dependent. We also show that the usual recursive construction of covariant tensors explicitly violates crossing symmetry, which would lead to different resonance parameters extracted from scattering and decay processes.

  3. 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.

  4. Heuristic Reasoning in Chemistry: Making decisions about acid strength

    NASA Astrophysics Data System (ADS)

    McClary, LaKeisha; Talanquer, Vicente

    2011-07-01

    The characterization of students' reasoning strategies is of central importance in the development of instructional strategies that foster meaningful learning. In particular, the identification of shortcut reasoning procedures (heuristics) used by students to reduce cognitive load can help us devise strategies to facilitate the development of more analytical ways of thinking. The central goal of this qualitative study was thus to investigate heuristic reasoning as used by organic chemistry college students, focusing our attention on their ability to predict the relative acid strength of chemical compounds represented using explicit composition and structural features (i.e., structural formulas). Our results indicated that many study participants relied heavily on one or more of the following heuristics to make most of their decisions: reduction, representativeness, and lexicographic. Despite having visual access to reach structural information about the substances included in each ranking task, many students relied on isolated composition features to make their decisions. However, the specific characteristics of the tasks seemed to trigger heuristic reasoning in different ways. Although the use of heuristics allowed students to simplify some components of the ranking tasks and generate correct responses, it often led them astray. Very few study participants predicted the correct trends based on scientifically acceptable arguments. Our results suggest the need for instructional interventions that explicitly develop college chemistry students' abilities to monitor their thinking and evaluate the effectiveness of analytical versus heuristic reasoning strategies in different contexts.

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

    Dalvit, Diego; Messina, Riccardo; Maia Neto, Paulo

    We develop the scattering approach for the dispersive force on a ground state atom on top of a corrugated surface. We present explicit results to first order in the corrugation amplitude. A variety of analytical results are derived in different limiting cases, including the van der Waals and Casimir-Polder regimes. We compute numerically the exact first-order dispersive potential for arbitrary separation distances and corrugation wavelengths, for a Rubidium atom on top of a silicon or gold corrugated surface. We consider in detail the correction to the proximity force approximation, and present a very simple approximation algorithm for computing the potential.

  6. Exact solution of a linear molecular motor model driven by two-step fluctuations and subject to protein friction.

    PubMed

    Fogedby, Hans C; Metzler, Ralf; Svane, Axel

    2004-08-01

    We investigate by analytical means the stochastic equations of motion of a linear molecular motor model based on the concept of protein friction. Solving the coupled Langevin equations originally proposed by Mogilner et al. [Phys. Lett. A 237, 297 (1998)], and averaging over both the two-step internal conformational fluctuations and the thermal noise, we present explicit, analytical expressions for the average motion and the velocity-force relationship. Our results allow for a direct interpretation of details of this motor model which are not readily accessible from numerical solutions. In particular, we find that the model is able to predict physiologically reasonable values for the load-free motor velocity and the motor mobility.

  7. Target annihilation by diffusing particles in inhomogeneous geometries

    NASA Astrophysics Data System (ADS)

    Cassi, Davide

    2009-09-01

    The survival probability of immobile targets annihilated by a population of random walkers on inhomogeneous discrete structures, such as disordered solids, glasses, fractals, polymer networks, and gels, is analytically investigated. It is shown that, while it cannot in general be related to the number of distinct visited points as in the case of homogeneous lattices, in the case of bounded coordination numbers its asymptotic behavior at large times can still be expressed in terms of the spectral dimension d˜ and its exact analytical expression is given. The results show that the asymptotic survival probability is site-independent of recurrent structures (d˜≤2) , while on transient structures (d˜>2) it can strongly depend on the target position, and such dependence is explicitly calculated.

  8. Relativistic calculation of correlational energy for a helium-like atom

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

    Palchikov, V.G.

    This paper presents an analytical method for calculating the firstorder correlational energy from the electron interaction, taking account of lag effects. Explicit analytical expressions are obtained for radial matrix elements. The nonrelativistic limit is investigated. The given method may be used to calculate correlation effects in higher orders of perturbation theory (second and higher orders with respect to 1/z) using the Strum expansion for the Coulomb Green's functions.

  9. Towards a minimal stochastic model for a large class of diffusion-reactions on biological membranes.

    PubMed

    Chevalier, Michael W; El-Samad, Hana

    2012-08-28

    Diffusion of biological molecules on 2D biological membranes can play an important role in the behavior of stochastic biochemical reaction systems. Yet, we still lack a fundamental understanding of circumstances where explicit accounting of the diffusion and spatial coordinates of molecules is necessary. In this work, we illustrate how time-dependent, non-exponential reaction probabilities naturally arise when explicitly accounting for the diffusion of molecules. We use the analytical expression of these probabilities to derive a novel algorithm which, while ignoring the exact position of the molecules, can still accurately capture diffusion effects. We investigate the regions of validity of the algorithm and show that for most parameter regimes, it constitutes an accurate framework for studying these systems. We also document scenarios where large spatial fluctuation effects mandate explicit consideration of all the molecules and their positions. Taken together, our results derive a fundamental understanding of the role of diffusion and spatial fluctuations in these systems. Simultaneously, they provide a general computational methodology for analyzing a broad class of biological networks whose behavior is influenced by diffusion on membranes.

  10. Understanding the Double Quantum Muonium RF Resonance

    NASA Astrophysics Data System (ADS)

    Kreitzman, S. R.; Cottrell, S. P.; Fleming, D. G.; Sun-Mack, S.

    A physically intuitive analytical solution to the Mu + RF Hamiltonian and lineshape is developed. The method is based on reformulating the problem in a basis set that explicitly accounts for the 1q RF transitions and identifying an isolated upper 1q quasi-eigenstate within that basis. Subsequently the double quantum resonance explicitly manifests itself via the non-zero interaction term between the pair of lower ortho-normalized 1q basis states, which in this field region are substantially the | \\uparrow \\uparrow > and | \\downarrow \\downarrow > Mu states.

  11. Time-shifted synchronization of chaotic oscillator chains without explicit coupling delays.

    PubMed

    Blakely, Jonathan N; Stahl, Mark T; Corron, Ned J

    2009-12-01

    We examine chains of unidirectionally coupled oscillators in which time-shifted synchronization occurs without explicit delays in the coupling. In numerical simulations and in an experimental system of electronic oscillators, we examine the time shift and the degree of distortion (primarily in the form of attenuation) of the waveforms of the oscillators located far from the drive oscillator. Surprisingly, under weak coupling we observe minimal attenuation in spite of a significant total time shift. In contrast, at higher coupling strengths the observed attenuation increases dramatically and approaches the value predicted by an analytically derived estimate. In this regime, we verify directly that generalized synchronization is maintained over the entire chain length despite severe attenuation. These results suggest that weak coupling generally may produce higher quality synchronization in systems for which truly identical synchronization is not possible.

  12. Analysis of composite ablators using massively parallel computation

    NASA Technical Reports Server (NTRS)

    Shia, David

    1995-01-01

    In this work, the feasibility of using massively parallel computation to study the response of ablative materials is investigated. Explicit and implicit finite difference methods are used on a massively parallel computer, the Thinking Machines CM-5. The governing equations are a set of nonlinear partial differential equations. The governing equations are developed for three sample problems: (1) transpiration cooling, (2) ablative composite plate, and (3) restrained thermal growth testing. The transpiration cooling problem is solved using a solution scheme based solely on the explicit finite difference method. The results are compared with available analytical steady-state through-thickness temperature and pressure distributions and good agreement between the numerical and analytical solutions is found. It is also found that a solution scheme based on the explicit finite difference method has the following advantages: incorporates complex physics easily, results in a simple algorithm, and is easily parallelizable. However, a solution scheme of this kind needs very small time steps to maintain stability. A solution scheme based on the implicit finite difference method has the advantage that it does not require very small times steps to maintain stability. However, this kind of solution scheme has the disadvantages that complex physics cannot be easily incorporated into the algorithm and that the solution scheme is difficult to parallelize. A hybrid solution scheme is then developed to combine the strengths of the explicit and implicit finite difference methods and minimize their weaknesses. This is achieved by identifying the critical time scale associated with the governing equations and applying the appropriate finite difference method according to this critical time scale. The hybrid solution scheme is then applied to the ablative composite plate and restrained thermal growth problems. The gas storage term is included in the explicit pressure calculation of both problems. Results from ablative composite plate problems are compared with previous numerical results which did not include the gas storage term. It is found that the through-thickness temperature distribution is not affected much by the gas storage term. However, the through-thickness pressure and stress distributions, and the extent of chemical reactions are different from the previous numerical results. Two types of chemical reaction models are used in the restrained thermal growth testing problem: (1) pressure-independent Arrhenius type rate equations and (2) pressure-dependent Arrhenius type rate equations. The numerical results are compared to experimental results and the pressure-dependent model is able to capture the trend better than the pressure-independent one. Finally, a performance study is done on the hybrid algorithm using the ablative composite plate problem. It is found that there is a good speedup of performance on the CM-5. For 32 CPU's, the speedup of performance is 20. The efficiency of the algorithm is found to be a function of the size and execution time of a given problem and the effective parallelization of the algorithm. It also seems that there is an optimum number of CPU's to use for a given problem.

  13. A Geographically Explicit Genetic Model of Worldwide Human-Settlement History

    PubMed Central

    Liu, Hua; Prugnolle, Franck; Manica, Andrea; Balloux, François

    2006-01-01

    Currently available genetic and archaeological evidence is generally interpreted as supportive of a recent single origin of modern humans in East Africa. However, this is where the near consensus on human settlement history ends, and considerable uncertainty clouds any more detailed aspect of human colonization history. Here, we present a dynamic genetic model of human settlement history coupled with explicit geographical distances from East Africa, the likely origin of modern humans. We search for the best-supported parameter space by fitting our analytical prediction to genetic data that are based on 52 human populations analyzed at 783 autosomal microsatellite markers. This framework allows us to jointly estimate the key parameters of the expansion of modern humans. Our best estimates suggest an initial expansion of modern humans ∼56,000 years ago from a small founding population of ∼1,000 effective individuals. Our model further points to high growth rates in newly colonized habitats. The general fit of the model with the data is excellent. This suggests that coupling analytical genetic models with explicit demography and geography provides a powerful tool for making inferences on human-settlement history. PMID:16826514

  14. Implicit motor learning promotes neural efficiency during laparoscopy.

    PubMed

    Zhu, Frank F; Poolton, Jamie M; Wilson, Mark R; Hu, Yong; Maxwell, Jon P; Masters, Rich S W

    2011-09-01

    An understanding of differences in expert and novice neural behavior can inform surgical skills training. Outside the surgical domain, electroencephalographic (EEG) coherence analyses have shown that during motor performance, experts display less coactivation between the verbal-analytic and motor planning regions than their less skilled counterparts. Reduced involvement of verbal-analytic processes suggests greater neural efficiency. The authors tested the utility of an implicit motor learning intervention specifically devised to promote neural efficiency by reducing verbal-analytic involvement in laparoscopic performance. In this study, 18 novices practiced a movement pattern on a laparoscopic trainer with either conscious awareness of the movement pattern (explicit motor learning) or suppressed awareness of the movement pattern (implicit motor learning). In a retention test, movement accuracy was compared between the conditions, and coactivation (EEG coherence) was assessed between the motor planning (Fz) region and both the verbal-analytic (T3) and the visuospatial (T4) cortical regions (T3-Fz and T4-Fz, respectively). Movement accuracy in the conditions was not different in a retention test (P = 0.231). Findings showed that the EEG coherence scores for the T3-Fz regions were lower for the implicit learners than for the explicit learners (P = 0.027), but no differences were apparent for the T4-Fz regions (P = 0.882). Implicit motor learning reduced EEG coactivation between verbal-analytic and motor planning regions, suggesting that verbal-analytic processes were less involved in laparoscopic performance. The findings imply that training techniques that discourage nonessential coactivation during motor performance may provide surgeons with more neural resources with which to manage other aspects of surgery.

  15. Computational study of the free energy landscape of the miniprotein CLN025 in explicit and implicit solvent.

    PubMed

    Rodriguez, Alex; Mokoema, Pol; Corcho, Francesc; Bisetty, Khrisna; Perez, Juan J

    2011-02-17

    The prediction capabilities of atomistic simulations of peptides are hampered by different difficulties, including the reliability of force fields, the treatment of the solvent or the adequate sampling of the conformational space. In this work, we have studied the conformational profile of the 10 residue miniprotein CLN025 known to exhibit a β-hairpin in its native state to understand the limitations of implicit methods to describe solvent effects and how these may be compensated by using different force fields. For this purpose, we carried out a thorough sampling of the conformational space of CLN025 in explicit solvent using the replica exchange molecular dynamics method as a sampling technique and compared the results with simulations of the system modeled using the analytical linearized Poisson-Boltzmann (ALPB) method with three different AMBER force fields: parm94, parm96, and parm99SB. The results show the peptide to exhibit a funnel-like free energy landscape with two minima in explicit solvent. In contrast, the higher minimum nearly disappears from the energy surface when the system is studied with an implicit representation of the solvent. Moreover, the different force fields used in combination with the ALPB method do not describe the system in the same manner. The results of this work suggest that the balance between intra- and intermolecular interactions is the cause of the differences between implicit and explicit solvent simulations in this system, stressing the role of the environment to define properly the conformational profile of a peptide in solution.

  16. Approximate analytical relationships for linear optimal aeroelastic flight control laws

    NASA Astrophysics Data System (ADS)

    Kassem, Ayman Hamdy

    1998-09-01

    This dissertation introduces new methods to uncover functional relationships between design parameters of a contemporary control design technique and the resulting closed-loop properties. Three new methods are developed for generating such relationships through analytical expressions: the Direct Eigen-Based Technique, the Order of Magnitude Technique, and the Cost Function Imbedding Technique. Efforts concentrated on the linear-quadratic state-feedback control-design technique applied to an aeroelastic flight control task. For this specific application, simple and accurate analytical expressions for the closed-loop eigenvalues and zeros in terms of basic parameters such as stability and control derivatives, structural vibration damping and natural frequency, and cost function weights are generated. These expressions explicitly indicate how the weights augment the short period and aeroelastic modes, as well as the closed-loop zeros, and by what physical mechanism. The analytical expressions are used to address topics such as damping, nonminimum phase behavior, stability, and performance with robustness considerations, and design modifications. This type of knowledge is invaluable to the flight control designer and would be more difficult to formulate when obtained from numerical-based sensitivity analysis.

  17. No further gravitational wave modes in F(T) gravity

    NASA Astrophysics Data System (ADS)

    Bamba, Kazuharu; Capozziello, Salvatore; De Laurentis, Mariafelicia; Nojiri, Shin'ichi; Sáez-Gómez, Diego

    2013-11-01

    We explore the possibility of further gravitational wave modes in F(T) gravity, where T is the torsion scalar in teleparallelism. It is explicitly demonstrated that gravitational wave modes in F(T) gravity are equivalent to those in General Relativity. This result is achieved by calculating the Minkowskian limit for a class of analytic function of F(T). This consequence is also confirmed by the preservative analysis around the flat background in the weak field limit with the scalar-tensor representation of F(T) gravity.

  18. An Exactly Soluble Model for Hopping Particles Moving with Correlations Between States due to Exchange Sites

    NASA Astrophysics Data System (ADS)

    Zhao, Xian-Geng; Jia, Sue-Tang

    1992-09-01

    The motion of hopping particles on an infinite chain is investigated. The model is characterized by the correlations between states due to exchange sites. The analytic solutions for this system are discussed in general case. For some special cases, exact results are obtained with the help of explicit calculations of propagators and mean square displacement deviation. Both probability propagators for the creation and annihilation of two particles or for the deformation and formation of Frenkel excitons are indicated.

  19. Scalar and tensor spherical harmonics expansion of the velocity correlation in homogeneous anisotropic turbulence

    DOE PAGES

    Rubinstein, Robert; Kurien, Susan; Cambon, Claude

    2015-06-22

    The representation theory of the rotation group is applied to construct a series expansion of the correlation tensor in homogeneous anisotropic turbulence. The resolution of angular dependence is the main analytical difficulty posed by anisotropic turbulence; representation theory parametrises this dependence by a tensor analogue of the standard spherical harmonics expansion of a scalar. As a result, the series expansion is formulated in terms of explicitly constructed tensor bases with scalar coefficients determined by angular moments of the correlation tensor.

  20. Corona graphs as a model of small-world networks

    NASA Astrophysics Data System (ADS)

    Lv, Qian; Yi, Yuhao; Zhang, Zhongzhi

    2015-11-01

    We introduce recursive corona graphs as a model of small-world networks. We investigate analytically the critical characteristics of the model, including order and size, degree distribution, average path length, clustering coefficient, and the number of spanning trees, as well as Kirchhoff index. Furthermore, we study the spectra for the adjacency matrix and the Laplacian matrix for the model. We obtain explicit results for all the quantities of the recursive corona graphs, which are similar to those observed in real-life networks.

  1. Triple collinear emissions in parton showers

    DOE PAGES

    Hoche, Stefan; Prestel, Stefan

    2017-10-17

    A framework to include triple collinear splitting functions into parton showers is presented, and the implementation of flavor-changing next-to-leading-order (NLO) splitting kernels is discussed as a first application. The correspondence between the Monte Carlo integration and the analytic computation of NLO DGLAP evolution kernels is made explicit for both timelike and spacelike parton evolution. Finally, numerical simulation results are obtained with two independent implementations of the new algorithm, using the two independent event generation frameworks PYTHIA and SHERPA.

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

    Wang, Y. B.; Zhu, X. W., E-mail: xiaowuzhu1026@znufe.edu.cn; Dai, H. H.

    Though widely used in modelling nano- and micro- structures, Eringen’s differential model shows some inconsistencies and recent study has demonstrated its differences between the integral model, which then implies the necessity of using the latter model. In this paper, an analytical study is taken to analyze static bending of nonlocal Euler-Bernoulli beams using Eringen’s two-phase local/nonlocal model. Firstly, a reduction method is proved rigorously, with which the integral equation in consideration can be reduced to a differential equation with mixed boundary value conditions. Then, the static bending problem is formulated and four types of boundary conditions with various loadings aremore » considered. By solving the corresponding differential equations, exact solutions are obtained explicitly in all of the cases, especially for the paradoxical cantilever beam problem. Finally, asymptotic analysis of the exact solutions reveals clearly that, unlike the differential model, the integral model adopted herein has a consistent softening effect. Comparisons are also made with existing analytical and numerical results, which further shows the advantages of the analytical results obtained. Additionally, it seems that the once controversial nonlocal bar problem in the literature is well resolved by the reduction method.« less

  3. Efficient Band-to-Trap Tunneling Model Including Heterojunction Band Offset

    DOE PAGES

    Gao, Xujiao; Huang, Andy; Kerr, Bert

    2017-10-25

    In this paper, we present an efficient band-to-trap tunneling model based on the Schenk approach, in which an analytic density-of-states (DOS) model is developed based on the open boundary scattering method. The new model explicitly includes the effect of heterojunction band offset, in addition to the well-known field effect. Its analytic form enables straightforward implementation into TCAD device simulators. It is applicable to all one-dimensional potentials, which can be approximated to a good degree such that the approximated potentials lead to piecewise analytic wave functions with open boundary conditions. The model allows for simulating both the electric-field-enhanced and band-offset-enhanced carriermore » recombination due to the band-to-trap tunneling near the heterojunction in a heterojunction bipolar transistor (HBT). Simulation results of an InGaP/GaAs/GaAs NPN HBT show that the proposed model predicts significantly increased base currents, due to the hole-to-trap tunneling enhanced by the emitter-base junction band offset. Finally, the results compare favorably with experimental observation.« less

  4. Efficient Band-to-Trap Tunneling Model Including Heterojunction Band Offset

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

    Gao, Xujiao; Huang, Andy; Kerr, Bert

    In this paper, we present an efficient band-to-trap tunneling model based on the Schenk approach, in which an analytic density-of-states (DOS) model is developed based on the open boundary scattering method. The new model explicitly includes the effect of heterojunction band offset, in addition to the well-known field effect. Its analytic form enables straightforward implementation into TCAD device simulators. It is applicable to all one-dimensional potentials, which can be approximated to a good degree such that the approximated potentials lead to piecewise analytic wave functions with open boundary conditions. The model allows for simulating both the electric-field-enhanced and band-offset-enhanced carriermore » recombination due to the band-to-trap tunneling near the heterojunction in a heterojunction bipolar transistor (HBT). Simulation results of an InGaP/GaAs/GaAs NPN HBT show that the proposed model predicts significantly increased base currents, due to the hole-to-trap tunneling enhanced by the emitter-base junction band offset. Finally, the results compare favorably with experimental observation.« less

  5. An Eight-Eyed Version of Hawkins and Shohet's Clinical Supervision Model: The Addition of the Cognitive Analytic Therapy Concept of the "Observing Eye/I" as the "Observing Us"

    ERIC Educational Resources Information Center

    Darongkamas, Jurai; John, Christopher; Walker, Mark James

    2014-01-01

    This paper proposes incorporating the concept of the "observing eye/I", from cognitive analytic therapy (CAT), to Hawkins and Shohet's seven modes of supervision, comprising their transtheoretical model of supervision. Each mode is described alongside explicit examples relating to CAT. This modification using a key idea from CAT (in…

  6. What is the right formalism to search for resonances?

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

    Mikhasenko, M.; Pilloni, A.; Nys, J.

    Hmore » adron decay chains constitute one of the main sources of information on the QCD spectrum. We discuss the differences between several partial wave analysis formalisms used in the literature to build the amplitudes. We match the helicity amplitudes to the covariant tensor basis. ereby, we pay attention to the analytical properties of the amplitudes and separate singularities of kinematical and dynamical nature. We study the analytical properties of the spin-orbit (LS) formalism, and some of the covariant tensor approaches. In particular, we explicitly build the amplitudes for the B → ψ π K and B → D ¯ π π decays, and show that the energy dependence of the covariant approach is model dependent. We also show that the usual recursive construction of covariant tensors explicitly violates crossing symmetry, which would lead to different resonance parameters extracted from scattering and decay processes.« less

  7. What is the right formalism to search for resonances?

    DOE PAGES

    Mikhasenko, M.; Pilloni, A.; Nys, J.; ...

    2018-03-17

    Hmore » adron decay chains constitute one of the main sources of information on the QCD spectrum. We discuss the differences between several partial wave analysis formalisms used in the literature to build the amplitudes. We match the helicity amplitudes to the covariant tensor basis. ereby, we pay attention to the analytical properties of the amplitudes and separate singularities of kinematical and dynamical nature. We study the analytical properties of the spin-orbit (LS) formalism, and some of the covariant tensor approaches. In particular, we explicitly build the amplitudes for the B → ψ π K and B → D ¯ π π decays, and show that the energy dependence of the covariant approach is model dependent. We also show that the usual recursive construction of covariant tensors explicitly violates crossing symmetry, which would lead to different resonance parameters extracted from scattering and decay processes.« less

  8. On pseudo-hyperkähler prepotentials

    NASA Astrophysics Data System (ADS)

    Devchand, Chandrashekar; Spiro, Andrea

    2016-10-01

    An explicit surjection from a set of (locally defined) unconstrained holomorphic functions on a certain submanifold of Sp1(ℂ) × ℂ4n onto the set HKp,q of local isometry classes of real analytic pseudo-hyperkähler metrics of signature (4p, 4q) in dimension 4n is constructed. The holomorphic functions, called prepotentials, are analogues of Kähler potentials for Kähler metrics and provide a complete parameterisation of HKp,q. In particular, there exists a bijection between HKp,q and the set of equivalence classes of prepotentials. This affords the explicit construction of pseudo-hyperkähler metrics from specified prepotentials. The construction generalises one due to Galperin, Ivanov, Ogievetsky, and Sokatchev. Their work is given a coordinate-free formulation and complete, self-contained proofs are provided. The Appendix provides a vital tool for this construction: a reformulation of real analytic G-structures in terms of holomorphic frame fields on complex manifolds.

  9. Analytical representation of dynamical quantities in G W from a matrix resolvent

    NASA Astrophysics Data System (ADS)

    Gesenhues, J.; Nabok, D.; Rohlfing, M.; Draxl, C.

    2017-12-01

    The power of the G W formalism is, to a large extent, based on the explicit treatment of dynamical correlations in the self-energy. This dynamics is taken into account by calculating the energy dependence of the screened Coulomb interaction W , followed by a convolution with the Green's function G . In order to obtain the energy dependence of W the prevalent methods are plasmon-pole models and numerical integration techniques. In this paper, we discuss an alternative approach, in which the energy-dependent screening is calculated by determining the resolvent, which is set up from a matrix representation of the dielectric function. On the one hand, this refrains from a numerical energy convolution and allows one to actually write down the energy dependence of W explicitly (like in the plasmon-pole models). On the other hand, the method is at least as accurate as the numerical approaches due to its multipole nature. We discuss the theoretical setup in some detail, give insight into the computational aspects, and present results for Si, C, GaAs, and LiF. Finally, we argue that the analytic representability is not only useful for educational purposes but may also be of avail for the development of theory that goes beyond G W .

  10. Water transport through tall trees: A vertically-explicit, analytical model of xylem hydraulic conductance in stems.

    PubMed

    Couvreur, Valentin; Ledder, Glenn; Manzoni, Stefano; Way, Danielle A; Muller, Erik B; Russo, Sabrina E

    2018-05-08

    Trees grow by vertically extending their stems, so accurate stem hydraulic models are fundamental to understanding the hydraulic challenges faced by tall trees. Using a literature survey, we showed that many tree species exhibit continuous vertical variation in hydraulic traits. To examine the effects of this variation on hydraulic function, we developed a spatially-explicit, analytical water transport model for stems. Our model allows Huber ratio, stem-saturated conductivity, pressure at 50% loss of conductivity, leaf area, and transpiration rate to vary continuously along the hydraulic path. Predictions from our model differ from a matric flux potential model parameterized with uniform traits. Analyses show that cavitation is a whole-stem emergent property resulting from nonlinear pressure-conductivity feedbacks that, with gravity, cause impaired water transport to accumulate along the path. Because of the compounding effects of vertical trait variation on hydraulic function, growing proportionally more sapwood and building tapered xylem with height, as well as reducing xylem vulnerability only at branch tips while maintaining transport capacity at the stem base, can compensate for these effects. We therefore conclude that the adaptive significance of vertical variation in stem hydraulic traits is to allow trees to grow tall and tolerate operating near their hydraulic limits. This article is protected by copyright. All rights reserved.

  11. Analytic integration of real-virtual counterterms in NNLO jet cross sections II

    NASA Astrophysics Data System (ADS)

    Bolzoni, Paolo; Moch, Sven-Olaf; Somogyi, Gábor; Trócsányi, Zoltán

    2009-08-01

    We present analytic expressions of all integrals required to complete the explicit evaluation of the real-virtual integrated counterterms needed to define a recently proposed subtraction scheme for jet cross sections at next-to-next-to-leading order in QCD. We use the Mellin-Barnes representation of these integrals in 4 - 2epsilon dimensions to obtain the coefficients of their Laurent expansions around epsilon = 0. These coefficients are given by linear combinations of multidimensional Mellin-Barnes integrals. We compute the coefficients of such expansions in epsilon both numerically and analytically by complex integration over the Mellin-Barnes contours.

  12. Static penetration resistance of soils

    NASA Technical Reports Server (NTRS)

    Durgunoglu, H. T.; Mitchell, J. K.

    1973-01-01

    Model test results were used to define the failure mechanism associated with the static penetration resistance of cohesionless and low-cohesion soils. Knowledge of this mechanism has permitted the development of a new analytical method for calculating the ultimate penetration resistance which explicitly accounts for penetrometer base apex angle and roughness, soil friction angle, and the ratio of penetration depth to base width. Curves relating the bearing capacity factors to the soil friction angle are presented for failure in general shear. Strength parameters and penetrometer interaction properties of a fine sand were determined and used as the basis for prediction of the penetration resistance encountered by wedge, cone, and flat-ended penetrometers of different surface roughness using the proposed analytical method. Because of the close agreement between predicted values and values measured in laboratory tests, it appears possible to deduce in-situ soil strength parameters and their variation with depth from the results of static penetration tests.

  13. Scaling and intermittency in incoherent α-shear dynamo

    NASA Astrophysics Data System (ADS)

    Mitra, Dhrubaditya; Brandenburg, Axel

    2012-03-01

    We consider mean-field dynamo models with fluctuating α effect, both with and without large-scale shear. The α effect is chosen to be Gaussian white noise with zero mean and a given covariance. In the presence of shear, we show analytically that (in infinitely large domains) the mean-squared magnetic field shows exponential growth. The growth rate of the fastest growing mode is proportional to the shear rate. This result agrees with earlier numerical results of Yousef et al. and the recent analytical treatment by Heinemann, McWilliams & Schekochihin who use a method different from ours. In the absence of shear, an incoherent α2 dynamo may also be possible. We further show by explicit calculation of the growth rate of third- and fourth-order moments of the magnetic field that the probability density function of the mean magnetic field generated by this dynamo is non-Gaussian.

  14. Polymorphic Evolutionary Games.

    PubMed

    Fishman, Michael A

    2016-06-07

    In this paper, I present an analytical framework for polymorphic evolutionary games suitable for explicitly modeling evolutionary processes in diploid populations with sexual reproduction. The principal aspect of the proposed approach is adding diploid genetics cum sexual recombination to a traditional evolutionary game, and switching from phenotypes to haplotypes as the new game׳s pure strategies. Here, the relevant pure strategy׳s payoffs derived by summing the payoffs of all the phenotypes capable of producing gametes containing that particular haplotype weighted by the pertinent probabilities. The resulting game is structurally identical to the familiar Evolutionary Games with non-linear pure strategy payoffs (Hofbauer and Sigmund, 1998. Cambridge University Press), and can be analyzed in terms of an established analytical framework for such games. And these results can be translated into the terms of genotypic, and whence, phenotypic evolutionary stability pertinent to the original game. Copyright © 2016 Elsevier Ltd. All rights reserved.

  15. A histogram-free multicanonical Monte Carlo algorithm for the construction of analytical density of states

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

    Eisenbach, Markus; Li, Ying Wai

    We report a new multicanonical Monte Carlo (MC) algorithm to obtain the density of states (DOS) for physical systems with continuous state variables in statistical mechanics. Our algorithm is able to obtain an analytical form for the DOS expressed in a chosen basis set, instead of a numerical array of finite resolution as in previous variants of this class of MC methods such as the multicanonical (MUCA) sampling and Wang-Landau (WL) sampling. This is enabled by storing the visited states directly in a data set and avoiding the explicit collection of a histogram. This practice also has the advantage ofmore » avoiding undesirable artificial errors caused by the discretization and binning of continuous state variables. Our results show that this scheme is capable of obtaining converged results with a much reduced number of Monte Carlo steps, leading to a significant speedup over existing algorithms.« less

  16. Solving time-dependent two-dimensional eddy current problems

    NASA Technical Reports Server (NTRS)

    Lee, Min Eig; Hariharan, S. I.; Ida, Nathan

    1988-01-01

    Results of transient eddy current calculations are reported. For simplicity, a two-dimensional transverse magnetic field which is incident on an infinitely long conductor is considered. The conductor is assumed to be a good but not perfect conductor. The resulting problem is an interface initial boundary value problem with the boundary of the conductor being the interface. A finite difference method is used to march the solution explicitly in time. The method is shown. Treatment of appropriate radiation conditions is given special consideration. Results are validated with approximate analytic solutions. Two stringent test cases of high and low frequency incident waves are considered to validate the results.

  17. Dynamic Investigation of Static Divergence: Analysis and Testing

    NASA Technical Reports Server (NTRS)

    Heeg, Jennifer

    2000-01-01

    The phenomenon known as aeroelastic divergence is the focus of this work. The analyses and experiment presented here show that divergence can occur without a structural dynamic mode losing its oscillatory nature. Aeroelastic divergence occurs when the structural restorative capability or stiffness of a structure is overwhelmed by the static aerodynamic moment. This static aeroelastic coupling does not require the structural dynamic system behavior to cease, however. Aeroelastic changes in the dynamic mode behavior are governed not only by the stiffness, but by damping and inertial properties. The work presented here supports these fundamental assertions by examining a simple system: a typical section airfoil with only a rotational structural degree of freedom. Analytical results identified configurations that exhibit different types of dynamic mode behavior as the system encounters divergence. A wind tunnel model was designed and tested to examine divergence experimentally. The experimental results validate the analytical calculations and explicitly examine the divergence phenomenon where the dynamic mode persists. Three configurations of the wind tunnel model were tested. The experimental results agree very well with the analytical predictions of subcritical characteristics, divergence velocity, and behavior of the noncritical dynamic mode at divergence.

  18. Shock-induced solitary waves in granular crystals.

    PubMed

    Hasan, M Arif; Nemat-Nasser, Sia

    2018-02-01

    Solitary waves (SWs) are generated in monoatomic (homogeneous) lightly contacting spherical granules by an applied input force of any time-variation and intensity. We consider finite duration shock loads on one-dimensional arrays of granules and focus on the transition regime that leads to the formation of SWs. Based on geometrical and material properties of the granules and the properties of the input shock, we provide explicit analytic expressions to calculate the peak value of the compressive contact force at each contact point in the transition regime that precedes the formation of a primary solitary wave. We also provide explicit expressions to estimate the number of granules involved in the transition regime and show its dependence on the characteristics of the input shock and material/geometrical properties of the interacting granules. Finally, we assess the accuracy of our theoretical results by comparing them with those obtained through numerical integration of the equations of motion.

  19. Performance analysis of junctionless double gate VeSFET considering the effects of thermal variation - An explicit 2D analytical model

    NASA Astrophysics Data System (ADS)

    Chaudhary, Tarun; Khanna, Gargi

    2017-03-01

    The purpose of this paper is to explore junctionless double gate vertical slit field effect transistor (JLDG VeSFET) with reduced short channel effects and to develop an analytical threshold voltage model for the device considering the impact of thermal variations for the very first time. The model has been derived by solving 2D Poisson's equation and the effects of variation in temperature on various electrical parameters of the device such as Rout, drain current, mobility, subthreshold slope and DIBL has been studied and described in the paper. The model provides a deep physical insight of the device behavior and is also very helpful in contributing to the design space exploration for JLDG VeSFET. The proposed model is verified with simulative analysis at different radii of the device and it has been observed that there is a good agreement between the analytical model and simulation results.

  20. Scattering of In-Plane Waves by Elastic Wedges

    NASA Astrophysics Data System (ADS)

    Mohammadi, K.; Asimaki, D.; Fradkin, L.

    2014-12-01

    The scattering of seismic waves by elastic wedges has been a topic of interest in seismology and geophysics for many decades. Analytical, semi-analytical, experimental and numerical studies on idealized wedges have provided insight into the seismic behavior of continental margins, mountain roots and crustal discontinuities. Published results, however, have almost exclusively focused on incident Rayleigh waves and out-of-plane body (SH) waves. Complementing the existing body of work, we here present results from our study on the res­ponse of elastic wedges to incident P or SV waves, an idealized pro­blem that can provide valuable insight to the understanding and parameterization of topographic ampli­fication of seismic ground mo­tion. We first show our earlier work on explicit finite difference simulations of SV-wave scattering by elastic wedges over a wide range of internal angles. We next present a semi-analytical solution that we developed using the approach proposed by Gautesen, to describe the scattered wavefield in the immediate vicinity of the wedge's tip (near-field). We use the semi-analytical solution to validate the numerical analyses, and improve resolution of the amplification factor at the wedge vertex that spikes when the internal wedge angle approaches the critical angle of incidence.

  1. SOMFlow: Guided Exploratory Cluster Analysis with Self-Organizing Maps and Analytic Provenance.

    PubMed

    Sacha, Dominik; Kraus, Matthias; Bernard, Jurgen; Behrisch, Michael; Schreck, Tobias; Asano, Yuki; Keim, Daniel A

    2018-01-01

    Clustering is a core building block for data analysis, aiming to extract otherwise hidden structures and relations from raw datasets, such as particular groups that can be effectively related, compared, and interpreted. A plethora of visual-interactive cluster analysis techniques has been proposed to date, however, arriving at useful clusterings often requires several rounds of user interactions to fine-tune the data preprocessing and algorithms. We present a multi-stage Visual Analytics (VA) approach for iterative cluster refinement together with an implementation (SOMFlow) that uses Self-Organizing Maps (SOM) to analyze time series data. It supports exploration by offering the analyst a visual platform to analyze intermediate results, adapt the underlying computations, iteratively partition the data, and to reflect previous analytical activities. The history of previous decisions is explicitly visualized within a flow graph, allowing to compare earlier cluster refinements and to explore relations. We further leverage quality and interestingness measures to guide the analyst in the discovery of useful patterns, relations, and data partitions. We conducted two pair analytics experiments together with a subject matter expert in speech intonation research to demonstrate that the approach is effective for interactive data analysis, supporting enhanced understanding of clustering results as well as the interactive process itself.

  2. Potential profile near singularity point in kinetic Tonks-Langmuir discharges as a function of the ion sources temperature

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

    Kos, L.; Tskhakaya, D. D.; Jelic, N.

    2011-05-15

    A plasma-sheath transition analysis requires a reliable mathematical expression for the plasma potential profile {Phi}(x) near the sheath edge x{sub s} in the limit {epsilon}{identical_to}{lambda}{sub D}/l=0 (where {lambda}{sub D} is the Debye length and l is a proper characteristic length of the discharge). Such expressions have been explicitly calculated for the fluid model and the singular (cold ion source) kinetic model, where exact analytic solutions for plasma equation ({epsilon}=0) are known, but not for the regular (warm ion source) kinetic model, where no analytic solution of the plasma equation has ever been obtained. For the latter case, Riemann [J. Phys.more » D: Appl. Phys. 24, 493 (1991)] only predicted a general formula assuming relatively high ion-source temperatures, i.e., much higher than the plasma-sheath potential drop. Riemann's formula, however, according to him, never was confirmed in explicit solutions of particular models (e.g., that of Bissell and Johnson [Phys. Fluids 30, 779 (1987)] and Scheuer and Emmert [Phys. Fluids 31, 3645 (1988)]) since ''the accuracy of the classical solutions is not sufficient to analyze the sheath vicinity''[Riemann, in Proceedings of the 62nd Annual Gaseous Electronic Conference, APS Meeting Abstracts, Vol. 54 (APS, 2009)]. Therefore, for many years, there has been a need for explicit calculation that might confirm the Riemann's general formula regarding the potential profile at the sheath edge in the cases of regular very warm ion sources. Fortunately, now we are able to achieve a very high accuracy of results [see, e.g., Kos et al., Phys. Plasmas 16, 093503 (2009)]. We perform this task by using both the analytic and the numerical method with explicit Maxwellian and ''water-bag'' ion source velocity distributions. We find the potential profile near the plasma-sheath edge in the whole range of ion source temperatures of general interest to plasma physics, from zero to ''practical infinity.'' While within limits of ''very low'' and ''relatively high'' ion source temperatures, the potential is proportional to the space coordinate powered by rational numbers {alpha}=1/2 and {alpha}=2/3, with medium ion source temperatures. We found {alpha} between these values being a non-rational number strongly dependent on the ion source temperature. The range of the non-rational power-law turns out to be a very narrow one, at the expense of the extension of {alpha}=2/3 region towards unexpectedly low ion source temperatures.« less

  3. A Fractal Permeability Model for Shale Oil Reservoir

    NASA Astrophysics Data System (ADS)

    Zhang, Tao; Dong, Mingzhe; Li, Yajun

    2018-01-01

    In this work, a fractal analytical model is proposed to predict the permeability of shale reservoir. The proposed model explicitly relates the permeability to the micro-structural parameters (tortuosity, pore area fractal dimensions, porosity and slip velocity coefficient) of shale.

  4. Predicted range expansion of Chinese tallow tree (Triadica sebifera) in forestlands of the southern United States

    Treesearch

    Hsiao-Hsuan Wang; William Grant; Todd Swannack; Jianbang Gan; William Rogers; Tomasz Koralewski; James Miller; John W. Taylor Jr.

    2011-01-01

    We present an integrated approach for predicting future range expansion of an invasive species (Chinese tallow tree) that incorporates statistical forecasting and analytical techniques within a spatially explicit, agent-based, simulation framework.

  5. Explicit formulas for effective piezoelectric coefficients of ferroelectric 0-3 composites based on effective medium theory

    NASA Astrophysics Data System (ADS)

    Wong, C. K.; Poon, Y. M.; Shin, F. G.

    2003-01-01

    Explicit formulas were derived for the effective piezoelectric stress coefficients of a 0-3 composite of ferroelectric spherical particles in a ferroelectric matrix which were then combined to give the more commonly used strain coefficients. Assuming that the elastic stiffness of the inclusion phase is sufficiently larger than that of the matrix phase, the previously derived explicit expressions for the case of a low volume concentration of inclusion particles [C. K. Wong, Y. M. Poon, and F. G. Shin, Ferroelectrics 264, 39 (2001); J. Appl. Phys. 90, 4690 (2001)] were "transformed" analytically by an effective medium theory (EMT) with appropriate approximations, to suit the case of a more concentrated suspension. Predictions of the EMT expressions were compared with the experimental values of composites of lead zirconate titanate ceramic particles dispersed in polyvinylidene fluoride and polyvinylidene fluoride-trifluoroethylene copolymer, reported by Furukawa [IEEE Trans. Electr. Insul. 24, 375 (1989)] and by Ng et al. [IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47, 1308 (2000)] respectively. Fairly good agreement was obtained. Comparisons with other predictions, including the predictions given by numerically solving the EMT scheme, were also made. It was found that the analytic and numeric EMT schemes agreed with each other very well for an inclusion of volume fraction not exceeding 60%.

  6. A simple method for finding explicit analytic transition densities of diffusion processes with general diploid selection.

    PubMed

    Song, Yun S; Steinrücken, Matthias

    2012-03-01

    The transition density function of the Wright-Fisher diffusion describes the evolution of population-wide allele frequencies over time. This function has important practical applications in population genetics, but finding an explicit formula under a general diploid selection model has remained a difficult open problem. In this article, we develop a new computational method to tackle this classic problem. Specifically, our method explicitly finds the eigenvalues and eigenfunctions of the diffusion generator associated with the Wright-Fisher diffusion with recurrent mutation and arbitrary diploid selection, thus allowing one to obtain an accurate spectral representation of the transition density function. Simplicity is one of the appealing features of our approach. Although our derivation involves somewhat advanced mathematical concepts, the resulting algorithm is quite simple and efficient, only involving standard linear algebra. Furthermore, unlike previous approaches based on perturbation, which is applicable only when the population-scaled selection coefficient is small, our method is nonperturbative and is valid for a broad range of parameter values. As a by-product of our work, we obtain the rate of convergence to the stationary distribution under mutation-selection balance.

  7. A Simple Method for Finding Explicit Analytic Transition Densities of Diffusion Processes with General Diploid Selection

    PubMed Central

    Song, Yun S.; Steinrücken, Matthias

    2012-01-01

    The transition density function of the Wright–Fisher diffusion describes the evolution of population-wide allele frequencies over time. This function has important practical applications in population genetics, but finding an explicit formula under a general diploid selection model has remained a difficult open problem. In this article, we develop a new computational method to tackle this classic problem. Specifically, our method explicitly finds the eigenvalues and eigenfunctions of the diffusion generator associated with the Wright–Fisher diffusion with recurrent mutation and arbitrary diploid selection, thus allowing one to obtain an accurate spectral representation of the transition density function. Simplicity is one of the appealing features of our approach. Although our derivation involves somewhat advanced mathematical concepts, the resulting algorithm is quite simple and efficient, only involving standard linear algebra. Furthermore, unlike previous approaches based on perturbation, which is applicable only when the population-scaled selection coefficient is small, our method is nonperturbative and is valid for a broad range of parameter values. As a by-product of our work, we obtain the rate of convergence to the stationary distribution under mutation–selection balance. PMID:22209899

  8. Shape anomaly detection under strong measurement noise: An analytical approach to adaptive thresholding

    NASA Astrophysics Data System (ADS)

    Krasichkov, Alexander S.; Grigoriev, Eugene B.; Bogachev, Mikhail I.; Nifontov, Eugene M.

    2015-10-01

    We suggest an analytical approach to the adaptive thresholding in a shape anomaly detection problem. We find an analytical expression for the distribution of the cosine similarity score between a reference shape and an observational shape hindered by strong measurement noise that depends solely on the noise level and is independent of the particular shape analyzed. The analytical treatment is also confirmed by computer simulations and shows nearly perfect agreement. Using this analytical solution, we suggest an improved shape anomaly detection approach based on adaptive thresholding. We validate the noise robustness of our approach using typical shapes of normal and pathological electrocardiogram cycles hindered by additive white noise. We show explicitly that under high noise levels our approach considerably outperforms the conventional tactic that does not take into account variations in the noise level.

  9. An Analytical State Transition Matrix for Orbits Perturbed by an Oblate Spheroid

    NASA Technical Reports Server (NTRS)

    Mueller, A. C.

    1977-01-01

    An analytical state transition matrix and its inverse, which include the short period and secular effects of the second zonal harmonic, were developed from the nonsingular PS satellite theory. The fact that the independent variable in the PS theory is not time is in no respect disadvantageous, since any explicit analytical solution must be expressed in the true or eccentric anomaly. This is shown to be the case for the simple conic matrix. The PS theory allows for a concise, accurate, and algorithmically simple state transition matrix. The improvement over the conic matrix ranges from 2 to 4 digits accuracy.

  10. Free vibration of functionally graded beams and frameworks using the dynamic stiffness method

    NASA Astrophysics Data System (ADS)

    Banerjee, J. R.; Ananthapuvirajah, A.

    2018-05-01

    The free vibration analysis of functionally graded beams (FGBs) and frameworks containing FGBs is carried out by applying the dynamic stiffness method and deriving the elements of the dynamic stiffness matrix in explicit algebraic form. The usually adopted rule that the material properties of the FGB vary continuously through the thickness according to a power law forms the fundamental basis of the governing differential equations of motion in free vibration. The differential equations are solved in closed analytical form when the free vibratory motion is harmonic. The dynamic stiffness matrix is then formulated by relating the amplitudes of forces to those of the displacements at the two ends of the beam. Next, the explicit algebraic expressions for the dynamic stiffness elements are derived with the help of symbolic computation. Finally the Wittrick-Williams algorithm is applied as solution technique to solve the free vibration problems of FGBs with uniform cross-section, stepped FGBs and frameworks consisting of FGBs. Some numerical results are validated against published results, but in the absence of published results for frameworks containing FGBs, consistency checks on the reliability of results are performed. The paper closes with discussion of results and conclusions.

  11. Regularity of Solutions of the Nonlinear Sigma Model with Gravitino

    NASA Astrophysics Data System (ADS)

    Jost, Jürgen; Keßler, Enno; Tolksdorf, Jürgen; Wu, Ruijun; Zhu, Miaomiao

    2018-02-01

    We propose a geometric setup to study analytic aspects of a variant of the super symmetric two-dimensional nonlinear sigma model. This functional extends the functional of Dirac-harmonic maps by gravitino fields. The system of Euler-Lagrange equations of the two-dimensional nonlinear sigma model with gravitino is calculated explicitly. The gravitino terms pose additional analytic difficulties to show smoothness of its weak solutions which are overcome using Rivière's regularity theory and Riesz potential theory.

  12. Measures and metrics for software development

    NASA Technical Reports Server (NTRS)

    1984-01-01

    The evaluations of and recommendations for the use of software development measures based on the practical and analytical experience of the Software Engineering Laboratory are discussed. The basic concepts of measurement and system of classification for measures are described. The principal classes of measures defined are explicit, analytic, and subjective. Some of the major software measurement schemes appearing in the literature are derived. The applications of specific measures in a production environment are explained. These applications include prediction and planning, review and assessment, and evaluation and selection.

  13. Nonlinear vibration of an axially loaded beam carrying rigid bodies

    NASA Astrophysics Data System (ADS)

    Barry, O.

    2016-12-01

    This paper investigates the nonlinear vibration due to mid-plane stretching of an axially loaded simply supported beam carrying multiple rigid masses. Explicit expressions and closed form solutions of both linear and nonlinear analysis of the present vibration problem are presented for the first time. The validity of the analytical model is demonstrated using finite element analysis and via comparison with the result in the literature. Parametric studies are conducted to examine how the nonlinear frequency and frequency response curve are affected by tension, rotational inertia, and number of intermediate rigid bodies.

  14. On the Theory of High-Power Ultrashort Pulse Propagation in Raman-Active Media

    NASA Technical Reports Server (NTRS)

    Belenov, E. M.; Isakov, V. A.; Kanavin, A. P.; Smetanin, I. V.

    1996-01-01

    The propagation of an intense femtosecond pulse in a Raman-active medium is analyzed. An analytic solution which describes in explicit form the evolution of the light pulse is derived. The field of an intense light wave undergoes a substantial transformation as the wave propagates through the medium. The nature of this transformation can change over time scales comparable to the period of the optical oscillations. As a result, the pulse of sufficiently high energy divides into stretched and compressed domains where the field decreases and increases respectively.

  15. Analytical study of robustness of a negative feedback oscillator by multiparameter sensitivity

    PubMed Central

    2014-01-01

    Background One of the distinctive features of biological oscillators such as circadian clocks and cell cycles is robustness which is the ability to resume reliable operation in the face of different types of perturbations. In the previous study, we proposed multiparameter sensitivity (MPS) as an intelligible measure for robustness to fluctuations in kinetic parameters. Analytical solutions directly connect the mechanisms and kinetic parameters to dynamic properties such as period, amplitude and their associated MPSs. Although negative feedback loops are known as common structures to biological oscillators, the analytical solutions have not been presented for a general model of negative feedback oscillators. Results We present the analytical expressions for the period, amplitude and their associated MPSs for a general model of negative feedback oscillators. The analytical solutions are validated by comparing them with numerical solutions. The analytical solutions explicitly show how the dynamic properties depend on the kinetic parameters. The ratio of a threshold to the amplitude has a strong impact on the period MPS. As the ratio approaches to one, the MPS increases, indicating that the period becomes more sensitive to changes in kinetic parameters. We present the first mathematical proof that the distributed time-delay mechanism contributes to making the oscillation period robust to parameter fluctuations. The MPS decreases with an increase in the feedback loop length (i.e., the number of molecular species constituting the feedback loop). Conclusions Since a general model of negative feedback oscillators was employed, the results shown in this paper are expected to be true for many of biological oscillators. This study strongly supports that the hypothesis that phosphorylations of clock proteins contribute to the robustness of circadian rhythms. The analytical solutions give synthetic biologists some clues to design gene oscillators with robust and desired period. PMID:25605374

  16. The PANTHER User Experience

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

    Coram, Jamie L.; Morrow, James D.; Perkins, David Nikolaus

    2015-09-01

    This document describes the PANTHER R&D Application, a proof-of-concept user interface application developed under the PANTHER Grand Challenge LDRD. The purpose of the application is to explore interaction models for graph analytics, drive algorithmic improvements from an end-user point of view, and support demonstration of PANTHER technologies to potential customers. The R&D Application implements a graph-centric interaction model that exposes analysts to the algorithms contained within the GeoGraphy graph analytics library. Users define geospatial-temporal semantic graph queries by constructing search templates based on nodes, edges, and the constraints among them. Users then analyze the results of the queries using bothmore » geo-spatial and temporal visualizations. Development of this application has made user experience an explicit driver for project and algorithmic level decisions that will affect how analysts one day make use of PANTHER technologies.« less

  17. Instability of displacement of Oldroyd-B fluid by air in a Hele-Shaw cell

    NASA Astrophysics Data System (ADS)

    Daripa, Prabir

    2014-03-01

    We study the displacement of an Oldroyd-B fluid in a Hele-Shaw cell when driven by air. In particular, we explicitly obtain an analytical expression for the growth rate of instability which depends on the relaxation and retardation (time) constants, denoted by λ, and λ1 respectively, appearing in the Oldroyd-B constitutive relations. When these two constants are zero, we recover the classical Saffman-Taylor result for a Newtonian liquid displaced by air. Our results show that this displacement process is more unstable than the case when a Newtonian fluid is displaced by air. The analytical results are plotted and compared with numerical results on this unstable displacement process available in the literature. The agreement is found to be excellent. In particular, results show that the non-Newtonian case (i.e., Oldroyd-B) is more unstable than the Newtonian case. Supported by an NPRP Grant # 08-777-1-141 from the Qatar National Research Fund (a member of the Qatar Foundation). The statements made herein are solely the responsibility of the author.

  18. Gaussian closure technique applied to the hysteretic Bouc model with non-zero mean white noise excitation

    NASA Astrophysics Data System (ADS)

    Waubke, Holger; Kasess, Christian H.

    2016-11-01

    Devices that emit structure-borne sound are commonly decoupled by elastic components to shield the environment from acoustical noise and vibrations. The elastic elements often have a hysteretic behavior that is typically neglected. In order to take hysteretic behavior into account, Bouc developed a differential equation for such materials, especially joints made of rubber or equipped with dampers. In this work, the Bouc model is solved by means of the Gaussian closure technique based on the Kolmogorov equation. Kolmogorov developed a method to derive probability density functions for arbitrary explicit first-order vector differential equations under white noise excitation using a partial differential equation of a multivariate conditional probability distribution. Up to now no analytical solution of the Kolmogorov equation in conjunction with the Bouc model exists. Therefore a wide range of approximate solutions, especially the statistical linearization, were developed. Using the Gaussian closure technique that is an approximation to the Kolmogorov equation assuming a multivariate Gaussian distribution an analytic solution is derived in this paper for the Bouc model. For the stationary case the two methods yield equivalent results, however, in contrast to statistical linearization the presented solution allows to calculate the transient behavior explicitly. Further, stationary case leads to an implicit set of equations that can be solved iteratively with a small number of iterations and without instabilities for specific parameter sets.

  19. Optimal time-domain technique for pulse width modulation in power electronics

    NASA Astrophysics Data System (ADS)

    Mayergoyz, I.; Tyagi, S.

    2018-05-01

    Optimal time-domain technique for pulse width modulation is presented. It is based on exact and explicit analytical solutions for inverter circuits, obtained for any sequence of input voltage rectangular pulses. Two optimal criteria are discussed and illustrated by numerical examples.

  20. Simple Analytic Expressions for the Magnetic Field of a Circular Current Loop

    NASA Technical Reports Server (NTRS)

    Simpson, James C.; Lane, John E.; Immer, Christopher D.; Youngquist, Robert C.

    2001-01-01

    Analytic expressions for the magnetic induction (magnetic flux density, B) of a simple planar circular current loop have been published in Cartesian and cylindrical coordinates [1,2], and are also known implicitly in spherical coordinates [3]. In this paper, we present explicit analytic expressions for B and its spatial derivatives in Cartesian, cylindrical, and spherical coordinates for a filamentary current loop. These results were obtained with extensive use of Mathematica "TM" and are exact throughout all space outside of the conductor. The field expressions reduce to the well-known limiting cases and satisfy V · B = 0 and V x B = 0 outside the conductor. These results are general and applicable to any model using filamentary circular current loops. Solenoids of arbitrary size may be easily modeled by approximating the total magnetic induction as the sum of those for the individual loops. The inclusion of the spatial derivatives expands their utility to magnetohydrodynamics where the derivatives are required. The equations can be coded into any high-level programming language. It is necessary to numerically evaluate complete elliptic integrals of the first and second kind, but this capability is now available with most programming packages.

  1. Exact solutions for the static bending of Euler-Bernoulli beams using Eringen's two-phase local/nonlocal model

    NASA Astrophysics Data System (ADS)

    Wang, Y. B.; Zhu, X. W.; Dai, H. H.

    2016-08-01

    Though widely used in modelling nano- and micro- structures, Eringen's differential model shows some inconsistencies and recent study has demonstrated its differences between the integral model, which then implies the necessity of using the latter model. In this paper, an analytical study is taken to analyze static bending of nonlocal Euler-Bernoulli beams using Eringen's two-phase local/nonlocal model. Firstly, a reduction method is proved rigorously, with which the integral equation in consideration can be reduced to a differential equation with mixed boundary value conditions. Then, the static bending problem is formulated and four types of boundary conditions with various loadings are considered. By solving the corresponding differential equations, exact solutions are obtained explicitly in all of the cases, especially for the paradoxical cantilever beam problem. Finally, asymptotic analysis of the exact solutions reveals clearly that, unlike the differential model, the integral model adopted herein has a consistent softening effect. Comparisons are also made with existing analytical and numerical results, which further shows the advantages of the analytical results obtained. Additionally, it seems that the once controversial nonlocal bar problem in the literature is well resolved by the reduction method.

  2. Non-axisymmetric local magnetostatic equilibrium

    DOE PAGES

    Candy, Jefferey M.; Belli, Emily A.

    2015-03-24

    In this study, we outline an approach to the problem of local equilibrium in non-axisymmetric configurations that adheres closely to Miller's original method for axisymmetric plasmas. Importantly, this method is novel in that it allows not only specification of 3D shape, but also explicit specification of the shear in the 3D shape. A spectrally-accurate method for solution of the resulting nonlinear partial differential equations is also developed. We verify the correctness of the spectral method, in the axisymmetric limit, through comparisons with an independent numerical solution. Some analytic results for the two-dimensional case are given, and the connection to Boozermore » coordinates is clarified.« less

  3. The Weyl-Lanczos equations and the Lanczos wave equation in four dimensions as systems in involution

    NASA Astrophysics Data System (ADS)

    Dolan, P.; Gerber, A.

    2003-07-01

    The Weyl-Lanczos equations in four dimensions form a system in involution. We compute its Cartan characters explicitly and use Janet-Riquier theory to confirm the results in the case of all space-times with a diagonal metric tensor and for the plane wave limit of space-times. We write the Lanczos wave equation as an exterior differential system and, with assistance from Janet-Riquier theory, we compute its Cartan characters and find that it forms a system in involution. We compare these Cartan characters with those of the Weyl-Lanczos equations. All results hold for the real analytic case.

  4. Cross-section fluctuations in chaotic scattering systems.

    PubMed

    Ericson, Torleif E O; Dietz, Barbara; Richter, Achim

    2016-10-01

    Exact analytical expressions for the cross-section correlation functions of chaotic scattering systems have hitherto been derived only under special conditions. The objective of the present article is to provide expressions that are applicable beyond these restrictions. The derivation is based on a statistical model of Breit-Wigner type for chaotic scattering amplitudes which has been shown to describe the exact analytical results for the scattering (S)-matrix correlation functions accurately. Our results are given in the energy and in the time representations and apply in the whole range from isolated to overlapping resonances. The S-matrix contributions to the cross-section correlations are obtained in terms of explicit irreducible and reducible correlation functions. Consequently, the model can be used for a detailed exploration of the key features of the cross-section correlations and the underlying physical mechanisms. In the region of isolated resonances, the cross-section correlations contain a dominant contribution from the self-correlation term. For narrow states the self-correlations originate predominantly from widely spaced states with exceptionally large partial width. In the asymptotic region of well-overlapping resonances, the cross-section autocorrelation functions are given in terms of the S-matrix autocorrelation functions. For inelastic correlations, in particular, the Ericson fluctuations rapidly dominate in that region. Agreement with known analytical and experimental results is excellent.

  5. Virtual photon impact factors with exact gluon kinematics

    NASA Astrophysics Data System (ADS)

    Bialas, A.; Navelet, H.; Peschanski, R.

    2001-06-01

    An explicit analytic formula for the transverse and longitudinal impact factors ST, L( N, γ) of the photon using kT factorization with exact gluon kinematics is given. Applications to the QCD dipole model and the extraction of the unintegrated gluon structure function from data are proposed.

  6. Following a trend with an exponential moving average: Analytical results for a Gaussian model

    NASA Astrophysics Data System (ADS)

    Grebenkov, Denis S.; Serror, Jeremy

    2014-01-01

    We investigate how price variations of a stock are transformed into profits and losses (P&Ls) of a trend following strategy. In the frame of a Gaussian model, we derive the probability distribution of P&Ls and analyze its moments (mean, variance, skewness and kurtosis) and asymptotic behavior (quantiles). We show that the asymmetry of the distribution (with often small losses and less frequent but significant profits) is reminiscent to trend following strategies and less dependent on peculiarities of price variations. At short times, trend following strategies admit larger losses than one may anticipate from standard Gaussian estimates, while smaller losses are ensured at longer times. Simple explicit formulas characterizing the distribution of P&Ls illustrate the basic mechanisms of momentum trading, while general matrix representations can be applied to arbitrary Gaussian models. We also compute explicitly annualized risk adjusted P&L and strategy turnover to account for transaction costs. We deduce the trend following optimal timescale and its dependence on both auto-correlation level and transaction costs. Theoretical results are illustrated on the Dow Jones index.

  7. Alternative Stable States, Coral Reefs, and Smooth Dynamics with a Kick.

    PubMed

    Ippolito, Stephen; Naudot, Vincent; Noonburg, Erik G

    2016-03-01

    We consider a computer simulation, which was found to be faithful to time series data for Caribbean coral reefs, and an analytical model to help understand the dynamics of the simulation. The analytical model is a system of ordinary differential equations (ODE), and the authors claim this model demonstrates the existence of alternative stable states. The existence of an alternative stable state should consider a sudden shift in coral and macroalgae populations, while the grazing rate remains constant. The results of such shifts, however, are often confounded by changes in grazing rate. Although the ODE suggest alternative stable states, the ODE need modification to explicitly account for shifts or discrete events such as hurricanes. The goal of this paper will be to study the simulation dynamics through a simplified analytical representation. We proceed by modifying the original analytical model through incorporating discrete changes into the ODE. We then analyze the resulting dynamics and their bifurcations with respect to changes in grazing rate and hurricane frequency. In particular, a "kick" enabling the ODE to consider impulse events is added. Beyond adding a "kick" we employ the grazing function that is suggested by the simulation. The extended model was fit to the simulation data to support its use and predicts the existence cycles depending nonlinearly on grazing rates and hurricane frequency. These cycles may bring new insights into consideration for reef health, restoration and dynamics.

  8. Investigation of the feasibility of an analytical method of accounting for the effects of atmospheric drag on satellite motion

    NASA Technical Reports Server (NTRS)

    Bozeman, Robert E.

    1987-01-01

    An analytic technique for accounting for the joint effects of Earth oblateness and atmospheric drag on close-Earth satellites is investigated. The technique is analytic in the sense that explicit solutions to the Lagrange planetary equations are given; consequently, no numerical integrations are required in the solution process. The atmospheric density in the technique described is represented by a rotating spherical exponential model with superposed effects of the oblate atmosphere and the diurnal variations. A computer program implementing the process is discussed and sample output is compared with output from program NSEP (Numerical Satellite Ephemeris Program). NSEP uses a numerical integration technique to account for atmospheric drag effects.

  9. Incorporating nuclear vibrational energies into the "atom in molecules" analysis: An analytical study

    NASA Astrophysics Data System (ADS)

    Gharabaghi, Masumeh; Shahbazian, Shant

    2017-04-01

    The quantum theory of atoms in molecules (QTAIM) is based on the clamped nucleus paradigm and solely working with the electronic wavefunctions, so does not include nuclear vibrations in the AIM analysis. On the other hand, the recently extended version of the QTAIM, called the multi-component QTAIM (MC-QTAIM), incorporates both electrons and quantum nuclei, i.e., those nuclei treated as quantum waves instead of clamped point charges, into the AIM analysis using non-adiabatic wavefunctions. Thus, the MC-QTAIM is the natural framework to incorporate the role of nuclear vibrations into the AIM analysis. In this study, within the context of the MC-QTAIM, the formalism of including nuclear vibrational energy in the atomic basin energy is developed in detail and its contribution is derived analytically using the recently proposed non-adiabatic Hartree product nuclear wavefunction. It is demonstrated that within the context of this wavefunction, the quantum nuclei may be conceived pseudo-adiabatically as quantum oscillators and both isotropic harmonic and anisotropic anharmonic oscillator models are used to compute the zero-point nuclear vibrational energy contribution to the basin energies explicitly. Inspired by the results gained within the context of the MC-QTAIM analysis, a heuristic approach is proposed within the context of the QTAIM to include nuclear vibrational energy in the basin energy from the vibrational wavefunction derived adiabatically. The explicit calculation of the basin contribution of the zero-point vibrational energy using the uncoupled harmonic oscillator model leads to results consistent with those derived from the MC-QTAIM.

  10. Modelling the dynamics of a minimal protocell container

    NASA Astrophysics Data System (ADS)

    Nilsson Jacobi, Martin; Rasmussen, Steen; Tunstrøm, Kolbjørn

    2005-01-01

    This paper is a discussion on how reaction kinetics and three-dimensional (3D) lattice simulations can be used to elucidate the dynamical properties of micelles as a possible minimal protocell container. We start with a general discussion on the role of molecular self-assembly in prebiotic and contemporary biological systems. A simple reaction kinetic model of a micellation process of amphiphilic molecules in water is then presented and solved analytically. Amphiphilic molecules are polymers with hydrophobic (water-fearing), e.g. hydrocarbon tail groups, and hydrophilic (water-loving) head groups, e.g. fatty acids. By making a few simplifying assumptions an analytical expression for the size distribution of the resulting micelles can be derived. The main part of the paper presents and discusses a lattice gas technique for a more detailed 3D simulation of molecular self-assembly of amphiphilic polymers in aqueous environments. Water molecules, hydrocarbon tail groups and hydrophilic head groups are explicitly represented on a three-dimensional discrete lattice. Molecules move on the lattice proportional to their continuous momentum. Collision rules preserve momentum and kinetic energy. Potential energy from molecular interactions are also included explicitly. The non-trivial thermodynamics of large-scale and long-time dynamics are studied. In this paper we specifically demonstrate how, from a random initial distribution, micelles are formed and grow until they destabilize and can divide. Eventually a steady state of growing and dividing micelles is formed. Towards the end of the paper we discuss the relevance of the presented results to the design of a minimal artificial protocell.

  11. Incorporating nuclear vibrational energies into the "atom in molecules" analysis: An analytical study.

    PubMed

    Gharabaghi, Masumeh; Shahbazian, Shant

    2017-04-21

    The quantum theory of atoms in molecules (QTAIM) is based on the clamped nucleus paradigm and solely working with the electronic wavefunctions, so does not include nuclear vibrations in the AIM analysis. On the other hand, the recently extended version of the QTAIM, called the multi-component QTAIM (MC-QTAIM), incorporates both electrons and quantum nuclei, i.e., those nuclei treated as quantum waves instead of clamped point charges, into the AIM analysis using non-adiabatic wavefunctions. Thus, the MC-QTAIM is the natural framework to incorporate the role of nuclear vibrations into the AIM analysis. In this study, within the context of the MC-QTAIM, the formalism of including nuclear vibrational energy in the atomic basin energy is developed in detail and its contribution is derived analytically using the recently proposed non-adiabatic Hartree product nuclear wavefunction. It is demonstrated that within the context of this wavefunction, the quantum nuclei may be conceived pseudo-adiabatically as quantum oscillators and both isotropic harmonic and anisotropic anharmonic oscillator models are used to compute the zero-point nuclear vibrational energy contribution to the basin energies explicitly. Inspired by the results gained within the context of the MC-QTAIM analysis, a heuristic approach is proposed within the context of the QTAIM to include nuclear vibrational energy in the basin energy from the vibrational wavefunction derived adiabatically. The explicit calculation of the basin contribution of the zero-point vibrational energy using the uncoupled harmonic oscillator model leads to results consistent with those derived from the MC-QTAIM.

  12. Clustering coefficients of protein-protein interaction networks

    NASA Astrophysics Data System (ADS)

    Miller, Gerald A.; Shi, Yi Y.; Qian, Hong; Bomsztyk, Karol

    2007-05-01

    The properties of certain networks are determined by hidden variables that are not explicitly measured. The conditional probability (propagator) that a vertex with a given value of the hidden variable is connected to k other vertices determines all measurable properties. We study hidden variable models and find an averaging approximation that enables us to obtain a general analytical result for the propagator. Analytic results showing the validity of the approximation are obtained. We apply hidden variable models to protein-protein interaction networks (PINs) in which the hidden variable is the association free energy, determined by distributions that depend on biochemistry and evolution. We compute degree distributions as well as clustering coefficients of several PINs of different species; good agreement with measured data is obtained. For the human interactome two different parameter sets give the same degree distributions, but the computed clustering coefficients differ by a factor of about 2. This shows that degree distributions are not sufficient to determine the properties of PINs.

  13. Chandrasekhar's dynamical friction and non-extensive statistics

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

    Silva, J.M.; Lima, J.A.S.; De Souza, R.E.

    2016-05-01

    The motion of a point like object of mass M passing through the background potential of massive collisionless particles ( m || M ) suffers a steady deceleration named dynamical friction. In his classical work, Chandrasekhar assumed a Maxwellian velocity distribution in the halo and neglected the self gravity of the wake induced by the gravitational focusing of the mass M . In this paper, by relaxing the validity of the Maxwellian distribution due to the presence of long range forces, we derive an analytical formula for the dynamical friction in the context of the q -nonextensive kinetic theory. Inmore » the extensive limiting case ( q = 1), the classical Gaussian Chandrasekhar result is recovered. As an application, the dynamical friction timescale for Globular Clusters spiraling to the galactic center is explicitly obtained. Our results suggest that the problem concerning the large timescale as derived by numerical N -body simulations or semi-analytical models can be understood as a departure from the standard extensive Maxwellian regime as measured by the Tsallis nonextensive q -parameter.« less

  14. Generalized analytical solutions to sequentially coupled multi-species advective-dispersive transport equations in a finite domain subject to an arbitrary time-dependent source boundary condition

    NASA Astrophysics Data System (ADS)

    Chen, Jui-Sheng; Liu, Chen-Wuing; Liang, Ching-Ping; Lai, Keng-Hsin

    2012-08-01

    SummaryMulti-species advective-dispersive transport equations sequentially coupled with first-order decay reactions are widely used to describe the transport and fate of the decay chain contaminants such as radionuclide, chlorinated solvents, and nitrogen. Although researchers attempted to present various types of methods for analytically solving this transport equation system, the currently available solutions are mostly limited to an infinite or a semi-infinite domain. A generalized analytical solution for the coupled multi-species transport problem in a finite domain associated with an arbitrary time-dependent source boundary is not available in the published literature. In this study, we first derive generalized analytical solutions for this transport problem in a finite domain involving arbitrary number of species subject to an arbitrary time-dependent source boundary. Subsequently, we adopt these derived generalized analytical solutions to obtain explicit analytical solutions for a special-case transport scenario involving an exponentially decaying Bateman type time-dependent source boundary. We test the derived special-case solutions against the previously published coupled 4-species transport solution and the corresponding numerical solution with coupled 10-species transport to conduct the solution verification. Finally, we compare the new analytical solutions derived for a finite domain against the published analytical solutions derived for a semi-infinite domain to illustrate the effect of the exit boundary condition on coupled multi-species transport with an exponential decaying source boundary. The results show noticeable discrepancies between the breakthrough curves of all the species in the immediate vicinity of the exit boundary obtained from the analytical solutions for a finite domain and a semi-infinite domain for the dispersion-dominated condition.

  15. Analytical study of exact solutions of the nonlinear Korteweg-de Vries equation with space-time fractional derivatives

    NASA Astrophysics Data System (ADS)

    Liu, Jiangen; Zhang, Yufeng

    2018-01-01

    This paper gives an analytical study of dynamic behavior of the exact solutions of nonlinear Korteweg-de Vries equation with space-time local fractional derivatives. By using the improved (G‧ G )-expansion method, the explicit traveling wave solutions including periodic solutions, dark soliton solutions, soliton solutions and soliton-like solutions, are obtained for the first time. They can better help us further understand the physical phenomena and provide a strong basis. Meanwhile, some solutions are presented through 3D-graphs.

  16. Analytical modeling of soliton interactions in a nonlocal nonlinear medium analogous to gravitational force

    NASA Astrophysics Data System (ADS)

    Zeng, Shihao; Chen, Manna; Zhang, Ting; Hu, Wei; Guo, Qi; Lu, Daquan

    2018-01-01

    We illuminate an analytical model of soliton interactions in lead glass by analogizing to a gravitational force system. The orbits of spiraling solitons under a long-range interaction are given explicitly and demonstrated to follow Newton's second law of motion and the Binet equation by numerical simulations. The condition for circular orbits is obtained and the oscillating orbits are proved not to be closed. We prove the analogy between the nonlocal nonlinear optical system and gravitational system and specify the quantitative relation of the quantity between the two models.

  17. Hill Problem Analytical Theory to the Order Four. Application to the Computation of Frozen Orbits around Planetary Satellites

    NASA Technical Reports Server (NTRS)

    Lara, Martin; Palacian, Jesus F.

    2007-01-01

    Frozen orbits of the Hill problem are determined in the double averaged problem, where short and long period terms are removed by means of Lie transforms. The computation of initial conditions of corresponding quasi periodic solutions in the non-averaged problem is straightforward for the perturbation method used provides the explicit equations of the transformation that connects the averaged and non-averaged models. A fourth order analytical theory reveals necessary for the accurate computation of quasi periodic, frozen orbits.

  18. The areal reduction factor: A new analytical expression for the Lazio Region in central Italy

    NASA Astrophysics Data System (ADS)

    Mineo, C.; Ridolfi, E.; Napolitano, F.; Russo, F.

    2018-05-01

    For the study and modeling of hydrological phenomena, both in urban and rural areas, a proper estimation of the areal reduction factor (ARF) is crucial. In this paper, we estimated the ARF from observed rainfall data as the ratio between the average rainfall occurring in a specific area and the point rainfall. Then, we compared the obtained ARF values with some of the most widespread empirical approaches in literature which are used when rainfall observations are not available. Results highlight that the literature formulations can lead to a substantial over- or underestimation of the ARF estimated from observed data. These findings can have severe consequences, especially in the design of hydraulic structures where empirical formulations are extensively applied. The aim of this paper is to present a new analytical relationship with an explicit dependence on the rainfall duration and area that can better represent the ARF-area trend over the area case of study. The analytical curve presented here can find an important application to estimate the ARF values for design purposes. The test study area is the Lazio Region (central Italy).

  19. High-order moments of spin-orbit energy in a multielectron configuration

    NASA Astrophysics Data System (ADS)

    Na, Xieyu; Poirier, M.

    2016-07-01

    In order to analyze the energy-level distribution in complex ions such as those found in warm dense plasmas, this paper provides values for high-order moments of the spin-orbit energy in a multielectron configuration. Using second-quantization results and standard angular algebra or fully analytical expressions, explicit values are given for moments up to 10th order for the spin-orbit energy. Two analytical methods are proposed, using the uncoupled or coupled orbital and spin angular momenta. The case of multiple open subshells is considered with the help of cumulants. The proposed expressions for spin-orbit energy moments are compared to numerical computations from Cowan's code and agree with them. The convergence of the Gram-Charlier expansion involving these spin-orbit moments is analyzed. While a spectrum with infinitely thin components cannot be adequately represented by such an expansion, a suitable convolution procedure ensures the convergence of the Gram-Charlier series provided high-order terms are accounted for. A corrected analytical formula for the third-order moment involving both spin-orbit and electron-electron interactions turns out to be in fair agreement with Cowan's numerical computations.

  20. The Legal Recognition of Sign Languages

    ERIC Educational Resources Information Center

    De Meulder, Maartje

    2015-01-01

    This article provides an analytical overview of the different types of explicit legal recognition of sign languages. Five categories are distinguished: constitutional recognition, recognition by means of general language legislation, recognition by means of a sign language law or act, recognition by means of a sign language law or act including…

  1. CTE method and interaction solutions for the Kadomtsev-Petviashvili equation

    NASA Astrophysics Data System (ADS)

    Ren, Bo

    2017-02-01

    The consistent tanh expansion method is applied to the Kadomtsev-Petviashvili equation. The interaction solutions among one soliton and other types of solitary waves, such as multiple resonant soliton solutions and cnoidal waves, are explicitly given. Some special concrete interaction solutions are discussed both in analytical and graphical ways.

  2. Influence of Familiar Features on Diagnosis: Instantiated Features in an Applied Setting

    ERIC Educational Resources Information Center

    Dore, Kelly L.; Brooks, Lee R.; Weaver, Bruce; Norman, Geoffrey R.

    2012-01-01

    Medical diagnosis can be viewed as a categorization task. There are two mechanisms whereby humans make categorical judgments: "analytical reasoning," based on explicit consideration of features and "nonanalytical reasoning," an unconscious holistic process of matching against prior exemplars. However, there is evidence that prior experience can…

  3. Knowing English Grammar--An Important Aid in Second Language Learning

    ERIC Educational Resources Information Center

    Cleary, Colin

    2004-01-01

    This article discusses a small-scale study that explored students', teachers', and university lecturers' beliefs about the value of studying English grammar in foreign and second language learning. A major debate in second language acquisition literature has been concerned with experiential (implicit) learning as opposed to analytical (explicit)…

  4. Completeness of the Coulomb Wave Functions in Quantum Mechanics

    ERIC Educational Resources Information Center

    Mukunda, N.

    1978-01-01

    Gives an explicit and elementary proof that the radial energy eigenfunctions for the hydrogen atom in quantum mechanics, bound and scattering states included, form a complete set. The proof uses some properties of the confluent hypergeometric functions and the Cauchy residue theorem from analytic function theory. (Author/GA)

  5. Transnationalisation within School Education:The Interconnection between Actors, Structures and Mechanisms

    ERIC Educational Resources Information Center

    Schneider, Claudia

    2017-01-01

    The current literature of school education, transnationalisation and migration explores actors, structures and social mechanisms, however, tends to focus on these analytical levels separately. This article advocates a more explicit analysis of the interconnections of structures, actors and mechanisms within and across schools and wider national…

  6. Joint multifractal analysis based on the partition function approach: analytical analysis, numerical simulation and empirical application

    NASA Astrophysics Data System (ADS)

    Xie, Wen-Jie; Jiang, Zhi-Qiang; Gu, Gao-Feng; Xiong, Xiong; Zhou, Wei-Xing

    2015-10-01

    Many complex systems generate multifractal time series which are long-range cross-correlated. Numerous methods have been proposed to characterize the multifractal nature of these long-range cross correlations. However, several important issues about these methods are not well understood and most methods consider only one moment order. We study the joint multifractal analysis based on partition function with two moment orders, which was initially invented to investigate fluid fields, and derive analytically several important properties. We apply the method numerically to binomial measures with multifractal cross correlations and bivariate fractional Brownian motions without multifractal cross correlations. For binomial multifractal measures, the explicit expressions of mass function, singularity strength and multifractal spectrum of the cross correlations are derived, which agree excellently with the numerical results. We also apply the method to stock market indexes and unveil intriguing multifractality in the cross correlations of index volatilities.

  7. Form of prior for constrained thermodynamic processes with uncertainty

    NASA Astrophysics Data System (ADS)

    Aneja, Preety; Johal, Ramandeep S.

    2015-05-01

    We consider the quasi-static thermodynamic processes with constraints, but with additional uncertainty about the control parameters. Motivated by inductive reasoning, we assign prior distribution that provides a rational guess about likely values of the uncertain parameters. The priors are derived explicitly for both the entropy-conserving and the energy-conserving processes. The proposed form is useful when the constraint equation cannot be treated analytically. The inference is performed using spin-1/2 systems as models for heat reservoirs. Analytical results are derived in the high-temperatures limit. An agreement beyond linear response is found between the estimates of thermal quantities and their optimal values obtained from extremum principles. We also seek an intuitive interpretation for the prior and the estimated value of temperature obtained therefrom. We find that the prior over temperature becomes uniform over the quantity kept conserved in the process.

  8. Anti-plane eigenstrain problem of an inclusion of arbitrary shape in an anisotropic bimaterial with a semi-infinite interface crack

    NASA Astrophysics Data System (ADS)

    Wang, Xu; Schiavone, Peter

    2018-02-01

    We consider an Eshelby inclusion of arbitrary shape with uniform anti-plane eigenstrains embedded in one of two bonded dissimilar anisotropic half planes containing a semi-infinite interface crack situated along the negative real axis. Using two consecutive conformal mappings, the upper and lower halves of the physical plane are first mapped onto two separate quarters of the image plane. The corresponding boundary value problem is then analyzed in this image plane rather than in the original physical plane. Corresponding analytic functions in all three phases of the composite are derived via the construction of an auxiliary function and repeated application of analytic continuation across the real and imaginary axes in the image plane. As a result, the local stress intensity factor is then obtained explicitly. Perhaps most interestingly, we find that the satisfaction of a particular condition makes the inclusion (stress) invisible to the crack.

  9. A spatially explicit model for an Allee effect: why wolves recolonize so slowly in Greater Yellowstone.

    PubMed

    Hurford, Amy; Hebblewhite, Mark; Lewis, Mark A

    2006-11-01

    A reduced probability of finding mates at low densities is a frequently hypothesized mechanism for a component Allee effect. At low densities dispersers are less likely to find mates and establish new breeding units. However, many mathematical models for an Allee effect do not make a distinction between breeding group establishment and subsequent population growth. Our objective is to derive a spatially explicit mathematical model, where dispersers have a reduced probability of finding mates at low densities, and parameterize the model for wolf recolonization in the Greater Yellowstone Ecosystem (GYE). In this model, only the probability of establishing new breeding units is influenced by the reduced probability of finding mates at low densities. We analytically and numerically solve the model to determine the effect of a decreased probability in finding mates at low densities on population spread rate and density. Our results suggest that a reduced probability of finding mates at low densities may slow recolonization rate.

  10. Complex dynamics of memristive circuits: Analytical results and universal slow relaxation

    NASA Astrophysics Data System (ADS)

    Caravelli, F.; Traversa, F. L.; Di Ventra, M.

    2017-02-01

    Networks with memristive elements (resistors with memory) are being explored for a variety of applications ranging from unconventional computing to models of the brain. However, analytical results that highlight the role of the graph connectivity on the memory dynamics are still few, thus limiting our understanding of these important dynamical systems. In this paper, we derive an exact matrix equation of motion that takes into account all the network constraints of a purely memristive circuit, and we employ it to derive analytical results regarding its relaxation properties. We are able to describe the memory evolution in terms of orthogonal projection operators onto the subspace of fundamental loop space of the underlying circuit. This orthogonal projection explicitly reveals the coupling between the spatial and temporal sectors of the memristive circuits and compactly describes the circuit topology. For the case of disordered graphs, we are able to explain the emergence of a power-law relaxation as a superposition of exponential relaxation times with a broad range of scales using random matrices. This power law is also universal, namely independent of the topology of the underlying graph but dependent only on the density of loops. In the case of circuits subject to alternating voltage instead, we are able to obtain an approximate solution of the dynamics, which is tested against a specific network topology. These results suggest a much richer dynamics of memristive networks than previously considered.

  11. A potential energy surface for the process H2 + H2O yielding H + H + H2O - Ab initio calculations and analytical representation

    NASA Technical Reports Server (NTRS)

    Schwenke, David W.; Walch, Stephen P.; Taylor, Peter R.

    1991-01-01

    Extensive ab initio calculations on the ground state potential energy surface of H2 + H2O were performed using a large contracted Gaussian basis set and a high level of correlation treatment. An analytical representation of the potential energy surface was then obtained which reproduces the calculated energies with an overall root-mean-square error of only 0.64 mEh. The analytic representation explicitly includes all nine internal degrees of freedom and is also well behaved as the H2 dissociates; it thus can be used to study collision-induced dissociation or recombination of H2. The strategy used to minimize the number of energy calculations is discussed, as well as other advantages of the present method for determining the analytical representation.

  12. Analytic Result for the Two-loop Six-point NMHV Amplitude in N = 4 Super Yang-Mills Theory

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

    Dixon, Lance J.; /SLAC; Drummond, James M.

    2012-02-15

    We provide a simple analytic formula for the two-loop six-point ratio function of planar N = 4 super Yang-Mills theory. This result extends the analytic knowledge of multi-loop six-point amplitudes beyond those with maximal helicity violation. We make a natural ansatz for the symbols of the relevant functions appearing in the two-loop amplitude, and impose various consistency conditions, including symmetry, the absence of spurious poles, the correct collinear behavior, and agreement with the operator product expansion for light-like (super) Wilson loops. This information reduces the ansatz to a small number of relatively simple functions. In order to fix these parametersmore » uniquely, we utilize an explicit representation of the amplitude in terms of loop integrals that can be evaluated analytically in various kinematic limits. The final compact analytic result is expressed in terms of classical polylogarithms, whose arguments are rational functions of the dual conformal cross-ratios, plus precisely two functions that are not of this type. One of the functions, the loop integral {Omega}{sup (2)}, also plays a key role in a new representation of the remainder function R{sub 6}{sup (2)} in the maximally helicity violating sector. Another interesting feature at two loops is the appearance of a new (parity odd) x (parity odd) sector of the amplitude, which is absent at one loop, and which is uniquely determined in a natural way in terms of the more familiar (parity even) x (parity even) part. The second non-polylogarithmic function, the loop integral {tilde {Omega}}{sup (2)}, characterizes this sector. Both {Omega}{sup (2)} and {tilde {Omega}}{sup (2)} can be expressed as one-dimensional integrals over classical polylogarithms with rational arguments.« less

  13. A new approach to the Schrödinger equation with rational potentials

    NASA Astrophysics Data System (ADS)

    Dong, Ming-de; Chu, Jue-Hui

    1984-04-01

    A new analytic theory is established for the Schrödinger equation with a rational potential, including a complete classification of the regular eigenfunctions into three different types, an exact method of obtaining wavefunctions, an explicit formulation of the spectral equation (3 x 3 determinant) etc. All representations are exhibited in a unifying way via function-theoretic methods and therefore given in explicit form, in contrast to the prevailing discussion appealing to perturbation or variation methods or continued-fraction techniques. The irregular eigenfunctions at infinity can be obtained analogously and will be discussed separately as another solvable case for singular potentials.

  14. Comments on higher rank Wilson loops in N = 2∗

    NASA Astrophysics Data System (ADS)

    Liu, James T.; Zayas, Leopoldo A. Pando; Zhou, Shan

    2018-01-01

    For N = 2∗ theory with U( N ) gauge group we evaluate expectation values of Wilson loops in representations described by a rectangular Young tableau with n rows and k columns. The evaluation reduces to a two-matrix model and we explain, using a combination of numerical and analytical techniques, the general properties of the eigen-value distributions in various regimes of parameters ( N, λ , n, k) where λ is the 't Hooft coupling. In the large N limit we present analytic results for the leading and sub-leading contributions. In the particular cases of only one row or one column we reproduce previously known results for the totally symmetry and totally antisymmetric representations. We also extensively discusss the N = 4 limit of the N = 2∗ theory. While establishing these connections we clarify aspects of various orders of limits and how to relax them; we also find it useful to explicitly address details of the genus expansion. As a result, for the totally symmetric Wilson loop we find new contributions that improve the comparison with the dual holographic computation at one loop order in the appropriate regime.

  15. A direct method for nonlinear ill-posed problems

    NASA Astrophysics Data System (ADS)

    Lakhal, A.

    2018-02-01

    We propose a direct method for solving nonlinear ill-posed problems in Banach-spaces. The method is based on a stable inversion formula we explicitly compute by applying techniques for analytic functions. Furthermore, we investigate the convergence and stability of the method and prove that the derived noniterative algorithm is a regularization. The inversion formula provides a systematic sensitivity analysis. The approach is applicable to a wide range of nonlinear ill-posed problems. We test the algorithm on a nonlinear problem of travel-time inversion in seismic tomography. Numerical results illustrate the robustness and efficiency of the algorithm.

  16. New more accurate calculations of the ground state potential energy surface of H(3) (+).

    PubMed

    Pavanello, Michele; Tung, Wei-Cheng; Leonarski, Filip; Adamowicz, Ludwik

    2009-02-21

    Explicitly correlated Gaussian functions with floating centers have been employed to recalculate the ground state potential energy surface (PES) of the H(3) (+) ion with much higher accuracy than it was done before. The nonlinear parameters of the Gaussians (i.e., the exponents and the centers) have been variationally optimized with a procedure employing the analytical gradient of the energy with respect to these parameters. The basis sets for calculating new PES points were guessed from the points already calculated. This allowed us to considerably speed up the calculations and achieve very high accuracy of the results.

  17. Quantum mechanics on Laakso spaces

    NASA Astrophysics Data System (ADS)

    Kauffman, Christopher J.; Kesler, Robert M.; Parshall, Amanda G.; Stamey, Evelyn A.; Steinhurst, Benjamin A.

    2012-04-01

    We first review the spectrum of the Laplacian operator on a general Laakso space before considering modified Hamiltonians for the infinite square well, parabola, and Coulomb potentials. Additionally, we compute the spectrum for the Laplacian and its multiplicities when certain regions of a Laakso space are compressed or stretched and calculate the Casimir force experienced by two uncharged conducting plates by imposing physically relevant boundary conditions and then analytically regularizing the resulting zeta function. Lastly, we derive a general formula for the spectral zeta function and its derivative for Laakso spaces with strict self-similar structure before listing explicit spectral values for some special cases

  18. Theory for the solvation of nonpolar solutes in water

    NASA Astrophysics Data System (ADS)

    Urbic, T.; Vlachy, V.; Kalyuzhnyi, Yu. V.; Dill, K. A.

    2007-11-01

    We recently developed an angle-dependent Wertheim integral equation theory (IET) of the Mercedes-Benz (MB) model of pure water [Silverstein et al., J. Am. Chem. Soc. 120, 3166 (1998)]. Our approach treats explicitly the coupled orientational constraints within water molecules. The analytical theory offers the advantage of being less computationally expensive than Monte Carlo simulations by two orders of magnitude. Here we apply the angle-dependent IET to studying the hydrophobic effect, the transfer of a nonpolar solute into MB water. We find that the theory reproduces the Monte Carlo results qualitatively for cold water and quantitatively for hot water.

  19. Theory for the solvation of nonpolar solutes in water.

    PubMed

    Urbic, T; Vlachy, V; Kalyuzhnyi, Yu V; Dill, K A

    2007-11-07

    We recently developed an angle-dependent Wertheim integral equation theory (IET) of the Mercedes-Benz (MB) model of pure water [Silverstein et al., J. Am. Chem. Soc. 120, 3166 (1998)]. Our approach treats explicitly the coupled orientational constraints within water molecules. The analytical theory offers the advantage of being less computationally expensive than Monte Carlo simulations by two orders of magnitude. Here we apply the angle-dependent IET to studying the hydrophobic effect, the transfer of a nonpolar solute into MB water. We find that the theory reproduces the Monte Carlo results qualitatively for cold water and quantitatively for hot water.

  20. On the Support of Minimizers of Causal Variational Principles

    NASA Astrophysics Data System (ADS)

    Finster, Felix; Schiefeneder, Daniela

    2013-11-01

    A class of causal variational principles on a compact manifold is introduced and analyzed both numerically and analytically. It is proved under general assumptions that the support of a minimizing measure is either completely timelike, or it is singular in the sense that its interior is empty. In the examples of the circle, the sphere and certain flag manifolds, the general results are supplemented by a more detailed and explicit analysis of the minimizers. On the sphere, we get a connection to packing problems and the Tammes distribution. Moreover, the minimal action is estimated from above and below.

  1. Analysis of potential trade-offs in regulation of disinfection by-products

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

    Cromwell, J.E.; Zhang, X.; Regli, S.

    1992-11-01

    Executive Order 12291 requires the preparation of a Regulatory Impact Analysis (RIA) on all new major federal regulations. The goal of an RIA is to develop and organize information on benefits, costs, and economic impacts so as to clarify trade-offs among alternative regulatory options. This paper outlines explicit methodology for assessing the technical potential for risk-risk tradeoffs. The strategies used to cope with complexities and uncertainties in developing the Disinfection By-Products Regulatory Analysis Model are explained. Results are presented and discussed in light of uncertainties, and in light of the analytical requirements for regulatory impact analysis.

  2. Effective diffusion of confined active Brownian swimmers

    NASA Astrophysics Data System (ADS)

    Sandoval, Mario; Dagdug, Leonardo

    2014-11-01

    We find theoretically the effect of confinement and thermal fluctuations, on the diffusivity of a spherical active swimmer moving inside a two-dimensional narrow cavity of general shape. The explicit formulas for the effective diffusion coefficient of a swimmer moving inside two particular cavities are presented. We also compare our analytical results with Brownian Dynamics simulations and we obtain excellent agreement. L.D. thanks Consejo Nacional de Ciencia y Tecnologia (CONACyT) Mexico, for partial support by Grant No. 176452. M. S. thanks CONACyT and Programa de Mejoramiento de Profesorado (PROMEP) for partially funding this work under Grant No. 103.5/13/6732.

  3. A Semi-Analytical Solution to Time Dependent Groundwater Flow Equation Incorporating Stream-Wetland-Aquifer Interactions

    NASA Astrophysics Data System (ADS)

    Boyraz, Uǧur; Melek Kazezyılmaz-Alhan, Cevza

    2017-04-01

    Groundwater is a vital element of hydrologic cycle and the analytical & numerical solutions of different forms of groundwater flow equations play an important role in understanding the hydrological behavior of subsurface water. The interaction between groundwater and surface water bodies can be determined using these solutions. In this study, new hypothetical approaches are implemented to groundwater flow system in order to contribute to the studies on surface water/groundwater interactions. A time dependent problem is considered in a 2-dimensional stream-wetland-aquifer system. The sloped stream boundary is used to represent the interaction between stream and aquifer. The rest of the aquifer boundaries are assumed as no-flux boundary. In addition, a wetland is considered as a surface water body which lies over the whole aquifer. The effect of the interaction between the wetland and the aquifer is taken into account with a source/sink term in the groundwater flow equation and the interaction flow is calculated by using Darcy's approach. A semi-analytical solution is developed for the 2-dimensional groundwater flow equation in 5 steps. First, Laplace and Fourier cosine transforms are employed to obtain the general solution in Fourier and Laplace domain. Then, the initial and boundary conditions are applied to obtain the particular solution. Finally, inverse Fourier transform is carried out analytically and inverse Laplace transform is carried out numerically to obtain the final solution in space and time domain, respectively. In order to verify the semi-analytical solution, an explicit finite difference algorithm is developed and analytical and numerical solutions are compared for synthetic examples. The comparison of the analytical and numerical solutions shows that the analytical solution gives accurate results.

  4. Why love has wings and sex has not: how reminders of love and sex influence creative and analytic thinking.

    PubMed

    Förster, Jens; Epstude, Kai; Ozelsel, Amina

    2009-11-01

    This article examines cognitive links between romantic love and creativity and between sexual desire and analytic thought based on construal level theory. It suggests that when in love, people typically focus on a long-term perspective, which should enhance holistic thinking and thereby creative thought, whereas when experiencing sexual encounters, they focus on the present and on concrete details enhancing analytic thinking. Because people automatically activate these processing styles when in love or when they experience sex, subtle or even unconscious reminders of love versus sex should suffice to change processing modes. Two studies explicitly or subtly reminded participants of situations of love or sex and found support for this hypothesis.

  5. Analytical ground state for the Jaynes-Cummings model with ultrastrong coupling

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

    Zhang Yuanwei; Institute of Theoretical Physics, Shanxi University, Taiyuan 030006; Chen Gang

    2011-06-15

    We present a generalized variational method to analytically obtain the ground-state properties of the Jaynes-Cummings model with the ultrastrong coupling. An explicit expression for the ground-state energy, which agrees well with the numerical simulation in a wide range of the experimental parameters, is given. In particular, the introduced method can successfully solve this Jaynes-Cummings model with the positive detuning (the atomic resonant level is larger than the photon frequency), which cannot be treated in the adiabatical approximation and the generalized rotating-wave approximation. Finally, we also demonstrate analytically how to control the mean photon number by means of the current experimentalmore » parameters including the photon frequency, the coupling strength, and especially the atomic resonant level.« less

  6. Analytical model of ground-state lasing phenomenon in broadband semiconductor quantum dot lasers

    NASA Astrophysics Data System (ADS)

    Korenev, Vladimir V.; Savelyev, Artem V.; Zhukov, Alexey E.; Omelchenko, Alexander V.; Maximov, Mikhail V.

    2013-05-01

    We introduce an analytical approach to the description of broadband lasing spectra of semiconductor quantum dot lasers emitting via ground-state optical transitions of quantum dots. The explicit analytical expressions describing the shape and the width of lasing spectra as well as their temperature and injection current dependences are obtained in the case of low homogeneous broadening. It is shown that in this case these dependences are determined by only two dimensionless parameters, which are the dispersion of the distribution of QDs over the energy normalized to the temperature and loss-to-maximum gain ratio. The possibility of optimization of laser's active region size and structure by using the intentionally introduced disorder is also carefully considered.

  7. Diffusion in confinement: kinetic simulations of self- and collective diffusion behavior of adsorbed gases

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

    Abouelnasr, MKF; Smit, B

    2012-01-01

    The self- and collective-diffusion behaviors of adsorbed methane, helium, and isobutane in zeolite frameworks LTA, MFI, AFI, and SAS were examined at various concentrations using a range of molecular simulation techniques including Molecular Dynamics (MD), Monte Carlo (MC), Bennett-Chandler (BC), and kinetic Monte Carlo (kMC). This paper has three main results. (1) A novel model for the process of adsorbate movement between two large cages was created, allowing the formulation of a mixing rule for the re-crossing coefficient between two cages of unequal loading. The predictions from this mixing rule were found to agree quantitatively with explicit simulations. (2) Amore » new approach to the dynamically corrected Transition State Theory method to analytically calculate self-diffusion properties was developed, explicitly accounting for nanoscale fluctuations in concentration. This approach was demonstrated to quantitatively agree with previous methods, but is uniquely suited to be adapted to a kMC simulation that can simulate the collective-diffusion behavior. (3) While at low and moderate loadings the self- and collective-diffusion behaviors in LTA are observed to coincide, at higher concentrations they diverge. A change in the adsorbate packing scheme was shown to cause this divergence, a trait which is replicated in a kMC simulation that explicitly models this behavior. These phenomena were further investigated for isobutane in zeolite MFI, where MD results showed a separation in self- and collective-diffusion behavior that was reproduced with kMC simulations.« less

  8. Diffusion in confinement: kinetic simulations of self- and collective diffusion behavior of adsorbed gases.

    PubMed

    Abouelnasr, Mahmoud K F; Smit, Berend

    2012-09-07

    The self- and collective-diffusion behaviors of adsorbed methane, helium, and isobutane in zeolite frameworks LTA, MFI, AFI, and SAS were examined at various concentrations using a range of molecular simulation techniques including Molecular Dynamics (MD), Monte Carlo (MC), Bennett-Chandler (BC), and kinetic Monte Carlo (kMC). This paper has three main results. (1) A novel model for the process of adsorbate movement between two large cages was created, allowing the formulation of a mixing rule for the re-crossing coefficient between two cages of unequal loading. The predictions from this mixing rule were found to agree quantitatively with explicit simulations. (2) A new approach to the dynamically corrected Transition State Theory method to analytically calculate self-diffusion properties was developed, explicitly accounting for nanoscale fluctuations in concentration. This approach was demonstrated to quantitatively agree with previous methods, but is uniquely suited to be adapted to a kMC simulation that can simulate the collective-diffusion behavior. (3) While at low and moderate loadings the self- and collective-diffusion behaviors in LTA are observed to coincide, at higher concentrations they diverge. A change in the adsorbate packing scheme was shown to cause this divergence, a trait which is replicated in a kMC simulation that explicitly models this behavior. These phenomena were further investigated for isobutane in zeolite MFI, where MD results showed a separation in self- and collective- diffusion behavior that was reproduced with kMC simulations.

  9. Why do ultrasoft repulsive particles cluster and crystallize? Analytical results from density-functional theory.

    PubMed

    Likos, Christos N; Mladek, Bianca M; Gottwald, Dieter; Kahl, Gerhard

    2007-06-14

    We demonstrate the accuracy of the hypernetted chain closure and of the mean-field approximation for the calculation of the fluid-state properties of systems interacting by means of bounded and positive pair potentials with oscillating Fourier transforms. Subsequently, we prove the validity of a bilinear, random-phase density functional for arbitrary inhomogeneous phases of the same systems. On the basis of this functional, we calculate analytically the freezing parameters of the latter. We demonstrate explicitly that the stable crystals feature a lattice constant that is independent of density and whose value is dictated by the position of the negative minimum of the Fourier transform of the pair potential. This property is equivalent with the existence of clusters, whose population scales proportionally to the density. We establish that regardless of the form of the interaction potential and of the location on the freezing line, all cluster crystals have a universal Lindemann ratio Lf=0.189 at freezing. We further make an explicit link between the aforementioned density functional and the harmonic theory of crystals. This allows us to establish an equivalence between the emergence of clusters and the existence of negative Fourier components of the interaction potential. Finally, we make a connection between the class of models at hand and the system of infinite-dimensional hard spheres, when the limits of interaction steepness and space dimension are both taken to infinity in a particularly described fashion.

  10. Time Evolution of Modeled Reynolds Stresses in Planar Homogeneous Flows

    NASA Technical Reports Server (NTRS)

    Jongen, T.; Gatski, T. B.

    1997-01-01

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

  11. Theory of particle detection and multiplicity counting with dead time effects

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

    Pal, L.; Pazsit, I.

    The subject of this paper is the investigation of the effect of the dead time on the statistics of the particle detection process. A theoretical treatment is provided with the application of the methods of renewal theory. The detector efficiency and various types of the dead time are accounted for. Exact analytical results are derived for the probability distribution functions, the expectations and the variances of the number of detected particles. Explicit solutions are given for a few representative cases. The results should serve for the evaluation of the measurements in view of the dead time correction effects for themore » higher moments of the detector counts. (authors)« less

  12. Hidden chiral symmetries in BDI multichannel Kitaev chains

    NASA Astrophysics Data System (ADS)

    Manesco, Antônio L. R.; Weber, Gabriel; Rodrigues, Durval, Jr.

    2018-05-01

    Realistic implementations of the Kitaev chain require, in general, the introduction of extra internal degrees of freedom. In the present work, we discuss the presence of hidden BDI symmetries for free Hamiltonians describing systems with an arbitrary number of internal degrees of freedom. We generalize results of a spinfull Kitaev chain to construct a Hamiltonian with n internal degrees of freedom and obtain the corresponding hidden chiral symmetry. As an explicit application of this generalized result, we exploit by analytical and numerical calculations the case of a spinful two-band Kitaev chain, which can host up to four Majorana bound states. We also observe the appearence of minigap states, when chiral symmetry is broken.

  13. The study of the behaviour of a disturbed semi-infinite liquid jet using a spatial instability method

    NASA Astrophysics Data System (ADS)

    Basu (‧nee De), Shukla

    2001-11-01

    A study has been made of the behaviour of a disturbed semi-infinite liquid jet using a spatial instability method. A sinusoidal disturbance in the axial component of jet velocity at the nozzle is considered which resulted in an elliptic free surface boundary value problem with two non-linear boundary conditions. The system is linearised using perturbation techniques and the first order solution resulted in the dispersion relation. The jet stability is found to depend explicitly on the frequency of the disturbance and the Weber number. The second and third order solutions have been derived analytically which are used to predict on jet break-up and satellite formation.

  14. The explicit and implicit dance in psychoanalytic change.

    PubMed

    Fosshage, James L

    2004-02-01

    How the implicit/non-declarative and explicit/declarative cognitive domains interact is centrally important in the consideration of effecting change within the psychoanalytic arena. Stern et al. (1998) declare that long-lasting change occurs in the domain of implicit relational knowledge. In the view of this author, the implicit and explicit domains are intricately intertwined in an interactive dance within a psychoanalytic process. The author views that a spirit of inquiry (Lichtenberg, Lachmann & Fosshage 2002) serves as the foundation of the psychoanalytic process. Analyst and patient strive to explore, understand and communicate and, thereby, create a 'spirit' of interaction that contributes, through gradual incremental learning, to new implicit relational knowledge. This spirit, as part of the implicit relational interaction, is a cornerstone of the analytic relationship. The 'inquiry' more directly brings explicit/declarative processing to the foreground in the joint attempt to explore and understand. The spirit of inquiry in the psychoanalytic arena highlights both the autobiographical scenarios of the explicit memory system and the mental models of the implicit memory system as each contributes to a sense of self, other, and self with other. This process facilitates the extrication and suspension of the old models, so that new models based on current relational experience can be gradually integrated into both memory systems for lasting change.

  15. Explicit Analytical Solution of a Pendulum with Periodically Varying Length

    ERIC Educational Resources Information Center

    Yang, Tianzhi; Fang, Bo; Li, Song; Huang, Wenhu

    2010-01-01

    A pendulum with periodically varying length is an interesting physical system. It has been studied by some researchers using traditional perturbation methods (for example, the averaging method). But due to the limitation of the conventional perturbation methods, the solutions are not valid for long-term prediction of the pendulum. In this paper,…

  16. Coherent control in simple quantum systems

    NASA Technical Reports Server (NTRS)

    Prants, Sergey V.

    1995-01-01

    Coherent dynamics of two, three, and four-level quantum systems, simultaneously driven by concurrent laser pulses of arbitrary and different forms, is treated by using a nonperturbative, group-theoretical approach. The respective evolution matrices are calculated in an explicit form. General aspects of controllability of few-level atoms by using laser fields are treated analytically.

  17. Linking climate change and fish conservation efforts using spatially explicit decision support tools

    Treesearch

    Douglas P. Peterson; Seth J. Wenger; Bruce E. Rieman; Daniel J. Isaak

    2013-01-01

    Fisheries professionals are increasingly tasked with incorporating climate change projections into their decisions. Here we demonstrate how a structured decision framework, coupled with analytical tools and spatial data sets, can help integrate climate and biological information to evaluate management alternatives. We present examples that link downscaled climate...

  18. The Impact of College Experiences on Conventional Career Logic

    ERIC Educational Resources Information Center

    Baumgardner, Steve R.

    1976-01-01

    The factors students consider in choosing a college major were scaled on an analytic-intuitive dimension. Differences in thinking orientation were found to be associated with students's sex, area of study, and year in school. Overall, the apparent lack of explicit rationality in student educational decisions appears to be adaptive. (Author)

  19. Assessing housing growth when census boundaries change

    Treesearch

    Alexandra D. Syphard; Susan I. Stewart; Jason McKeefry; Roger B. Hammer; Jeremy S. Fried; Sherry Holcomb; Volker C. Radeloff

    2009-01-01

    The US Census provides the primary source of spatially explicit social data, but changing block boundaries complicate analyses of housing growth over time. We compared procedures for reconciling housing density data between 1990 and 2000 census block boundaries in order to assess the sensitivity of analytical methods to estimates of housing growth in Oregon. Estimates...

  20. Performance Assessment in Serious Games: Compensating for the Effects of Randomness

    ERIC Educational Resources Information Center

    Westera, Wim

    2016-01-01

    This paper is about performance assessment in serious games. We conceive serious gaming as a process of player-lead decision taking. Starting from combinatorics and item-response theory we provide an analytical model that makes explicit to what extent observed player performances (decisions) are blurred by chance processes (guessing behaviors). We…

  1. Validating Grammaticality Judgment Tests: Evidence from Two New Psycholinguistic Measures

    ERIC Educational Resources Information Center

    Vafaee, Payman; Suzuki, Yuichi; Kachisnke, Ilina

    2017-01-01

    Several previous factor-analytic studies on the construct validity of grammaticality judgment tests (GJTs) concluded that untimed GJTs measure explicit knowledge (EK) and timed GJTs measure implicit knowledge (IK) (Bowles, 2011; R. Ellis, 2005; R. Ellis & Loewen, 2007). It has also been shown that, irrespective of the time condition chosen,…

  2. Metalinguistic Knowledge and Cognitive Style in Polish Classroom Learners of English

    ERIC Educational Resources Information Center

    Zietek, Agnieszka A.; Roehr, Karen

    2011-01-01

    In this exploratory study, we investigated the relationship between level of English metalinguistic knowledge, or explicit knowledge about the English language, and cognitive style on the wholist/analytic dimension in an intact group of young adult Polish learners of English as a foreign language. Contrary to expectation, metalinguistic knowledge…

  3. Sign(al)s: Living and Learning as Semiotic Engagement

    ERIC Educational Resources Information Center

    Stables, Andrew

    2006-01-01

    Cartesian mind-body dualism, while often explicitly denied, has left a legacy of conceptions that remain highly influential in education. I argue that trends in both analytic and continental philosophy of language point towards a post-Cartesian settlement in which the distinction between "signs" and "signals" is collapsed, and which thus construes…

  4. Traveling wave solutions to a reaction-diffusion equation

    NASA Astrophysics Data System (ADS)

    Feng, Zhaosheng; Zheng, Shenzhou; Gao, David Y.

    2009-07-01

    In this paper, we restrict our attention to traveling wave solutions of a reaction-diffusion equation. Firstly we apply the Divisor Theorem for two variables in the complex domain, which is based on the ring theory of commutative algebra, to find a quasi-polynomial first integral of an explicit form to an equivalent autonomous system. Then through this first integral, we reduce the reaction-diffusion equation to a first-order integrable ordinary differential equation, and a class of traveling wave solutions is obtained accordingly. Comparisons with the existing results in the literature are also provided, which indicates that some analytical results in the literature contain errors. We clarify the errors and instead give a refined result in a simple and straightforward manner.

  5. A Framework for Integrating Environmental Justice in Regulatory Analysis

    PubMed Central

    Nweke, Onyemaechi C.

    2011-01-01

    With increased interest in integrating environmental justice into the process for developing environmental regulations in the United States, analysts and decision makers are confronted with the question of what methods and data can be used to assess disproportionate environmental health impacts. However, as a first step to identifying data and methods, it is important that analysts understand what information on equity impacts is needed for decision making. Such knowledge originates from clearly stated equity objectives and the reflection of those objectives throughout the analytical activities that characterize Regulatory Impact Analysis (RIA), a process that is traditionally used to inform decision making. The framework proposed in this paper advocates structuring analyses to explicitly provide pre-defined output on equity impacts. Specifically, the proposed framework emphasizes: (a) defining equity objectives for the proposed regulatory action at the onset of the regulatory process, (b) identifying specific and related sub-objectives for key analytical steps in the RIA process, and (c) developing explicit analytical/research questions to assure that stated sub-objectives and objectives are met. In proposing this framework, it is envisioned that information on equity impacts informs decision-making in regulatory development, and that this is achieved through a systematic and consistent approach that assures linkages between stated equity objectives, regulatory analyses, selection of policy options, and the design of compliance and enforcement activities. PMID:21776235

  6. First-order analytic propagation of satellites in the exponential atmosphere of an oblate planet

    NASA Astrophysics Data System (ADS)

    Martinusi, Vladimir; Dell'Elce, Lamberto; Kerschen, Gaëtan

    2017-04-01

    The paper offers the fully analytic solution to the motion of a satellite orbiting under the influence of the two major perturbations, due to the oblateness and the atmospheric drag. The solution is presented in a time-explicit form, and takes into account an exponential distribution of the atmospheric density, an assumption that is reasonably close to reality. The approach involves two essential steps. The first one concerns a new approximate mathematical model that admits a closed-form solution with respect to a set of new variables. The second step is the determination of an infinitesimal contact transformation that allows to navigate between the new and the original variables. This contact transformation is obtained in exact form, and afterwards a Taylor series approximation is proposed in order to make all the computations explicit. The aforementioned transformation accommodates both perturbations, improving the accuracy of the orbit predictions by one order of magnitude with respect to the case when the atmospheric drag is absent from the transformation. Numerical simulations are performed for a low Earth orbit starting at an altitude of 350 km, and they show that the incorporation of drag terms into the contact transformation generates an error reduction by a factor of 7 in the position vector. The proposed method aims at improving the accuracy of analytic orbit propagation and transforming it into a viable alternative to the computationally intensive numerical methods.

  7. Is the Jeffreys' scale a reliable tool for Bayesian model comparison in cosmology?

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

    Nesseris, Savvas; García-Bellido, Juan, E-mail: savvas.nesseris@uam.es, E-mail: juan.garciabellido@uam.es

    2013-08-01

    We are entering an era where progress in cosmology is driven by data, and alternative models will have to be compared and ruled out according to some consistent criterium. The most conservative and widely used approach is Bayesian model comparison. In this paper we explicitly calculate the Bayes factors for all models that are linear with respect to their parameters. We do this in order to test the so called Jeffreys' scale and determine analytically how accurate its predictions are in a simple case where we fully understand and can calculate everything analytically. We also discuss the case of nestedmore » models, e.g. one with M{sub 1} and another with M{sub 2} superset of M{sub 1} parameters and we derive analytic expressions for both the Bayes factor and the figure of Merit, defined as the inverse area of the model parameter's confidence contours. With all this machinery and the use of an explicit example we demonstrate that the threshold nature of Jeffreys' scale is not a ''one size fits all'' reliable tool for model comparison and that it may lead to biased conclusions. Furthermore, we discuss the importance of choosing the right basis in the context of models that are linear with respect to their parameters and how that basis affects the parameter estimation and the derived constraints.« less

  8. An Analytical Model for Two-Order Asperity Degradation of Rock Joints Under Constant Normal Stiffness Conditions

    NASA Astrophysics Data System (ADS)

    Li, Yingchun; Wu, Wei; Li, Bo

    2018-05-01

    Jointed rock masses during underground excavation are commonly located under the constant normal stiffness (CNS) condition. This paper presents an analytical formulation to predict the shear behaviour of rough rock joints under the CNS condition. The dilatancy and deterioration of two-order asperities are quantified by considering the variation of normal stress. We separately consider the dilation angles of waviness and unevenness, which decrease to zero as the normal stress approaches the transitional stress. The sinusoidal function naturally yields the decay of dilation angle as a function of relative normal stress. We assume that the magnitude of transitional stress is proportionate to the square root of asperity geometric area. The comparison between the analytical prediction and experimental data shows the reliability of the analytical model. All the parameters involved in the analytical model possess explicit physical meanings and are measurable from laboratory tests. The proposed model is potentially practicable for assessing the stability of underground structures at various field scales.

  9. Boundary enhanced effects on the existence of quadratic solitons

    NASA Astrophysics Data System (ADS)

    Chen, Manna; Zhang, Ting; Li, Wenjie; Lu, Daquan; Guo, Qi; Hu, Wei

    2018-05-01

    We investigate, both analytically and numerically, the boundary enhanced effects exerted on the quadratic solitons consisting of fundamental waves and oscillatory second harmonics in the presence of boundary conditions. The nonlocal analogy predicts that the soliton for fundamental wave is supported by the balance between equivalent nonlinear confinement and diffraction (or dispersion). Under Snyder and Mitchell's strongly nonlocal approximation, we obtain the analytical soliton solutions both with and without the boundary conditions to show the impact of boundary conditions. We can distinguish explicitly the nonlinear confinement between the second harmonic mutual interaction and the enhanced effects caused by remote boundaries. Those boundary enhanced effects on the existence of solitons can be positive or negative, which depend on both sample size and nonlocal parameter. The piecewise existence regime of solitons can be explained analytically. The analytical soliton solutions are verified by the numerical ones and the discrepancy between them is also discussed.

  10. What values in design? The challenge of incorporating moral values into design.

    PubMed

    Manders-Huits, Noëmi

    2011-06-01

    Recently, there is increased attention to the integration of moral values into the conception, design, and development of emerging IT. The most reviewed approach for this purpose in ethics and technology so far is Value-Sensitive Design (VSD). This article considers VSD as the prime candidate for implementing normative considerations into design. Its methodology is considered from a conceptual, analytical, normative perspective. The focus here is on the suitability of VSD for integrating moral values into the design of technologies in a way that joins in with an analytical perspective on ethics of technology. Despite its promising character, it turns out that VSD falls short in several respects: (1) VSD does not have a clear methodology for identifying stakeholders, (2) the integration of empirical methods with conceptual research within the methodology of VSD is obscure, (3) VSD runs the risk of committing the naturalistic fallacy when using empirical knowledge for implementing values in design, (4) the concept of values, as well as their realization, is left undetermined and (5) VSD lacks a complimentary or explicit ethical theory for dealing with value trade-offs. For the normative evaluation of a technology, I claim that an explicit and justified ethical starting point or principle is required. Moreover, explicit attention should be given to the value aims and assumptions of a particular design. The criteria of adequacy for such an approach or methodology follow from the evaluation of VSD as the prime candidate for implementing moral values in design.

  11. Q-controlled amplitude modulation atomic force microscopy in liquids: An analysis

    NASA Astrophysics Data System (ADS)

    Hölscher, H.; Schwarz, U. D.

    2006-08-01

    An analysis of amplitude modulation atomic force microscopy in liquids is presented with respect to the application of the Q-Control technique. The equation of motion is solved by numerical and analytic methods with and without Q-Control in the presence of a simple model interaction force adequate for many liquid environments. In addition, the authors give an explicit analytical formula for the tip-sample indentation showing that higher Q factors reduce the tip-sample force. It is found that Q-Control suppresses unwanted deformations of the sample surface, leading to the enhanced image quality reported in several experimental studies.

  12. Analytical formulation of selected activities of the remote manipulator system

    NASA Technical Reports Server (NTRS)

    Zimmerman, K. J.

    1977-01-01

    Existing analysis of Orbiter-RMS-Payload kinematics were surveyed, including equations dealing with the two body kinematics in the presence of a massless RMS and compares analytical explicit solutions with numerical solutions. For the following operational phases of the RMS numerical demonstration, problems are provided: (1) payload capture; (2) payload stowage and removal from cargo bay; and (3) payload deployment. The equation of motion provided accounted for RMS control forces and torque moments and could be extended to RMS flexibility and control loop simulation without increasing the degrees of freedom of the two body system.

  13. Multi-model predictive control based on LMI: from the adaptation of the state-space model to the analytic description of the control law

    NASA Astrophysics Data System (ADS)

    Falugi, P.; Olaru, S.; Dumur, D.

    2010-08-01

    This article proposes an explicit robust predictive control solution based on linear matrix inequalities (LMIs). The considered predictive control strategy uses different local descriptions of the system dynamics and uncertainties and thus allows the handling of less conservative input constraints. The computed control law guarantees constraint satisfaction and asymptotic stability. The technique is effective for a class of nonlinear systems embedded into polytopic models. A detailed discussion of the procedures which adapt the partition of the state space is presented. For the practical implementation the construction of suitable (explicit) descriptions of the control law are described upon concrete algorithms.

  14. Highly Accurate Analytical Approximate Solution to a Nonlinear Pseudo-Oscillator

    NASA Astrophysics Data System (ADS)

    Wu, Baisheng; Liu, Weijia; Lim, C. W.

    2017-07-01

    A second-order Newton method is presented to construct analytical approximate solutions to a nonlinear pseudo-oscillator in which the restoring force is inversely proportional to the dependent variable. The nonlinear equation is first expressed in a specific form, and it is then solved in two steps, a predictor and a corrector step. In each step, the harmonic balance method is used in an appropriate manner to obtain a set of linear algebraic equations. With only one simple second-order Newton iteration step, a short, explicit, and highly accurate analytical approximate solution can be derived. The approximate solutions are valid for all amplitudes of the pseudo-oscillator. Furthermore, the method incorporates second-order Taylor expansion in a natural way, and it is of significant faster convergence rate.

  15. Opening up the Profession: Inclusive Messages for Pre-Service Teachers from a Pedagogy Textbook

    ERIC Educational Resources Information Center

    Brass, Amber

    2016-01-01

    Textbooks are a ubiquitous part of classrooms in all levels of education. Whilst textbooks used in tertiary content subjects have been examined in several studies, research focused on textbooks used in mathematics pedagogy subjects is scarce. Using a discourse analytic framework, this paper presents data about the implicit and explicit messages…

  16. Handling Errors as They Arise in Whole-Class Interactions

    ERIC Educational Resources Information Center

    Ingram, Jenni; Pitt, Andrea; Baldry, Fay

    2015-01-01

    There has been a long history of research into errors and their role in the teaching and learning of mathematics. This research has led to a change to pedagogical recommendations from avoiding errors to explicitly using them in lessons. In this study, 22 mathematics lessons were video-recorded and transcribed. A conversation analytic (CA) approach…

  17. Phase transitions in single macromolecules: Loop-stretch transition versus loop adsorption transition in end-grafted polymer chains

    NASA Astrophysics Data System (ADS)

    Zhang, Shuangshuang; Qi, Shuanhu; Klushin, Leonid I.; Skvortsov, Alexander M.; Yan, Dadong; Schmid, Friederike

    2018-01-01

    We use Brownian dynamics simulations and analytical theory to compare two prominent types of single molecule transitions. One is the adsorption transition of a loop (a chain with two ends bound to an attractive substrate) driven by an attraction parameter ɛ and the other is the loop-stretch transition in a chain with one end attached to a repulsive substrate, driven by an external end-force F applied to the free end. Specifically, we compare the behavior of the respective order parameters of the transitions, i.e., the mean number of surface contacts in the case of the adsorption transition and the mean position of the chain end in the case of the loop-stretch transition. Close to the transition points, both the static behavior and the dynamic behavior of chains with different length N are very well described by a scaling ansatz with the scaling parameters (ɛ - ɛ*)Nϕ (adsorption transition) and (F - F*)Nν (loop-stretch transition), respectively, where ϕ is the crossover exponent of the adsorption transition and ν is the Flory exponent. We show that both the loop-stretch and the loop adsorption transitions provide an exceptional opportunity to construct explicit analytical expressions for the crossover functions which perfectly describe all simulation results on static properties in the finite-size scaling regime. Explicit crossover functions are based on the ansatz for the analytical form of the order parameter distributions at the respective transition points. In contrast to the close similarity in equilibrium static behavior, the dynamic relaxation at the two transitions shows qualitative differences, especially in the strongly ordered regimes. This is attributed to the fact that the surface contact dynamics in a strongly adsorbed chain is governed by local processes, whereas the end height relaxation of a strongly stretched chain involves the full spectrum of Rouse modes.

  18. Universal statistics of vortex tangles in three-dimensional random waves

    NASA Astrophysics Data System (ADS)

    Taylor, Alexander J.

    2018-02-01

    The tangled nodal lines (wave vortices) in random, three-dimensional wavefields are studied as an exemplar of a fractal loop soup. Their statistics are a three-dimensional counterpart to the characteristic random behaviour of nodal domains in quantum chaos, but in three dimensions the filaments can wind around one another to give distinctly different large scale behaviours. By tracing numerically the structure of the vortices, their conformations are shown to follow recent analytical predictions for random vortex tangles with periodic boundaries, where the local disorder of the model ‘averages out’ to produce large scale power law scaling relations whose universality classes do not depend on the local physics. These results explain previous numerical measurements in terms of an explicit effect of the periodic boundaries, where the statistics of the vortices are strongly affected by the large scale connectedness of the system even at arbitrarily high energies. The statistics are investigated primarily for static (monochromatic) wavefields, but the analytical results are further shown to directly describe the reconnection statistics of vortices evolving in certain dynamic systems, or occurring during random perturbations of the static configuration.

  19. Adding a solar-radiance function to the Hošek-Wilkie skylight model.

    PubMed

    Hošek, Lukáš; Wilkie, Alexander

    2013-01-01

    One prerequisite for realistic renderings of outdoor scenes is the proper capturing of the sky's appearance. Currently, an explicit simulation of light scattering in the atmosphere isn't computationally feasible, and won't be in the foreseeable future. Captured luminance patterns have proven their usefulness in practice but can't meet all user needs. To fill this capability gap, computer graphics technology has employed analytical models of sky-dome luminance patterns for more than two decades. For technical reasons, such models deal with only the sky dome's appearance, though, and exclude the solar disc. The widely used model proposed by Arcot Preetham and colleagues employed a separately derived analytical formula for adding a solar emitter of suitable radiant intensity. Although this yields reasonable results, the formula is derived in a manner that doesn't exactly match the conditions in their sky-dome model. But the more sophisticated a skylight model is and the more subtly it can represent different conditions, the more the solar radiance should exactly match the skylight's conditions. Toward that end, researchers propose a solar-radiance function that exactly matches a recently published high-quality analytical skylight model.

  20. Spectral Deformation for Two-Body Dispersive Systems with e.g. the Yukawa Potential

    NASA Astrophysics Data System (ADS)

    Engelmann, Matthias; Rasmussen, Morten Grud

    2016-12-01

    We find an explicit closed formula for the k'th iterated commutator {{ad}Ak}(HV(ξ )) of arbitrary order k ⩾ 1 between a Hamiltonian HV(ξ )=M_{ω _{ξ }}+S_{\\check V} and a conjugate operator A={i}/2(v_{ξ}\\cdotnabla+nabla\\cdot v_{ξ}), where M_{ω _{ξ }} is the operator of multiplication with the real analytic function ω ξ which depends real analytically on the parameter ξ, and the operator S_{\\check V} is the operator of convolution with the (sufficiently nice) function \\check V, and v ξ is some vector field determined by ω ξ . Under certain assumptions, which are satisfied for the Yukawa potential, we then prove estimates of the form {{{ad}Ak}(HV(ξ ))(H0(ξ )+{i} )}|≤ C_{ξ }kk! where C ξ is some constant which depends continuously on ξ. The Hamiltonian is the fixed total momentum fiber Hamiltonian of an abstract two-body dispersive system and the work is inspired by a recent result [3] which, under conditions including estimates of the mentioned type, opens up for spectral deformation and analytic perturbation theory of embedded eigenvalues of finite multiplicity.

  1. Analytical design of an industrial two-term controller for optimal regulatory control of open-loop unstable processes under operational constraints.

    PubMed

    Tchamna, Rodrigue; Lee, Moonyong

    2018-01-01

    This paper proposes a novel optimization-based approach for the design of an industrial two-term proportional-integral (PI) controller for the optimal regulatory control of unstable processes subjected to three common operational constraints related to the process variable, manipulated variable and its rate of change. To derive analytical design relations, the constrained optimal control problem in the time domain was transformed into an unconstrained optimization problem in a new parameter space via an effective parameterization. The resulting optimal PI controller has been verified to yield optimal performance and stability of an open-loop unstable first-order process under operational constraints. The proposed analytical design method explicitly takes into account the operational constraints in the controller design stage and also provides useful insights into the optimal controller design. Practical procedures for designing optimal PI parameters and a feasible constraint set exclusive of complex optimization steps are also proposed. The proposed controller was compared with several other PI controllers to illustrate its performance. The robustness of the proposed controller against plant-model mismatch has also been investigated. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

  2. A study of density effects in plasmas using analytical approximations for the self-consistent potential

    NASA Astrophysics Data System (ADS)

    Poirier, M.

    2015-06-01

    Density effects in ionized matter require particular attention since they modify energies, wavefunctions and transition rates with respect to the isolated-ion situation. The approach chosen in this paper is based on the ion-sphere model involving a Thomas-Fermi-like description for free electrons, the bound electrons being described by a full quantum mechanical formalism. This permits to deal with plasmas out of thermal local equilibrium, assuming only a Maxwell distribution for free electrons. For H-like ions, such a theory provides simple and rather accurate analytical approximations for the potential created by free electrons. Emphasis is put on the plasma potential rather than on the electron density, since the energies and wavefunctions depend directly on this potential. Beyond the uniform electron gas model, temperature effects may be analyzed. In the case of H-like ions, this formalism provides analytical perturbative expressions for the energies, wavefunctions and transition rates. Explicit expressions are given in the case of maximum orbital quantum number, and compare satisfactorily with results from a direct integration of the radial Schrödinger equation. Some formulas for lower orbital quantum numbers are also proposed.

  3. Construction of optimal resources for concatenated quantum protocols

    NASA Astrophysics Data System (ADS)

    Pirker, A.; Wallnöfer, J.; Briegel, H. J.; Dür, W.

    2017-06-01

    We consider the explicit construction of resource states for measurement-based quantum information processing. We concentrate on special-purpose resource states that are capable to perform a certain operation or task, where we consider unitary Clifford circuits as well as non-trace-preserving completely positive maps, more specifically probabilistic operations including Clifford operations and Pauli measurements. We concentrate on 1 →m and m →1 operations, i.e., operations that map one input qubit to m output qubits or vice versa. Examples of such operations include encoding and decoding in quantum error correction, entanglement purification, or entanglement swapping. We provide a general framework to construct optimal resource states for complex tasks that are combinations of these elementary building blocks. All resource states only contain input and output qubits, and are hence of minimal size. We obtain a stabilizer description of the resulting resource states, which we also translate into a circuit pattern to experimentally generate these states. In particular, we derive recurrence relations at the level of stabilizers as key analytical tool to generate explicit (graph) descriptions of families of resource states. This allows us to explicitly construct resource states for encoding, decoding, and syndrome readout for concatenated quantum error correction codes, code switchers, multiple rounds of entanglement purification, quantum repeaters, and combinations thereof (such as resource states for entanglement purification of encoded states).

  4. Modeling the heterogeneous catalytic activity of a single nanoparticle using a first passage time distribution formalism

    NASA Astrophysics Data System (ADS)

    Das, Anusheela; Chaudhury, Srabanti

    2015-11-01

    Metal nanoparticles are heterogeneous catalysts and have a multitude of non-equivalent, catalytic sites on the nanoparticle surface. The product dissociation step in such reaction schemes can follow multiple pathways. Proposed here for the first time is a completely analytical theoretical framework, based on the first passage time distribution, that incorporates the effect of heterogeneity in nanoparticle catalysis explicitly by considering multiple, non-equivalent catalytic sites on the nanoparticle surface. Our results show that in nanoparticle catalysis, the effect of dynamic disorder is manifested even at limiting substrate concentrations in contrast to an enzyme that has only one well-defined active site.

  5. A closed expression for the UV-divergent parts of one-loop tensor integrals in dimensional regularization

    NASA Astrophysics Data System (ADS)

    Sulyok, G.

    2017-07-01

    Starting from the general definition of a one-loop tensor N-point function, we use its Feynman parametrization to calculate the ultraviolet (UV-)divergent part of an arbitrary tensor coefficient in the framework of dimensional regularization. In contrast to existing recursion schemes, we are able to present a general analytic result in closed form that enables direct determination of the UV-divergent part of any one-loop tensor N-point coefficient independent from UV-divergent parts of other one-loop tensor N-point coefficients. Simplified formulas and explicit expressions are presented for A-, B-, C-, D-, E-, and F-functions.

  6. Influence of the electron intrinsic magnetic moment on the transverse dielectric permittivity of degenerate electron gas

    NASA Astrophysics Data System (ADS)

    Maslov, S. A.; Bobrov, V. B.; Kirillin, A. V.; Trigger, S. A.

    2018-01-01

    Using the linear response theory, the transverse dielectric permittivity of a homogeneous and isotropic system of charged particles is considered. In the ideal gas approximation for the polarization function, an explicit analytical expression for the transverse permittivity of a degenerate electron plasma, which takes into account electron spin, is found. This result describes both the Landau diamagnetism and Pauli paramagnetism in electron plasma. The influence of the electron intrinsic magnetic moment on the spatial and frequency dispersion of the transverse dielectric permittivity of degenerate electron plasma is numerically studied, that is crucial for determining the optical characteristics of plasma.

  7. Layerwise Finite Elements for Smart Piezoceramic Composite Plates in Thermal Environments

    NASA Technical Reports Server (NTRS)

    Saravanos, Dimitris A.; Lee, Ho-Jun

    1996-01-01

    Analytical formulations are presented which account for the coupled mechanical, electrical, and thermal response of piezoelectric composite laminates and plate structures. A layerwise theory is formulated with the inherent capability to explicitly model the active and sensory response of piezoelectric composite plates having arbitrary laminate configurations in thermal environments. Finite element equations are derived and implemented for a bilinear 4-noded plate element. Application cases demonstrate the capability to manage thermally induced bending and twisting deformations in symmetric and antisymmetric composite plates with piezoelectric actuators, and show the corresponding electrical response of distributed piezoelectric sensors. Finally, the resultant stresses in the thermal piezoelectric composite laminates are investigated.

  8. Recurrences and explicit formulae for the expansion and connection coefficients in series of Bessel polynomials

    NASA Astrophysics Data System (ADS)

    Doha, E. H.; Ahmed, H. M.

    2004-08-01

    A formula expressing explicitly the derivatives of Bessel polynomials of any degree and for any order in terms of the Bessel polynomials themselves is proved. Another explicit formula, which expresses the Bessel expansion coefficients of a general-order derivative of an infinitely differentiable function in terms of its original Bessel coefficients, is also given. A formula for the Bessel coefficients of the moments of one single Bessel polynomial of certain degree is proved. A formula for the Bessel coefficients of the moments of a general-order derivative of an infinitely differentiable function in terms of its Bessel coefficients is also obtained. Application of these formulae for solving ordinary differential equations with varying coefficients, by reducing them to recurrence relations in the expansion coefficients of the solution, is explained. An algebraic symbolic approach (using Mathematica) in order to build and solve recursively for the connection coefficients between Bessel-Bessel polynomials is described. An explicit formula for these coefficients between Jacobi and Bessel polynomials is given, of which the ultraspherical polynomial and its consequences are important special cases. Two analytical formulae for the connection coefficients between Laguerre-Bessel and Hermite-Bessel are also developed.

  9. Size-dependent resonance frequencies of cantilevered and bridged nanosensors

    NASA Astrophysics Data System (ADS)

    Shi, W.; Zou, J.; Lee, K. Y.; Li, X. F.

    2018-03-01

    This paper studies transverse vibration of nanoscale cantilevered and bridged sensors carrying a nanoparticle. The nanoscale sensors are modelled as Euler-Bernoulli beams with surface effect and nanoparticle as a concentrated mass. Frequency equations of cantilevered and bridged beam-mass system are derived and exact resonance frequencies are calculated. An alternative Fredholm integral equation method is used to obtain an approximate explicit expression for the fundamental frequency for both cases. A comparison between the approximate and analytical results is made and the approximation accuracy is satisfactory. The influences of the residual surface stress, surface elasticity, and attached mass on the resonance frequencies and mode shapes are discussed. These results are useful to illustrate the surface phenomena and are helpful to design micro-/nano-mechanical sensors.

  10. Transient modeling/analysis of hyperbolic heat conduction problems employing mixed implicit-explicit alpha method

    NASA Technical Reports Server (NTRS)

    Tamma, Kumar K.; D'Costa, Joseph F.

    1991-01-01

    This paper describes the evaluation of mixed implicit-explicit finite element formulations for hyperbolic heat conduction problems involving non-Fourier effects. In particular, mixed implicit-explicit formulations employing the alpha method proposed by Hughes et al. (1987, 1990) are described for the numerical simulation of hyperbolic heat conduction models, which involves time-dependent relaxation effects. Existing analytical approaches for modeling/analysis of such models involve complex mathematical formulations for obtaining closed-form solutions, while in certain numerical formulations the difficulties include severe oscillatory solution behavior (which often disguises the true response) in the vicinity of the thermal disturbances, which propagate with finite velocities. In view of these factors, the alpha method is evaluated to assess the control of the amount of numerical dissipation for predicting the transient propagating thermal disturbances. Numerical test models are presented, and pertinent conclusions are drawn for the mixed-time integration simulation of hyperbolic heat conduction models involving non-Fourier effects.

  11. Universality of long-range correlations in expansion randomization systems

    NASA Astrophysics Data System (ADS)

    Messer, P. W.; Lässig, M.; Arndt, P. F.

    2005-10-01

    We study the stochastic dynamics of sequences evolving by single-site mutations, segmental duplications, deletions, and random insertions. These processes are relevant for the evolution of genomic DNA. They define a universality class of non-equilibrium 1D expansion-randomization systems with generic stationary long-range correlations in a regime of growing sequence length. We obtain explicitly the two-point correlation function of the sequence composition and the distribution function of the composition bias in sequences of finite length. The characteristic exponent χ of these quantities is determined by the ratio of two effective rates, which are explicitly calculated for several specific sequence evolution dynamics of the universality class. Depending on the value of χ, we find two different scaling regimes, which are distinguished by the detectability of the initial composition bias. All analytic results are accurately verified by numerical simulations. We also discuss the non-stationary build-up and decay of correlations, as well as more complex evolutionary scenarios, where the rates of the processes vary in time. Our findings provide a possible example for the emergence of universality in molecular biology.

  12. Development of a Coherent Bistatic Vegetation Model for Signal of Opportunity Applications at VHF UHF-Bands

    NASA Technical Reports Server (NTRS)

    Kurum, Mehmet; Deshpande, Manohar; Joseph, Alicia T.; O'Neill, Peggy E.; Lang, Roger H.; Eroglu, Orhan

    2017-01-01

    A coherent bistatic vegetation scattering model, based on a Monte Carlo simulation, is being developed to simulate polarimetric bi-static reflectometry at VHF/UHF-bands (240-270 MHz). The model is aimed to assess the value of geostationary satellite signals of opportunity to enable estimation of the Earth's biomass and root-zone soil moisture. An expression for bistatic scattering from a vegetation canopy is derived for the practical case of a ground-based/low altitude platforms with passive receivers overlooking vegetation. Using analytical wave theory in conjunction with distorted Born approximation (DBA), the transmit and receive antennas effects (i.e., polarization, orientation, height, etc.) are explicitly accounted for. Both the coherency nature of the model (joint phase and amplitude information) and the explicit account of system parameters (antenna, altitude, polarization, etc) enable one to perform various beamforming techniques to evaluate realistic deployment configurations. In this paper, several test scenarios will be presented and the results will be evaluated for feasibility for future biomass and root-zone soil moisture application using geostationary communication satellite signals of opportunity at low frequencies.

  13. A time-spectral approach to numerical weather prediction

    NASA Astrophysics Data System (ADS)

    Scheffel, Jan; Lindvall, Kristoffer; Yik, Hiu Fai

    2018-05-01

    Finite difference methods are traditionally used for modelling the time domain in numerical weather prediction (NWP). Time-spectral solution is an attractive alternative for reasons of accuracy and efficiency and because time step limitations associated with causal CFL-like criteria, typical for explicit finite difference methods, are avoided. In this work, the Lorenz 1984 chaotic equations are solved using the time-spectral algorithm GWRM (Generalized Weighted Residual Method). Comparisons of accuracy and efficiency are carried out for both explicit and implicit time-stepping algorithms. It is found that the efficiency of the GWRM compares well with these methods, in particular at high accuracy. For perturbative scenarios, the GWRM was found to be as much as four times faster than the finite difference methods. A primary reason is that the GWRM time intervals typically are two orders of magnitude larger than those of the finite difference methods. The GWRM has the additional advantage to produce analytical solutions in the form of Chebyshev series expansions. The results are encouraging for pursuing further studies, including spatial dependence, of the relevance of time-spectral methods for NWP modelling.

  14. Comments on higher rank Wilson loops in N$$ \\mathcal{N} $$ = 2∗

    DOE PAGES

    Liu, James T.; Zayas, Leopoldo A. Pando; Zhou, Shan

    2018-01-01

    For N = 2∗ theory with U(N) gauge group we evaluate expectation values of Wilson loops in representations described by a rectangular Young tableau with n rows and k columns. The evaluation reduces to a two-matrix model and we explain, using a combination of numerical and analytical techniques, the general properties of the eigenvalue distributions in various regimes of parameters (N, λ, n, k) where λ is the ’t Hooft coupling. In the large N limit we present analytic results for the leading and sub-leading contributions. In the particular cases of only one row or one column we reproduce previouslymore » known results for the totally symmetry and totally antisymmetric representations. We also extensively discusss the N = 4 limit of the N = 2∗ theory. While establishing these connections we clarify aspects of various orders of limits and how to relax them; we also find it useful to explicitly address details of the genus expansion. As a result, for the totally symmetric Wilson loop we find new contributions that improve the comparison with the dual holographic computation at one loop order in the appropriate regime.« less

  15. Retardation effects on the dispersion and propagation of plasmons in metallic nanoparticle chains

    NASA Astrophysics Data System (ADS)

    Downing, Charles A.; Mariani, Eros; Weick, Guillaume

    2018-01-01

    We consider a chain of regularly-spaced spherical metallic nanoparticles, where each particle supports three degenerate localized surface plasmons. Due to the dipolar interaction between the nanoparticles, the localized plasmons couple to form extended collective modes. Using an open quantum system approach in which the collective plasmons are interacting with vacuum electromagnetic modes and which, importantly, readily incorporates retardation via the light-matter coupling, we analytically evaluate the resulting radiative frequency shifts of the plasmonic bandstructure. For subwavelength-sized nanoparticles, our analytical treatment provides an excellent quantitative agreement with the results stemming from laborious numerical calculations based on fully-retarded solutions to Maxwell’s equations. Indeed, the explicit expressions for the plasmonic spectrum which we provide showcase how including retardation gives rise to a logarithmic singularity in the bandstructure of transverse-polarized plasmons. We further study the impact of retardation effects on the propagation of plasmonic excitations along the chain. While for the longitudinal modes, retardation has a negligible effect, we find that the retarded dipolar interaction can significantly modify the plasmon propagation in the case of transverse-polarized modes. Moreover, our results elucidate the analogy between radiative effects in nanoplasmonic systems and the cooperative Lamb shift in atomic physics.

  16. Theoretical Treatment of Ion Transfers in Two Polarizable Interface Systems When the Analyte Has Access to Both Interfaces.

    PubMed

    Olmos, José Manuel; Molina, Ángela; Laborda, Eduardo; Millán-Barrios, Enrique; Ortuño, Joaquín Ángel

    2018-02-06

    A new theory is presented to tackle the study of transfer processes of hydrophilic ions in two polarizable interface systems when the analyte is initially present in both aqueous phases. The treatment is applied to macrointerfaces (linear diffusion) and microholes (highly convergent diffusion), obtaining analytical equations for the current response in any voltammetric technique. The novel equations predict two signals in the current-potential curves that are symmetric when the compositions of the aqueous phases are identical while asymmetries appear otherwise. The theoretical results show good agreement with the experimental behavior of the "double transfer voltammograms" reported by Dryfe et al. in cyclic voltammetry (CV) ( Anal. Chem. 2014 , 86 , 435 - 442 ) as well as with cyclic square wave voltammetry (cSWV) experiments performed in the current work. The theoretical treatment is also extended to the situation where the target ion is lipophilic and initially present in the organic phase. The theory predicts an opposite effect of the lipophilicity of the ion on the shape of the voltammograms, which is validated experimentally via both CV and cSWV. For the above two cases, simple and manageable expressions and diagnosis criteria are derived for the qualitative and quantitative study of ion lipophilicity. The ion-transfer potentials can be easily quantified from the separation between the two signals making use of explicit analytical equations.

  17. Analytically Solvable Model of Spreading Dynamics with Non-Poissonian Processes

    NASA Astrophysics Data System (ADS)

    Jo, Hang-Hyun; Perotti, Juan I.; Kaski, Kimmo; Kertész, János

    2014-01-01

    Non-Poissonian bursty processes are ubiquitous in natural and social phenomena, yet little is known about their effects on the large-scale spreading dynamics. In order to characterize these effects, we devise an analytically solvable model of susceptible-infected spreading dynamics in infinite systems for arbitrary inter-event time distributions and for the whole time range. Our model is stationary from the beginning, and the role of the lower bound of inter-event times is explicitly considered. The exact solution shows that for early and intermediate times, the burstiness accelerates the spreading as compared to a Poisson-like process with the same mean and same lower bound of inter-event times. Such behavior is opposite for late-time dynamics in finite systems, where the power-law distribution of inter-event times results in a slower and algebraic convergence to a fully infected state in contrast to the exponential decay of the Poisson-like process. We also provide an intuitive argument for the exponent characterizing algebraic convergence.

  18. Layer-switching cost and optimality in information spreading on multiplex networks

    PubMed Central

    Min, Byungjoon; Gwak, Sang-Hwan; Lee, Nanoom; Goh, K. -I.

    2016-01-01

    We study a model of information spreading on multiplex networks, in which agents interact through multiple interaction channels (layers), say online vs. offline communication layers, subject to layer-switching cost for transmissions across different interaction layers. The model is characterized by the layer-wise path-dependent transmissibility over a contact, that is dynamically determined dependently on both incoming and outgoing transmission layers. We formulate an analytical framework to deal with such path-dependent transmissibility and demonstrate the nontrivial interplay between the multiplexity and spreading dynamics, including optimality. It is shown that the epidemic threshold and prevalence respond to the layer-switching cost non-monotonically and that the optimal conditions can change in abrupt non-analytic ways, depending also on the densities of network layers and the type of seed infections. Our results elucidate the essential role of multiplexity that its explicit consideration should be crucial for realistic modeling and prediction of spreading phenomena on multiplex social networks in an era of ever-diversifying social interaction layers. PMID:26887527

  19. Role of polarizer-tilting-angle in zero-field spin-transfer nano-oscillators with perpendicular anisotropy

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

    Gonzalez-Fuentes, C.; Gallardo, R. A., E-mail: rodolfo.gallardo@usm.cl; Landeros, P.

    2015-10-05

    An analytical model for studying the stability of a single domain ferromagnetic layer under the influence of a spin-polarized current is presented. The theory is applied to bias-field-free nano-oscillators with perpendicular anisotropy, which allows to obtain a polarizer-angle vs. current phase diagram that describes the stability of magnetic states. Explicit formulae for the critical current densities unveil the influence of the relative orientation between free and polarizer layers, allowing the emergence of precessional steady-states, and also the possibility to reduce the magnitude of the threshold current density to produce microwave oscillations. It is shown that oscillating steady-states arise in amore » broad angular region, and the dependence of their boundaries is fully specified by the model. The reliability of the analytical results has been corroborated by comparison to numerical calculations. Such structures are currently under intense research because of remarkable properties offering new prospects for microwave applications in communication technologies.« less

  20. Nonlinearity in bacterial population dynamics: Proposal for experiments for the observation of abrupt transitions in patches

    PubMed Central

    Kenkre, V. M.; Kumar, Niraj

    2008-01-01

    An explicit proposal for experiments leading to abrupt transitions in spatially extended bacterial populations in a Petri dish is presented on the basis of an exact formula obtained through an analytic theory. The theory provides accurately the transition expressions despite the fact that the actual solutions, which involve strong nonlinearity, are inaccessible to it. The analytic expressions are verified through numerical solutions of the relevant nonlinear equation. The experimental setup suggested uses opaque masks in a Petri dish bathed in ultraviolet radiation [Lin A-L, et al. (2004) Biophys J 87:75–80 and Perry N (2005) J R Soc Interface 2:379–387], but is based on the interplay of two distances the bacteria must traverse, one of them favorable and the other adverse. As a result of this interplay feature, the experiments proposed introduce highly enhanced reliability in interpretation of observations and in the potential for extraction of system parameters. PMID:19033185

  1. Decision-making under risk conditions is susceptible to interference by a secondary executive task.

    PubMed

    Starcke, Katrin; Pawlikowski, Mirko; Wolf, Oliver T; Altstötter-Gleich, Christine; Brand, Matthias

    2011-05-01

    Recent research suggests two ways of making decisions: an intuitive and an analytical one. The current study examines whether a secondary executive task interferes with advantageous decision-making in the Game of Dice Task (GDT), a decision-making task with explicit and stable rules that taps executive functioning. One group of participants performed the original GDT solely, two groups performed either the GDT and a 1-back or a 2-back working memory task as a secondary task simultaneously. Results show that the group which performed the GDT and the secondary task with high executive load (2-back) decided less advantageously than the group which did not perform a secondary executive task. These findings give further evidence for the view that decision-making under risky conditions taps into the rational-analytical system which acts in a serial and not parallel way as performance on the GDT is disturbed by a parallel task that also requires executive resources.

  2. Stability analysis of confined V-shaped flames in high-velocity streams.

    PubMed

    El-Rabii, Hazem; Joulin, Guy; Kazakov, Kirill A

    2010-06-01

    The problem of linear stability of confined V-shaped flames with arbitrary gas expansion is addressed. Using the on-shell description of flame dynamics, a general equation governing propagation of disturbances of an anchored flame is obtained. This equation is solved analytically for V-flames anchored in high-velocity channel streams. It is demonstrated that dynamics of the flame disturbances in this case is controlled by the memory effects associated with vorticity generated by the perturbed flame. The perturbation growth rate spectrum is determined, and explicit analytical expressions for the eigenfunctions are given. It is found that the piecewise linear V structure is unstable for all values of the gas expansion coefficient. Despite the linearity of the basic pattern, however, evolutions of the V-flame disturbances are completely different from those found for freely propagating planar flames or open anchored flames. The obtained results reveal strong influence of the basic flow and the channel walls on the stability properties of confined V-flames.

  3. Analytic Morse/long-range potential energy surfaces and "adiabatic-hindered-rotor" treatment for a symmetric top-linear molecule dimer: A case study of CH3F-H2

    NASA Astrophysics Data System (ADS)

    Zhang, Xiao-Long; Ma, Yong-Tao; Zhai, Yu; Li, Hui

    2018-03-01

    A first effective six-dimensional ab initio potential energy surface (PES) for CH3F-H2 which explicitly includes the intramolecular Q3 stretching normal mode of the CH3F monomer is presented. The electronic structure computations have been carried out at the explicitly correlated coupled cluster level of theory [CCSD(T)-F12a] with an augmented correlation-consistent triple zeta basis set. Five-dimensional analytical intermolecular PESs for ν3(CH3F) = 0 and 1 are then obtained by fitting the vibrationally averaged potentials to the Morse/Long-Range (MLR) potential function form. The MLR function form is applied to the nonlinear molecule-linear molecule case for the first time. These fits to 25 015 points have root-mean-square deviations of 0.74 cm-1 and 0.082 cm-1 for interaction energies less than 0.0 cm-1. Using the adiabatic hindered-rotor approximation, three-dimensional PESs for CH3F-paraH2 are generated from the 5D PESs over all possible orientations of the hydrogen monomer. The infrared and microwave spectra for CH3F-paraH2 dimer are predicted for the first time. These analytic PESs can be used for modeling the dynamical behavior in CH3F-(H2)N clusters, including the possible appearance of microscopic superfluidity.

  4. Analytical steady-state solutions for water-limited cropping systems using saline irrigation water

    NASA Astrophysics Data System (ADS)

    Skaggs, T. H.; Anderson, R. G.; Corwin, D. L.; Suarez, D. L.

    2014-12-01

    Due to the diminishing availability of good quality water for irrigation, it is increasingly important that irrigation and salinity management tools be able to target submaximal crop yields and support the use of marginal quality waters. In this work, we present a steady-state irrigated systems modeling framework that accounts for reduced plant water uptake due to root zone salinity. Two explicit, closed-form analytical solutions for the root zone solute concentration profile are obtained, corresponding to two alternative functional forms of the uptake reduction function. The solutions express a general relationship between irrigation water salinity, irrigation rate, crop salt tolerance, crop transpiration, and (using standard approximations) crop yield. Example applications are illustrated, including the calculation of irrigation requirements for obtaining targeted submaximal yields, and the generation of crop-water production functions for varying irrigation waters, irrigation rates, and crops. Model predictions are shown to be mostly consistent with existing models and available experimental data. Yet the new solutions possess advantages over available alternatives, including: (i) the solutions were derived from a complete physical-mathematical description of the system, rather than based on an ad hoc formulation; (ii) the analytical solutions are explicit and can be evaluated without iterative techniques; (iii) the solutions permit consideration of two common functional forms of salinity induced reductions in crop water uptake, rather than being tied to one particular representation; and (iv) the utilized modeling framework is compatible with leading transient-state numerical models.

  5. Rate-loss analysis of an efficient quantum repeater architecture

    NASA Astrophysics Data System (ADS)

    Guha, Saikat; Krovi, Hari; Fuchs, Christopher A.; Dutton, Zachary; Slater, Joshua A.; Simon, Christoph; Tittel, Wolfgang

    2015-08-01

    We analyze an entanglement-based quantum key distribution (QKD) architecture that uses a linear chain of quantum repeaters employing photon-pair sources, spectral-multiplexing, linear-optic Bell-state measurements, multimode quantum memories, and classical-only error correction. Assuming perfect sources, we find an exact expression for the secret-key rate, and an analytical description of how errors propagate through the repeater chain, as a function of various loss-and-noise parameters of the devices. We show via an explicit analytical calculation, which separately addresses the effects of the principle nonidealities, that this scheme achieves a secret-key rate that surpasses the Takeoka-Guha-Wilde bound—a recently found fundamental limit to the rate-vs-loss scaling achievable by any QKD protocol over a direct optical link—thereby providing one of the first rigorous proofs of the efficacy of a repeater protocol. We explicitly calculate the end-to-end shared noisy quantum state generated by the repeater chain, which could be useful for analyzing the performance of other non-QKD quantum protocols that require establishing long-distance entanglement. We evaluate that shared state's fidelity and the achievable entanglement-distillation rate, as a function of the number of repeater nodes, total range, and various loss-and-noise parameters of the system. We extend our theoretical analysis to encompass sources with nonzero two-pair-emission probability, using an efficient exact numerical evaluation of the quantum state propagation and measurements. We expect our results to spur formal rate-loss analysis of other repeater protocols and also to provide useful abstractions to seed analyses of quantum networks of complex topologies.

  6. The full spectrum of climate change adaptation: testing an analytical framework in Tyrolean mountain agriculture (Austria).

    PubMed

    Grüneis, Heidelinde; Penker, Marianne; Höferl, Karl-Michael

    2016-01-01

    Our scientific view on climate change adaptation (CCA) is unsatisfying in many ways: It is often dominated by a modernistic perspective of planned pro-active adaptation, with a selective focus on measures directly responding to climate change impacts and thus it is far from real-life conditions of those who are actually affected by climate change. Farmers have to simultaneously adapt to multiple changes. Therefore, also empirical climate change adaptation research needs a more integrative perspective on real-life climate change adaptations. This also has to consider "hidden" adaptations, which are not explicitly and directly motivated by CCA but actually contribute to the sector's adaptability to climate change. The aim of the present study is to develop and test an analytic framework that contributes to a broader understanding of CCA and to bridge the gap between scientific expertise and practical action. The framework distinguishes three types of CCA according to their climate related motivations: explicit adaptations, multi-purpose adaptations, and hidden adaptations. Although agriculture is among the sectors that are most affected by climate change, results from the case study of Tyrolean mountain agriculture show that climate change is ranked behind other more pressing "real-life-challenges" such as changing agricultural policies or market conditions. We identified numerous hidden adaptations which make a valuable contribution when dealing with climate change impacts. We conclude that these hidden adaptations have not only to be considered to get an integrative und more realistic view on CCA; they also provide a great opportunity for linking adaptation strategies to farmers' realities.

  7. Analytic approximations to the modon dispersion relation. [in oceanography

    NASA Technical Reports Server (NTRS)

    Boyd, J. P.

    1981-01-01

    Three explicit analytic approximations are given to the modon dispersion relation developed by Flierl et al. (1980) to describe Gulf Stream rings and related phenomena in the oceans and atmosphere. The solutions are in the form of k(q), and are developed in the form of a power series in q for small q, an inverse power series in 1/q for large q, and a two-point Pade approximant. The low order Pade approximant is shown to yield a solution for the dispersion relation with a maximum relative error for the lowest branch of the function equal to one in 700 in the q interval zero to infinity.

  8. Exact solutions to the fermion propagator Schwinger-Dyson equation in Minkowski space with on-shell renormalization for quenched QED

    DOE PAGES

    Jia, Shaoyang; Pennington, M. R.

    2017-08-01

    With the introduction of a spectral representation, the Schwinger-Dyson equation (SDE) for the fermion propagator is formulated in Minkowski space in QED. After imposing the on-shell renormalization conditions, analytic solutions for the fermion propagator spectral functions are obtained in four dimensions with a renormalizable version of the Gauge Technique anzatz for the fermion-photon vertex in the quenched approximation in the Landau gauge. Despite the limitations of this model, having an explicit solution provides a guiding example of the fermion propagator with the correct analytic structure. The Padé approximation for the spectral functions is also investigated.

  9. Exact solutions to the fermion propagator Schwinger-Dyson equation in Minkowski space with on-shell renormalization for quenched QED

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

    Jia, Shaoyang; Pennington, M. R.

    With the introduction of a spectral representation, the Schwinger-Dyson equation (SDE) for the fermion propagator is formulated in Minkowski space in QED. After imposing the on-shell renormalization conditions, analytic solutions for the fermion propagator spectral functions are obtained in four dimensions with a renormalizable version of the Gauge Technique anzatz for the fermion-photon vertex in the quenched approximation in the Landau gauge. Despite the limitations of this model, having an explicit solution provides a guiding example of the fermion propagator with the correct analytic structure. The Padé approximation for the spectral functions is also investigated.

  10. Analysis of random point images with the use of symbolic computation codes and generalized Catalan numbers

    NASA Astrophysics Data System (ADS)

    Reznik, A. L.; Tuzikov, A. V.; Solov'ev, A. A.; Torgov, A. V.

    2016-11-01

    Original codes and combinatorial-geometrical computational schemes are presented, which are developed and applied for finding exact analytical formulas that describe the probability of errorless readout of random point images recorded by a scanning aperture with a limited number of threshold levels. Combinatorial problems encountered in the course of the study and associated with the new generalization of Catalan numbers are formulated and solved. An attempt is made to find the explicit analytical form of these numbers, which is, on the one hand, a necessary stage of solving the basic research problem and, on the other hand, an independent self-consistent problem.

  11. Explicit analytical tuning rules for digital PID controllers via the magnitude optimum criterion.

    PubMed

    Papadopoulos, Konstantinos G; Yadav, Praveen K; Margaris, Nikolaos I

    2017-09-01

    Analytical tuning rules for digital PID type-I controllers are presented regardless of the process complexity. This explicit solution allows control engineers 1) to make an accurate examination of the effect of the controller's sampling time to the control loop's performance both in the time and frequency domain 2) to decide when the control has to be I, PI and when the derivative, D, term has to be added or omitted 3) apply this control action to a series of stable benchmark processes regardless of their complexity. The former advantages are considered critical in industry applications, since 1) most of the times the choice of the digital controller's sampling time is based on heuristics and past criteria, 2) there is little a-priori knowledge of the controlled process making the choice of the type of the controller a trial and error exercise 3) model parameters change often depending on the control loop's operating point making in this way, the problem of retuning the controller's parameter a much challenging issue. Basis of the proposed control law is the principle of the PID tuning via the Magnitude Optimum criterion. The final control law involves the controller's sampling time T s within the explicit solution of the controller's parameters. Finally, the potential of the proposed method is justified by comparing its performance with the conventional PID tuning when controlling the same process. Further investigation regarding the choice of the controller's sampling time T s is also presented and useful conclusions for control engineers are derived. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

  12. Navy Interest Inventory: Approach Development

    DTIC Science & Technology

    2006-12-01

    lacking social skills” • Investigative is “analytical, intelligent , skeptical and having academic talent– lacking interpersonal skills” • Artistic is...explicit scales to assess RIASEC types or methods to convert their interest scale scores to Holland’s system. Gottfredson and Holland (1996) have given...universality of vocational interest structure among racial/ethnic minorities. American Psychologist, 53, 728-736. Gottfredson , G. D., & Holland, J. L. (1996

  13. A Multiple Group Measurement Model of Children's Reports of Parental Socioeconomic Status. Discussion Papers No. 531-78.

    ERIC Educational Resources Information Center

    Mare, Robert D.; Mason, William M.

    An important class of applications of measurement error or constrained factor analytic models consists of comparing models for several populations. In such cases, it is appropriate to make explicit statistical tests of model similarity across groups and to constrain some parameters of the models to be equal across groups using a priori substantive…

  14. Polarization effects in recoil-induced resonances

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

    Lazebnyi, D. B., E-mail: becks.ddf@gmail.com; Brazhnikov, D. V.; Taichenachev, A. V.

    2017-01-15

    The effect of the field polarization on the amplitude of recoil-induced resonances (RIRs) is considered for laser-cooled free atoms and for atoms in a working magneto-optical trap (MOT). For all closed dipole transitions, explicit analytical expressions are obtained for the polarization dependence of the resonance amplitudes within a perturbation theory. Optimal polarization conditions are found for the observation of resonances.

  15. Therapists' Attitudes about and Preferences to Use Relationship Focused Interventions: New Tools to Measure a Critical Component of Functional Analytic Psychotherapy (FAP)

    ERIC Educational Resources Information Center

    Terry, Christeine M.; Kohlenberg, Robert J.

    2012-01-01

    The primary study aims were to create reliable measures of therapists' attitudes about and preferences to use Relationship Focused Interventions (RFIs), and investigate factors that influence them. Explicit and implicit measures of therapists' attitudes and preferences were administered to a national sample of mental health trainees and FAP…

  16. Aircraft electric field measurements: Calibration and ambient field retrieval

    NASA Technical Reports Server (NTRS)

    Koshak, William J.; Bailey, Jeff; Christian, Hugh J.; Mach, Douglas M.

    1994-01-01

    An aircraft locally distorts the ambient thundercloud electric field. In order to determine the field in the absence of the aircraft, an aircraft calibration is required. In this work a matrix inversion method is introduced for calibrating an aircraft equipped with four or more electric field sensors and a high-voltage corona point that is capable of charging the aircraft. An analytic, closed form solution for the estimate of a (3 x 3) aircraft calibration matrix is derived, and an absolute calibration experiment is used to improve the relative magnitudes of the elements of this matrix. To demonstrate the calibration procedure, we analyze actual calibration date derived from a Lear jet 28/29 that was equipped with five shutter-type field mill sensors (each with sensitivities of better than 1 V/m) located on the top, bottom, port, starboard, and aft positions. As a test of the calibration method, we analyze computer-simulated calibration data (derived from known aircraft and ambient fields) and explicitly determine the errors involved in deriving the variety of calibration matrices. We extend our formalism to arrive at an analytic solution for the ambient field, and again carry all errors explicitly.

  17. Analytic Theory for the Yarkovsky-O Effect on Obliquity

    NASA Astrophysics Data System (ADS)

    Nesvorný, David; Vokrouhlický, David

    2008-07-01

    The Yarkovsky-O'Keefe-Radzievski-Paddack (YORP) effect is a thermal radiation torque that causes small objects to speed up or slow down their rotation and modify their spin vector orientation. This effect has important implications for spin dynamics of diameter D lsim 50 km asteroids. In our previous work we developed an analytic theory for the component of the YORP torque that affects the spin rate. Here we extend these calculations to determine the effect of the YORP torque on obliquity. Our theory is limited to objects with near-spherical shapes. Two limiting cases are studied: (1) immediate emission of the thermal energy that occurs for surface thermal conductivity K = 0; (2) the effects of K ≠ 0 in the limit of small temporal variations of the surface temperature. We use the linearized heat transport equation to model (2). The results include explicit scaling of the YORP torque on obliquity with physical and dynamical parameters such as the thermal conductivity and spin rate. The dependence of torques on the obliquity is given as series of the Legendre polynomials. Comparisons show excellent agreement of the analytic results with the numerically calculated YORP torques for objects such as asteroids 1998 KY26 and (66391) 1999 KW4. We suggest that an important fraction of main belt asteroids may have specific obliquity values (generalized Slivan states) arising from the roots of the Legendre polynomials.

  18. Analytical flow duration curves for summer streamflow in Switzerland

    NASA Astrophysics Data System (ADS)

    Santos, Ana Clara; Portela, Maria Manuela; Rinaldo, Andrea; Schaefli, Bettina

    2018-04-01

    This paper proposes a systematic assessment of the performance of an analytical modeling framework for streamflow probability distributions for a set of 25 Swiss catchments. These catchments show a wide range of hydroclimatic regimes, including namely snow-influenced streamflows. The model parameters are calculated from a spatially averaged gridded daily precipitation data set and from observed daily discharge time series, both in a forward estimation mode (direct parameter calculation from observed data) and in an inverse estimation mode (maximum likelihood estimation). The performance of the linear and the nonlinear model versions is assessed in terms of reproducing observed flow duration curves and their natural variability. Overall, the nonlinear model version outperforms the linear model for all regimes, but the linear model shows a notable performance increase with catchment elevation. More importantly, the obtained results demonstrate that the analytical model performs well for summer discharge for all analyzed streamflow regimes, ranging from rainfall-driven regimes with summer low flow to snow and glacier regimes with summer high flow. These results suggest that the model's encoding of discharge-generating events based on stochastic soil moisture dynamics is more flexible than previously thought. As shown in this paper, the presence of snowmelt or ice melt is accommodated by a relative increase in the discharge-generating frequency, a key parameter of the model. Explicit quantification of this frequency increase as a function of mean catchment meteorological conditions is left for future research.

  19. Explicit equilibria in a kinetic model of gambling

    NASA Astrophysics Data System (ADS)

    Bassetti, F.; Toscani, G.

    2010-06-01

    We introduce and discuss a nonlinear kinetic equation of Boltzmann type which describes the evolution of wealth in a pure gambling process, where the entire sum of wealths of two agents is up for gambling, and randomly shared between the agents. For this equation the analytical form of the steady states is found for various realizations of the random fraction of the sum which is shared to the agents. Among others, the exponential distribution appears as steady state in case of a uniformly distributed random fraction, while Gamma distribution appears for a random fraction which is Beta distributed. The case in which the gambling game is only conservative-in-the-mean is shown to lead to an explicit heavy tailed distribution.

  20. Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters

    NASA Astrophysics Data System (ADS)

    Bubin, Sergiy; Adamowicz, Ludwik

    2006-06-01

    In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.

  1. Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters.

    PubMed

    Bubin, Sergiy; Adamowicz, Ludwik

    2006-06-14

    In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programmed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.

  2. Flux and Hall states in ABJM with dynamical flavors

    NASA Astrophysics Data System (ADS)

    Bea, Yago; Jokela, Niko; Lippert, Matthew; Ramallo, Alfonso V.; Zoakos, Dimitrios

    2015-03-01

    We study the physics of probe D6-branes with quantized internal worldvolume flux in the ABJM background with unquenched massless flavors. This flux breaks parity in the (2+1)-dimensional gauge theory and allows quantum Hall states. Parity breaking is also explicitly demonstrated via the helicity dependence of the meson spectrum. We obtain general expressions for the conductivities, both in the gapped Minkowski embeddings and in the compressible black hole ones. These conductivities depend on the flux and contain a contribution from the dynamical flavors which can be regarded as an effect of intrinsic disorder due to quantum fluctuations of the fundamentals. We present an explicit, analytic family of supersymmetric solutions with nonzero charge density, electric, and magnetic fields.

  3. Analytical Sociology: A Bungean Appreciation

    NASA Astrophysics Data System (ADS)

    Wan, Poe Yu-ze

    2012-10-01

    Analytical sociology, an intellectual project that has garnered considerable attention across a variety of disciplines in recent years, aims to explain complex social processes by dissecting them, accentuating their most important constituent parts, and constructing appropriate models to understand the emergence of what is observed. To achieve this goal, analytical sociologists demonstrate an unequivocal focus on the mechanism-based explanation grounded in action theory. In this article I attempt a critical appreciation of analytical sociology from the perspective of Mario Bunge's philosophical system, which I characterize as emergentist systemism. I submit that while the principles of analytical sociology and those of Bunge's approach share a lot in common, the latter brings to the fore the ontological status and explanatory importance of supra-individual actors (as concrete systems endowed with emergent causal powers) and macro-social mechanisms (as processes unfolding in and among social systems), and therefore it does not stipulate that every causal explanation of social facts has to include explicit references to individual-level actors and mechanisms. In this sense, Bunge's approach provides a reasonable middle course between the Scylla of sociological reification and the Charybdis of ontological individualism, and thus serves as an antidote to the untenable "strong program of microfoundations" to which some analytical sociologists are committed.

  4. Analytic Approximations to the Free Boundary and Multi-dimensional Problems in Financial Derivatives Pricing

    NASA Astrophysics Data System (ADS)

    Lau, Chun Sing

    This thesis studies two types of problems in financial derivatives pricing. The first type is the free boundary problem, which can be formulated as a partial differential equation (PDE) subject to a set of free boundary condition. Although the functional form of the free boundary condition is given explicitly, the location of the free boundary is unknown and can only be determined implicitly by imposing continuity conditions on the solution. Two specific problems are studied in details, namely the valuation of fixed-rate mortgages and CEV American options. The second type is the multi-dimensional problem, which involves multiple correlated stochastic variables and their governing PDE. One typical problem we focus on is the valuation of basket-spread options, whose underlying asset prices are driven by correlated geometric Brownian motions (GBMs). Analytic approximate solutions are derived for each of these three problems. For each of the two free boundary problems, we propose a parametric moving boundary to approximate the unknown free boundary, so that the original problem transforms into a moving boundary problem which can be solved analytically. The governing parameter of the moving boundary is determined by imposing the first derivative continuity condition on the solution. The analytic form of the solution allows the price and the hedging parameters to be computed very efficiently. When compared against the benchmark finite-difference method, the computational time is significantly reduced without compromising the accuracy. The multi-stage scheme further allows the approximate results to systematically converge to the benchmark results as one recasts the moving boundary into a piecewise smooth continuous function. For the multi-dimensional problem, we generalize the Kirk (1995) approximate two-asset spread option formula to the case of multi-asset basket-spread option. Since the final formula is in closed form, all the hedging parameters can also be derived in closed form. Numerical examples demonstrate that the pricing and hedging errors are in general less than 1% relative to the benchmark prices obtained by numerical integration or Monte Carlo simulation. By exploiting an explicit relationship between the option price and the underlying probability distribution, we further derive an approximate distribution function for the general basket-spread variable. It can be used to approximate the transition probability distribution of any linear combination of correlated GBMs. Finally, an implicit perturbation is applied to reduce the pricing errors by factors of up to 100. When compared against the existing methods, the basket-spread option formula coupled with the implicit perturbation turns out to be one of the most robust and accurate approximation methods.

  5. Analytical results for a stochastic model of gene expression with arbitrary partitioning of proteins

    NASA Astrophysics Data System (ADS)

    Tschirhart, Hugo; Platini, Thierry

    2018-05-01

    In biophysics, the search for analytical solutions of stochastic models of cellular processes is often a challenging task. In recent work on models of gene expression, it was shown that a mapping based on partitioning of Poisson arrivals (PPA-mapping) can lead to exact solutions for previously unsolved problems. While the approach can be used in general when the model involves Poisson processes corresponding to creation or degradation, current applications of the method and new results derived using it have been limited to date. In this paper, we present the exact solution of a variation of the two-stage model of gene expression (with time dependent transition rates) describing the arbitrary partitioning of proteins. The methodology proposed makes full use of the PPA-mapping by transforming the original problem into a new process describing the evolution of three biological switches. Based on a succession of transformations, the method leads to a hierarchy of reduced models. We give an integral expression of the time dependent generating function as well as explicit results for the mean, variance, and correlation function. Finally, we discuss how results for time dependent parameters can be extended to the three-stage model and used to make inferences about models with parameter fluctuations induced by hidden stochastic variables.

  6. Neurocognitive mechanisms underlying the experience of flow.

    PubMed

    Dietrich, Arne

    2004-12-01

    Recent theoretical and empirical work in cognitive science and neuroscience is brought into contact with the concept of the flow experience. After a brief exposition of brain function, the explicit-implicit distinction is applied to the effortless information processing that is so characteristic of the flow state. The explicit system is associated with the higher cognitive functions of the frontal lobe and medial temporal lobe structures and has evolved to increase cognitive flexibility. In contrast, the implicit system is associated with the skill-based knowledge supported primarily by the basal ganglia and has the advantage of being more efficient. From the analysis of this flexibility/efficiency trade-off emerges a thesis that identifies the flow state as a period during which a highly practiced skill that is represented in the implicit system's knowledge base is implemented without interference from the explicit system. It is proposed that a necessary prerequisite to the experience of flow is a state of transient hypofrontality that enables the temporary suppression of the analytical and meta-conscious capacities of the explicit system. Examining sensory-motor integration skills that seem to typify flow such as athletic performance, writing, and free-jazz improvisation, the new framework clarifies how this concept relates to creativity and opens new avenues of research.

  7. Examining the Affordances of Dual Cognitive Processing to Explain the Development of High School Students' Nature of Science Views

    ERIC Educational Resources Information Center

    Jackson, Luke M.

    2017-01-01

    This mixed method study was aimed at examining the influence of dual processing (Type 1 and Type 2 thinking) on the development of high school students' nature of science (NOS) views. Type 1 thinking is intuitive, experiential, and heuristic. Type 2 thinking is rational, analytical, and explicit. Three research questions were asked: (1) Do the…

  8. Compact Q-balls in the complex signum-Gordon model

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

    Arodz, H.; Lis, J.

    2008-05-15

    We discuss Q-balls in the complex signum-Gordon model in d-dimensional space for d=1, 2, 3. The Q-balls have strictly finite size. Their total energy is a powerlike function of the conserved U(1) charge with the exponent equal to (d+2)(d+3){sup -1}. In the cases d=1 and d=3 explicit analytic solutions are presented.

  9. Phase estimation without a priori phase knowledge in the presence of loss

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

    Kolodynski, Jan; Demkowicz-Dobrzanski, Rafal

    2010-11-15

    We find the optimal scheme for quantum phase estimation in the presence of loss when no a priori knowledge on the estimated phase is available. We prove analytically an explicit lower bound on estimation uncertainty, which shows that, as a function of the number of probes, quantum precision enhancement amounts at most to a constant factor improvement over classical strategies.

  10. Transformation of the optical vortex dipole by an astigmatic lens

    NASA Astrophysics Data System (ADS)

    Yan, Hongwei; Lü, Baida

    2009-06-01

    The transformation of the optical vortex dipole (OVD) by an astigmatic lens is studied. The explicit propagation expression of the OVD nested in a Gaussian beam is derived and used to analytically determine the position of the OVD after the passage through the astigmatic lens. The transformation by an aberration-free lens is treated as a special case. It is shown that, depending on the propagation distance, waist width, off-axis distance and astigmatic coefficient, the motion, annihilation and revival of the OVD and the inversion of the topological charge may take place. Specifically, the creation of two OVDs may appear under certain conditions. The results are illustrated by numerical examples.

  11. Domain wall suppression in trapped mixtures of Bose-Einstein condensates

    NASA Astrophysics Data System (ADS)

    Pepe, Francesco V.; Facchi, Paolo; Florio, Giuseppe; Pascazio, Saverio

    2012-08-01

    The ground-state energy of a binary mixture of Bose-Einstein condensates can be estimated for large atomic samples by making use of suitably regularized Thomas-Fermi density profiles. By exploiting a variational method on the trial densities the energy can be computed by explicitly taking into account the normalization condition. This yields analytical results and provides the basis for further improvement of the approximation. As a case study, we consider a binary mixture of 87Rb atoms in two different hyperfine states in a double-well potential and discuss the energy crossing between density profiles with different numbers of domain walls, as the number of particles and the interspecies interaction vary.

  12. Ab initio calculation of the G peak intensity of graphene: Laser-energy and Fermi-energy dependence and importance of quantum interference effects

    NASA Astrophysics Data System (ADS)

    Reichardt, Sven; Wirtz, Ludger

    2017-05-01

    We present the results of a diagrammatic, fully ab initio calculation of the G peak intensity of graphene. The flexibility and generality of our approach enables us to go beyond the previous analytical calculations in the low-energy regime. We study the laser and Fermi energy dependence of the G peak intensity and analyze the contributions from resonant and nonresonant electronic transitions. In particular, we explicitly demonstrate the importance of quantum interference and nonresonant states for the G peak process. Our method of analysis and computational concept is completely general and can easily be applied to study other materials as well.

  13. Nonperturbative quark-gluon thermodynamics at finite density

    NASA Astrophysics Data System (ADS)

    Andreichikov, M. A.; Lukashov, M. S.; Simonov, Yu. A.

    2018-03-01

    Thermodynamics of the quark-gluon plasma at finite density is studied in the framework of the Field Correlator Method, where thermodynamical effects of Polyakov loops and color magnetic confinement are taken into account. Having found good agreement with numerical lattice data for zero density, we calculate pressure P(T,μ), for 0 < μ < 400 MeV and 150 < T < 1000 MeV. For the first time, the explicit integral form is found in this region, demonstrating analytic structure in the complex μ plane. The resulting multiple complex branch points are found at the Roberge-Weiss values of Imμ, with Reμ defined by the values of Polyakov lines and color magnetic confinement.

  14. The design of photovoltaic plants - An optimization procedure

    NASA Astrophysics Data System (ADS)

    Bartoli, B.; Cuomo, V.; Fontana, F.; Serio, C.; Silvestrini, V.

    An analytical model is developed to match the components and overall size of a solar power facility (comprising photovoltaic array), maximum-power tracker, battery storage system, and inverter) to the load requirements and climatic conditions of a proposed site at the smallest possible cost. Input parameters are the efficiencies and unit costs of the components, the load fraction to be covered (for stand-alone systems), the statistically analyzed meteorological data, and the cost and efficiency data of the support system (for fuel-generator-assisted plants). Numerical results are presented in graphs and tables for sites in Italy, and it is found that the explicit form of the model equation is independent of locality, at least for this region.

  15. The circulation of a baroclinic ocean around planetary scale islands with topography

    NASA Astrophysics Data System (ADS)

    Pedlosky, J.

    2010-12-01

    The circulation around planetary-scale islands is considered for an island with a topographic skirt for a stratified ocean. The simplest model of the ocean is a two layer ocean in a circular domain with the island in the center. When the girdling topography is steep, closed geostrophic contours guide the flow in each of the two layers although that guiding occurs at different horizontal locations in each layer. For flows with weak dissipation, modeled as bottom and interfacial friction, explicit formulae are given for the dependence of the streamfunction in each layer on the ambient potential vorticity, f/(layer depth). Numerical model calculations will be presented to supplement the analytical results.

  16. Explicit role of ionic strength in retention behavior of polystyrene latex particles in sedimentation field-flow fractionation: Slip boundary model.

    PubMed

    Rah, Kyunil; Han, Sujeong; Choi, Jaeyeong; Eum, Chul Hun; Lee, Seungho

    2017-12-15

    We investigate an explicit role of the ionic strength in the retention behaviors of polystyrene (PS) latex particles in sedimentation field-flow fractionation (SdFFF) by hinging upon the retention theory recently developed [1] asR=(R o +v b * )/(1+v b * ). Here R is an experimental retention ratio, and R o is the analytical expression of the standard retention theory based on the parabolic flow velocity. The reduced boundary velocityv b * is expressed in terms of the ionic strength I of the carrier liquid as v b * =v b,o * /(1+εI), where v b,o * =0.070and ε=60 mM -1 for all the PS latex systems under investigation. We then apply this to study the explicit ionic strength effect on the retention behaviors of PS beads of 200, 300, 400, and 500nm, respectively. As a primary result, the strong dependence of the retention ratio on the ionic strength can be quantitatively accounted for in an excellent accuracy: The slip effect at the channel surface is significant, particularly when I≲0.5mM, without showing any distinguishable dependence on the specific additives to control I, such as FL-70, SDS, NaNO 3 , and NaN 3 . Based on the present study, we put forward an experimental means to estimate the ionic strength of an aqueous solution using an FFF technique. Copyright © 2017. Published by Elsevier B.V.

  17. Casual Sexual Scripts on the Screen: A Quantitative Content Analysis.

    PubMed

    Timmermans, Elisabeth; Van den Bulck, Jan

    2018-07-01

    While existing content analyses have provided insightful information in terms of contextual factors and frequency of sexual behaviors, not much is known about the relational context in which sexual depictions generally occur. The current study addresses this void by employing content analytic methods to measure the frequency and context of depictions of sexual behavior within nine popular television shows produced in the U.S., while taking into account the type of sexual behavior. The results suggest that, in the analyzed television shows, sexual behaviors within a casual sexual context were almost as frequently shown as sexual behaviors within a committed relationship context. Whereas sexual behaviors within a committed relationship context were mainly limited to passionate kissing, sexual behaviors within a casual sexual context mostly consisted of explicit portrayals of sexual intercourse. Additionally, genre seemed to be an important factor when examining casual sexual television content. The situational comedy genre, for example, had no explicit portrayals of intercourse and mainly portrayed kissing couples within a committed relationship. The comedy drama genre, on the contrary, had the largest proportion of explicit sexual portrayals, usually between casual sexual partners. A second goal of this study was to analyze the portrayals of the typical casual sexual experience script and the typical casual sexual relationship script in which these sexual behaviors often occur. For instance, our analyses revealed that female characters were more likely to initiate casual sex compared to male characters. Moreover, casual sex often occurred between former partners.

  18. Nonlocal gradient corrections to the exchange free energy of an inhomogeneous many-fermion system at finite temperature

    NASA Astrophysics Data System (ADS)

    Geldart, D. J. W.; Dunlap, E.; Glasser, M. L.; Shegelski, Mark R. A.

    1993-10-01

    A general exact result is derived for the coefficient B x( n; T) which determines the first gradient correction to the leading exchange contribution to the free energy at finite temperature of a weakly inhomogeneous extended many fermion system having arbitrary two-body interactions. Explicit analytical results are given in the case of bare Coulomb interactions, and the case of statically screened Coulomb interactions is studied numerically. It is shown that nonanalytical structure leads to different limiting values of B x( n; T) when the inverse screening length and the temperature are both small. Some implications for physical many-electron systems are discussed, including the reasons for discrepancies between the first principles and semiempirical gradient coefficients for atomic exchange energies.

  19. DROMO formulation for planar motions: solution to the Tsien problem

    NASA Astrophysics Data System (ADS)

    Urrutxua, Hodei; Morante, David; Sanjurjo-Rivo, Manuel; Peláez, Jesús

    2015-06-01

    The two-body problem subject to a constant radial thrust is analyzed as a planar motion. The description of the problem is performed in terms of three perturbation methods: DROMO and two others due to Deprit. All of them rely on Hansen's ideal frame concept. An explicit, analytic, closed-form solution is obtained for this problem when the initial orbit is circular (Tsien problem), based on the DROMO special perturbation method, and expressed in terms of elliptic integral functions. The analytical solution to the Tsien problem is later used as a reference to test the numerical performance of various orbit propagation methods, including DROMO and Deprit methods, as well as Cowell and Kustaanheimo-Stiefel methods.

  20. Pressure and wall shear stress in blood hammer - Analytical theory.

    PubMed

    Mei, Chiang C; Jing, Haixiao

    2016-10-01

    We describe an analytical theory of blood hammer in a long and stiffened artery due to sudden blockage. Based on the model of a viscous fluid in laminar flow, we derive explicit expressions of oscillatory pressure and wall shear stress. To examine the effects on local plaque formation we also allow the blood vessel radius to be slightly nonuniform. Without resorting to discrete computation, the asymptotic method of multiple scales is utilized to deal with the sharp contrast of time scales. The effects of plaque and blocking time on blood pressure and wall shear stress are studied. The theory is validated by comparison with existing water hammer experiments. Copyright © 2016. Published by Elsevier Inc.

  1. Nonlinear Effects in Three-minute Oscillations of the Solar Chromosphere. I. An Analytical Nonlinear Solution and Detection of the Second Harmonic

    NASA Astrophysics Data System (ADS)

    Chae, Jongchul; Litvinenko, Yuri E.

    2017-08-01

    The vertical propagation of nonlinear acoustic waves in an isothermal atmosphere is considered. A new analytical solution that describes a finite-amplitude wave of an arbitrary wavelength is obtained. Although the short- and long-wavelength limits were previously considered separately, the new solution describes both limiting cases within a common framework and provides a straightforward way of interpolating between the two limits. Physical features of the nonlinear waves in the chromosphere are described, including the dispersive nature of low-frequency waves, the steepening of the wave profile, and the influence of the gravitational field on wavefront breaking and shock formation. The analytical results suggest that observations of three-minute oscillations in the solar chromosphere may reveal the basic nonlinear effect of oscillations with combination frequencies, superposed on the normal oscillations of the system. Explicit expressions for a second-harmonic signal and the ratio of its amplitude to the fundamental harmonic amplitude are derived. Observational evidence of the second harmonic, obtained with the Fast Imaging Solar Spectrograph, installed at the 1.6 m New Solar Telescope of the Big Bear Observatory, is presented. The presented data are based on the time variations of velocity determined from the Na I D2 and Hα lines.

  2. A First-Principles Analytical Theory for 2D Magnetic Reconnection in Electron and Hall Magnetohydrodynamics

    NASA Astrophysics Data System (ADS)

    Chacon, L.; Simakov, A. N.; Zocco, A.

    2007-12-01

    Although the relevance of two-fluid effects in fast magnetic reconnection is well-known, (J. Birn et al., J. Geophys. Res., 106 (A3), 3715 (2001) a first-principles theory -- akin to Sweet and Parker's in resistive MHD -- has been elusive. Here, we present such a first principles steady-state analytical theory for electron MHD, (L. Chacón, A. N. Simakov, A. Zocco, Phys. Rev. Lett., submitted) and its extension to Hall MHD. (A. N. Simakov, L. Chacón, in preparation) The theory discretizes the extended MHD equations at the reconnection site, leading to a set of time-dependent ODEs. Their steady-state analysis, which describes the system at or around the point of maximum reconnection rate, provides predictions for the scaling of relevant quantities with the dissipation coefficients (e.g, resistivity and hyper-resistivity) and other relevant parameters. In particular, we will show that EMHD admits both elongated and open-X point configurations of the reconnection region, and that the reconnection rate can be shown not to scale explicitly with the dissipation parameters. This result is, to our knowledge, the first analytical confirmation of the possibility of fast magnetic reconnection in EMHD. In Hall MHD, the transition between resistive MHD and EMHD is studied, and scalings with the ion inertial length are obtained.

  3. SoftWAXS: a computational tool for modeling wide-angle X-ray solution scattering from biomolecules.

    PubMed

    Bardhan, Jaydeep; Park, Sanghyun; Makowski, Lee

    2009-10-01

    This paper describes a computational approach to estimating wide-angle X-ray solution scattering (WAXS) from proteins, which has been implemented in a computer program called SoftWAXS. The accuracy and efficiency of SoftWAXS are analyzed for analytically solvable model problems as well as for proteins. Key features of the approach include a numerical procedure for performing the required spherical averaging and explicit representation of the solute-solvent boundary and the surface of the hydration layer. These features allow the Fourier transform of the excluded volume and hydration layer to be computed directly and with high accuracy. This approach will allow future investigation of different treatments of the electron density in the hydration shell. Numerical results illustrate the differences between this approach to modeling the excluded volume and a widely used model that treats the excluded-volume function as a sum of Gaussians representing the individual atomic excluded volumes. Comparison of the results obtained here with those from explicit-solvent molecular dynamics clarifies shortcomings inherent to the representation of solvent as a time-averaged electron-density profile. In addition, an assessment is made of how the calculated scattering patterns depend on input parameters such as the solute-atom radii, the width of the hydration shell and the hydration-layer contrast. These results suggest that obtaining predictive calculations of high-resolution WAXS patterns may require sophisticated treatments of solvent.

  4. Analytical solution for the diffusion of a capacitor discharge generated magnetic field pulse in a conductor

    NASA Astrophysics Data System (ADS)

    Grants, Ilmārs; Bojarevičs, Andris; Gerbeth, Gunter

    2016-06-01

    Powerful forces arise when a pulse of a magnetic field in the order of a few tesla diffuses into a conductor. Such pulses are used in electromagnetic forming, impact welding of dissimilar materials and grain refinement of solidifying alloys. Strong magnetic field pulses are generated by the discharge current of a capacitor bank. We consider analytically the penetration of such pulse into a conducting half-space. Besides the exact solution we obtain two simple self-similar approximate solutions for two sequential stages of the initial transient. Furthermore, a general solution is provided for the external field given as a power series of time. Each term of this solution represents a self-similar function for which we obtain an explicit expression. The validity range of various approximate analytical solutions is evaluated by comparison to the exact solution.

  5. High-temperature ratchets with sawtooth potentials

    NASA Astrophysics Data System (ADS)

    Rozenbaum, Viktor M.; Shapochkina, Irina V.; Sheu, Sheh-Yi; Yang, Dah-Yen; Lin, Sheng Hsien

    2016-11-01

    The concept of the effective potential is suggested as an efficient instrument to get a uniform analytical description of stochastic high-temperature on-off flashing and rocking ratchets. The analytical representation for the average particle velocity, obtained within this technique, allows description of ratchets with sharp potentials (and potentials with jumps in particular). For sawtooth potentials, the explicit analytical expressions for the average velocity of on-off flashing and rocking ratchets valid for arbitrary frequencies of potential energy fluctuations are derived; the difference in their high-frequency asymptotics is explored for the smooth and cusped profiles, and profiles with jumps. The origin of the difference as well as the appearance of the jump behavior in ratchet characteristics are interpreted in terms of self-similar universal solutions which give the continuous description of the effect. It is shown how the jump behavior in motor characteristics arises from the competition between the characteristic times of the system.

  6. Analytical mass formula and nuclear surface properties in the ETF approximation. Part II: asymmetric nuclei

    NASA Astrophysics Data System (ADS)

    Aymard, François; Gulminelli, Francesca; Margueron, Jérôme

    2016-08-01

    We have recently addressed the problem of the determination of the nuclear surface energy for symmetric nuclei in the framework of the extended Thomas-Fermi (ETF) approximation using Skyrme functionals. We presently extend this formalism to the case of asymmetric nuclei and the question of the surface symmetry energy. We propose an approximate expression for the diffuseness and the surface energy. These quantities are analytically related to the parameters of the energy functional. In particular, the influence of the different equation of state parameters can be explicitly quantified. Detailed analyses of the different energy components (local/non-local, isoscalar/isovector, surface/curvature and higher order) are also performed. Our analytical solution of the ETF integral improves previous models and leads to a precision of better than 200 keV per nucleon in the determination of the nuclear binding energy for dripline nuclei.

  7. Analytic theory of orbit contraction

    NASA Technical Reports Server (NTRS)

    Vinh, N. X.; Longuski, J. M.; Busemann, A.; Culp, R. D.

    1977-01-01

    The motion of a satellite in orbit, subject to atmospheric force and the motion of a reentry vehicle are governed by gravitational and aerodynamic forces. This suggests the derivation of a uniform set of equations applicable to both cases. For the case of satellite motion, by a proper transformation and by the method of averaging, a technique appropriate for long duration flight, the classical nonlinear differential equation describing the contraction of the major axis is derived. A rigorous analytic solution is used to integrate this equation with a high degree of accuracy, using Poincare's method of small parameters and Lagrange's expansion to explicitly express the major axis as a function of the eccentricity. The solution is uniformly valid for moderate and small eccentricities. For highly eccentric orbits, the asymptotic equation is derived directly from the general equation. Numerical solutions were generated to display the accuracy of the analytic theory.

  8. Equilibrium Solutions of the Logarithmic Hamiltonian Leapfrog for the N-body Problem

    NASA Astrophysics Data System (ADS)

    Minesaki, Yukitaka

    2018-04-01

    We prove that a second-order logarithmic Hamiltonian leapfrog for the classical general N-body problem (CGNBP) designed by Mikkola and Tanikawa and some higher-order logarithmic Hamiltonian methods based on symmetric multicompositions of the logarithmic algorithm exactly reproduce the orbits of elliptic relative equilibrium solutions in the original CGNBP. These methods are explicit symplectic methods. Before this proof, only some implicit discrete-time CGNBPs proposed by Minesaki had been analytically shown to trace the orbits of elliptic relative equilibrium solutions. The proof is therefore the first existence proof for explicit symplectic methods. Such logarithmic Hamiltonian methods with a variable time step can also precisely retain periodic orbits in the classical general three-body problem, which generic numerical methods with a constant time step cannot do.

  9. Explicit solutions from eigenfunction symmetry of the Korteweg-de Vries equation.

    PubMed

    Hu, Xiao-Rui; Lou, Sen-Yue; Chen, Yong

    2012-05-01

    In nonlinear science, it is very difficult to find exact interaction solutions among solitons and other kinds of complicated waves such as cnoidal waves and Painlevé waves. Actually, even if for the most well-known prototypical models such as the Kortewet-de Vries (KdV) equation and the Kadomtsev-Petviashvili (KP) equation, this kind of problem has not yet been solved. In this paper, the explicit analytic interaction solutions between solitary waves and cnoidal waves are obtained through the localization procedure of nonlocal symmetries which are related to Darboux transformation for the well-known KdV equation. The same approach also yields some other types of interaction solutions among different types of solutions such as solitary waves, rational solutions, Bessel function solutions, and/or general Painlevé II solutions.

  10. On sequential data assimilation for scalar macroscopic traffic flow models

    NASA Astrophysics Data System (ADS)

    Blandin, Sébastien; Couque, Adrien; Bayen, Alexandre; Work, Daniel

    2012-09-01

    We consider the problem of sequential data assimilation for transportation networks using optimal filtering with a scalar macroscopic traffic flow model. Properties of the distribution of the uncertainty on the true state related to the specific nonlinearity and non-differentiability inherent to macroscopic traffic flow models are investigated, derived analytically and analyzed. We show that nonlinear dynamics, by creating discontinuities in the traffic state, affect the performances of classical filters and in particular that the distribution of the uncertainty on the traffic state at shock waves is a mixture distribution. The non-differentiability of traffic dynamics around stationary shock waves is also proved and the resulting optimality loss of the estimates is quantified numerically. The properties of the estimates are explicitly studied for the Godunov scheme (and thus the Cell-Transmission Model), leading to specific conclusions about their use in the context of filtering, which is a significant contribution of this article. Analytical proofs and numerical tests are introduced to support the results presented. A Java implementation of the classical filters used in this work is available on-line at http://traffic.berkeley.edu for facilitating further efforts on this topic and fostering reproducible research.

  11. Driver fatigue and highway driving: a simulator study.

    PubMed

    Ting, Ping-Huang; Hwang, Jiun-Ren; Doong, Ji-Liang; Jeng, Ming-Chang

    2008-06-09

    Long duration of driving is a significant cause of fatigue-related accidents on motorways or major roadways. The fatigue caused by driving for extended periods acutely impairs driver alertness and performance and can compromise transportation safety. This study quantitatively measured the progression of driver fatigue and identified the conservative safe duration of continuous highway driving. Thirty young male subjects were analyzed during 90 min of laboratory-simulated highway driving. Sleepiness ratings (SSS) and reaction time (RT) tests were used to assess impairment of driver alertness and vigilance. Additionally, various measures of driving performance recorded throughout the experiment were used to measure temporal deterioration of driver performance from alert to fatigued using principal component analysis (PCA). The analytical results revealed that SSS scores, reaction times (RTs) and unstable driving performance significantly increased over time, indicating that excessive driving time is a significant fatigue factor and potential cause of fatigue-related accidents. Moreover, the analytical results indicated that 80 min was the safe limit for monotonous highway driving. Based on the experimental findings of this study, public awareness of the adverse affects of driver fatigue during long-distance driving should be enhanced. This study provides explicit information of fatigue development that can be used to prevent fatigue-related accidents.

  12. Spatially explicit spectral analysis of point clouds and geospatial data

    USGS Publications Warehouse

    Buscombe, Daniel D.

    2015-01-01

    The increasing use of spatially explicit analyses of high-resolution spatially distributed data (imagery and point clouds) for the purposes of characterising spatial heterogeneity in geophysical phenomena necessitates the development of custom analytical and computational tools. In recent years, such analyses have become the basis of, for example, automated texture characterisation and segmentation, roughness and grain size calculation, and feature detection and classification, from a variety of data types. In this work, much use has been made of statistical descriptors of localised spatial variations in amplitude variance (roughness), however the horizontal scale (wavelength) and spacing of roughness elements is rarely considered. This is despite the fact that the ratio of characteristic vertical to horizontal scales is not constant and can yield important information about physical scaling relationships. Spectral analysis is a hitherto under-utilised but powerful means to acquire statistical information about relevant amplitude and wavelength scales, simultaneously and with computational efficiency. Further, quantifying spatially distributed data in the frequency domain lends itself to the development of stochastic models for probing the underlying mechanisms which govern the spatial distribution of geological and geophysical phenomena. The software packagePySESA (Python program for Spatially Explicit Spectral Analysis) has been developed for generic analyses of spatially distributed data in both the spatial and frequency domains. Developed predominantly in Python, it accesses libraries written in Cython and C++ for efficiency. It is open source and modular, therefore readily incorporated into, and combined with, other data analysis tools and frameworks with particular utility for supporting research in the fields of geomorphology, geophysics, hydrography, photogrammetry and remote sensing. The analytical and computational structure of the toolbox is described, and its functionality illustrated with an example of a high-resolution bathymetric point cloud data collected with multibeam echosounder.

  13. Exploring a multi-scale method for molecular simulation in continuum solvent model: Explicit simulation of continuum solvent as an incompressible fluid.

    PubMed

    Xiao, Li; Luo, Ray

    2017-12-07

    We explored a multi-scale algorithm for the Poisson-Boltzmann continuum solvent model for more robust simulations of biomolecules. In this method, the continuum solvent/solute interface is explicitly simulated with a numerical fluid dynamics procedure, which is tightly coupled to the solute molecular dynamics simulation. There are multiple benefits to adopt such a strategy as presented below. At this stage of the development, only nonelectrostatic interactions, i.e., van der Waals and hydrophobic interactions, are included in the algorithm to assess the quality of the solvent-solute interface generated by the new method. Nevertheless, numerical challenges exist in accurately interpolating the highly nonlinear van der Waals term when solving the finite-difference fluid dynamics equations. We were able to bypass the challenge rigorously by merging the van der Waals potential and pressure together when solving the fluid dynamics equations and by considering its contribution in the free-boundary condition analytically. The multi-scale simulation method was first validated by reproducing the solute-solvent interface of a single atom with analytical solution. Next, we performed the relaxation simulation of a restrained symmetrical monomer and observed a symmetrical solvent interface at equilibrium with detailed surface features resembling those found on the solvent excluded surface. Four typical small molecular complexes were then tested, both volume and force balancing analyses showing that these simple complexes can reach equilibrium within the simulation time window. Finally, we studied the quality of the multi-scale solute-solvent interfaces for the four tested dimer complexes and found that they agree well with the boundaries as sampled in the explicit water simulations.

  14. Interactions Between Mathematics and Physics: The History of the Concept of Function—Teaching with and About Nature of Mathematics

    NASA Astrophysics Data System (ADS)

    Kjeldsen, Tinne Hoff; Lützen, Jesper

    2015-07-01

    In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another variable. The change was required when mathematicians discovered that analytic expressions were not sufficient to represent physical phenomena such as the vibration of a string (Euler) and heat conduction (Fourier and Dirichlet). The introduction of generalized functions or distributions is shown to stem partly from the development of new theories of physics such as electrical engineering and quantum mechanics that led to the use of improper functions such as the delta function that demanded a proper foundation. We argue that the development of student understanding of mathematics and its nature is enhanced by embedding mathematical concepts and theories, within an explicit-reflective framework, into a rich historical context emphasizing its interaction with other disciplines such as physics. Students recognize and become engaged with meta-discursive rules governing mathematics. Mathematics teachers can thereby teach inquiry in mathematics as it occurs in the sciences, as mathematical practice aimed at obtaining new mathematical knowledge. We illustrate such a historical teaching and learning of mathematics within an explicit and reflective framework by two examples of student-directed, problem-oriented project work following the Roskilde Model, in which the connection to physics is explicit and provides a learning space where the nature of mathematics and mathematical practices are linked to natural science.

  15. On Nomological Validity and Auxiliary Assumptions: The Importance of Simultaneously Testing Effects in Social Cognitive Theories Applied to Health Behavior and Some Guidelines

    PubMed Central

    Hagger, Martin S.; Gucciardi, Daniel F.; Chatzisarantis, Nikos L. D.

    2017-01-01

    Tests of social cognitive theories provide informative data on the factors that relate to health behavior, and the processes and mechanisms involved. In the present article, we contend that tests of social cognitive theories should adhere to the principles of nomological validity, defined as the degree to which predictions in a formal theoretical network are confirmed. We highlight the importance of nomological validity tests to ensure theory predictions can be disconfirmed through observation. We argue that researchers should be explicit on the conditions that lead to theory disconfirmation, and identify any auxiliary assumptions on which theory effects may be conditional. We contend that few researchers formally test the nomological validity of theories, or outline conditions that lead to model rejection and the auxiliary assumptions that may explain findings that run counter to hypotheses, raising potential for ‘falsification evasion.’ We present a brief analysis of studies (k = 122) testing four key social cognitive theories in health behavior to illustrate deficiencies in reporting theory tests and evaluations of nomological validity. Our analysis revealed that few articles report explicit statements suggesting that their findings support or reject the hypotheses of the theories tested, even when findings point to rejection. We illustrate the importance of explicit a priori specification of fundamental theory hypotheses and associated auxiliary assumptions, and identification of the conditions which would lead to rejection of theory predictions. We also demonstrate the value of confirmatory analytic techniques, meta-analytic structural equation modeling, and Bayesian analyses in providing robust converging evidence for nomological validity. We provide a set of guidelines for researchers on how to adopt and apply the nomological validity approach to testing health behavior models. PMID:29163307

  16. Charge Transport in Spiro-OMeTAD Investigated through Space-Charge-Limited Current Measurements

    NASA Astrophysics Data System (ADS)

    Röhr, Jason A.; Shi, Xingyuan; Haque, Saif A.; Kirchartz, Thomas; Nelson, Jenny

    2018-04-01

    Extracting charge-carrier mobilities for organic semiconductors from space-charge-limited conduction measurements is complicated in practice by nonideal factors such as trapping in defects and injection barriers. Here, we show that by allowing the bandlike charge-carrier mobility, trap characteristics, injection barrier heights, and the shunt resistance to vary in a multiple-trapping drift-diffusion model, a numerical fit can be obtained to the entire current density-voltage curve from experimental space-charge-limited current measurements on both symmetric and asymmetric 2 ,2',7 ,7' -tetrakis(N ,N -di-4-methoxyphenylamine)-9 ,9' -spirobifluorene (spiro-OMeTAD) single-carrier devices. This approach yields a bandlike mobility that is more than an order of magnitude higher than the effective mobility obtained using analytical approximations, such as the Mott-Gurney law and the moving-electrode equation. It is also shown that where these analytical approximations require a temperature-dependent effective mobility to achieve fits, the numerical model can yield a temperature-, electric-field-, and charge-carrier-density-independent mobility. Finally, we present an analytical model describing trap-limited current flow through a semiconductor in a symmetric single-carrier device. We compare the obtained charge-carrier mobility and trap characteristics from this analytical model to the results from the numerical model, showing excellent agreement. This work shows the importance of accounting for traps and injection barriers explicitly when analyzing current density-voltage curves from space-charge-limited current measurements.

  17. Investigating Compaction by Intergranular Pressure Solution Using the Discrete Element Method

    NASA Astrophysics Data System (ADS)

    van den Ende, M. P. A.; Marketos, G.; Niemeijer, A. R.; Spiers, C. J.

    2018-01-01

    Intergranular pressure solution creep is an important deformation mechanism in the Earth's crust. The phenomenon has been frequently studied and several analytical models have been proposed that describe its constitutive behavior. These models require assumptions regarding the geometry of the aggregate and the grain size distribution in order to solve for the contact stresses and often neglect shear tractions. Furthermore, analytical models tend to overestimate experimental compaction rates at low porosities, an observation for which the underlying mechanisms remain to be elucidated. Here we present a conceptually simple, 3-D discrete element method (DEM) approach for simulating intergranular pressure solution creep that explicitly models individual grains, relaxing many of the assumptions that are required by analytical models. The DEM model is validated against experiments by direct comparison of macroscopic sample compaction rates. Furthermore, the sensitivity of the overall DEM compaction rate to the grain size and applied stress is tested. The effects of the interparticle friction and of a distributed grain size on macroscopic strain rates are subsequently investigated. Overall, we find that the DEM model is capable of reproducing realistic compaction behavior, and that the strain rates produced by the model are in good agreement with uniaxial compaction experiments. Characteristic features, such as the dependence of the strain rate on grain size and applied stress, as predicted by analytical models, are also observed in the simulations. DEM results show that interparticle friction and a distributed grain size affect the compaction rates by less than half an order of magnitude.

  18. Extension of the KLI approximation toward the exact optimized effective potential.

    PubMed

    Iafrate, G J; Krieger, J B

    2013-03-07

    The integral equation for the optimized effective potential (OEP) is utilized in a compact form from which an accurate OEP solution for the spin-unrestricted exchange-correlation potential, Vxcσ, is obtained for any assumed orbital-dependent exchange-correlation energy functional. The method extends beyond the Krieger-Li-Iafrate (KLI) approximation toward the exact OEP result. The compact nature of the OEP equation arises by replacing the integrals involving the Green's function terms in the traditional OEP equation by an equivalent first-order perturbation theory wavefunction often referred to as the "orbital shift" function. Significant progress is then obtained by solving the equation for the first order perturbation theory wavefunction by use of Dalgarno functions which are determined from well known methods of partial differential equations. The use of Dalgarno functions circumvents the need to explicitly address the Green's functions and the associated problems with "sum over states" numerics; as well, the Dalgarno functions provide ease in dealing with inherent singularities arising from the origin and the zeros of the occupied orbital wavefunctions. The Dalgarno approach for finding a solution to the OEP equation is described herein, and a detailed illustrative example is presented for the special case of a spherically symmetric exchange-correlation potential. For the case of spherical symmetry, the relevant Dalgarno function is derived by direct integration of the appropriate radial equation while utilizing a user friendly method which explicitly treats the singular behavior at the origin and at the nodal singularities arising from the zeros of the occupied states. The derived Dalgarno function is shown to be an explicit integral functional of the exact OEP Vxcσ, thus allowing for the reduction of the OEP equation to a self-consistent integral equation for the exact exchange-correlation potential; the exact solution to this integral equation can be determined by iteration with the natural zeroth order correction given by the KLI exchange-correlation potential. Explicit analytic results are provided to illustrate the first order iterative correction beyond the KLI approximation. The derived correction term to the KLI potential explicitly involves spatially weighted products of occupied orbital densities in any assumed orbital-dependent exchange-correlation energy functional; as well, the correction term is obtained with no adjustable parameters. Moreover, if the equation for the exact optimized effective potential is further iterated, one can obtain the OEP as accurately as desired.

  19. Extension of the KLI approximation toward the exact optimized effective potential

    NASA Astrophysics Data System (ADS)

    Iafrate, G. J.; Krieger, J. B.

    2013-03-01

    The integral equation for the optimized effective potential (OEP) is utilized in a compact form from which an accurate OEP solution for the spin-unrestricted exchange-correlation potential, Vxcσ, is obtained for any assumed orbital-dependent exchange-correlation energy functional. The method extends beyond the Krieger-Li-Iafrate (KLI) approximation toward the exact OEP result. The compact nature of the OEP equation arises by replacing the integrals involving the Green's function terms in the traditional OEP equation by an equivalent first-order perturbation theory wavefunction often referred to as the "orbital shift" function. Significant progress is then obtained by solving the equation for the first order perturbation theory wavefunction by use of Dalgarno functions which are determined from well known methods of partial differential equations. The use of Dalgarno functions circumvents the need to explicitly address the Green's functions and the associated problems with "sum over states" numerics; as well, the Dalgarno functions provide ease in dealing with inherent singularities arising from the origin and the zeros of the occupied orbital wavefunctions. The Dalgarno approach for finding a solution to the OEP equation is described herein, and a detailed illustrative example is presented for the special case of a spherically symmetric exchange-correlation potential. For the case of spherical symmetry, the relevant Dalgarno function is derived by direct integration of the appropriate radial equation while utilizing a user friendly method which explicitly treats the singular behavior at the origin and at the nodal singularities arising from the zeros of the occupied states. The derived Dalgarno function is shown to be an explicit integral functional of the exact OEP Vxcσ, thus allowing for the reduction of the OEP equation to a self-consistent integral equation for the exact exchange-correlation potential; the exact solution to this integral equation can be determined by iteration with the natural zeroth order correction given by the KLI exchange-correlation potential. Explicit analytic results are provided to illustrate the first order iterative correction beyond the KLI approximation. The derived correction term to the KLI potential explicitly involves spatially weighted products of occupied orbital densities in any assumed orbital-dependent exchange-correlation energy functional; as well, the correction term is obtained with no adjustable parameters. Moreover, if the equation for the exact optimized effective potential is further iterated, one can obtain the OEP as accurately as desired.

  20. Traveling waves and conservation laws for highly nonlinear wave equations modeling Hertz chains

    NASA Astrophysics Data System (ADS)

    Przedborski, Michelle; Anco, Stephen C.

    2017-09-01

    A highly nonlinear, fourth-order wave equation that models the continuum theory of long wavelength pulses in weakly compressed, homogeneous, discrete chains with a general power-law contact interaction is studied. For this wave equation, all solitary wave solutions and all nonlinear periodic wave solutions, along with all conservation laws, are derived. The solutions are explicitly parameterized in terms of the asymptotic value of the wave amplitude in the case of solitary waves and the peak of the wave amplitude in the case of nonlinear periodic waves. All cases in which the solution expressions can be stated in an explicit analytic form using elementary functions are worked out. In these cases, explicit expressions for the total energy and total momentum for all solutions are obtained as well. The derivation of the solutions uses the conservation laws combined with an energy analysis argument to reduce the wave equation directly to a separable first-order differential equation that determines the wave amplitude in terms of the traveling wave variable. This method can be applied more generally to other highly nonlinear wave equations.

  1. Using social autopsy to understand maternal, newborn, and child mortality in low-resource settings: a systematic review of the literature

    PubMed Central

    Moyer, Cheryl A.; Johnson, Cassidy; Kaselitz, Elizabeth; Aborigo, Raymond

    2017-01-01

    ABSTRACT Background: Social, cultural, and behavioral factors are often potent upstream contributors to maternal, neonatal, and child mortality, especially in low- and middle-income countries (LMICs). Social autopsy is one method of identifying the impact of such factors, yet it is unclear how social autopsy methods are being used in LMICs. Objective: This study aimed to identify the most common social autopsy instruments, describe overarching findings across populations and geography, and identify gaps in the existing social autopsy literature. Methods: A systematic search of the peer-reviewed literature from 2005 to 2016 was conducted. Studies were included if they were conducted in an LMIC, focused on maternal/neonatal/infant/child health, reported on the results of original research, and explicitly mentioned the use of a social autopsy tool. Results: Sixteen articles out of 1950 citations were included, representing research conducted in 11 countries. Five different tools were described, with two primary conceptual frameworks used to guide analysis: Pathway to Survival and Three Delays models. Studies varied in methods for identifying deaths, and recall periods for respondents ranged from 6 weeks to 5+ years. Across studies, recognition of danger signs appeared to be high, while subsequent care-seeking was inconsistent. Cost, distance to facility, and transportation issues were frequently cited barriers to care-seeking, however, additional barriers were reported that varied by location. Gaps in the social autopsy literature include the lack of: harmonized tools and analytical methods that allow for cross-study comparisons, discussion of complexity of decision making for care seeking, qualitative narratives that address inconsistencies in responses, and the explicit inclusion of perspectives from husbands and fathers. Conclusion: Despite the nascence of the field, research across 11 countries has included social autopsy methods, using a variety of tools, sampling methods, and analytical frameworks to determine how social factors impact maternal, neonatal, and child health outcomes. PMID:29261449

  2. Cumulative biological impacts framework for solar energy projects in the California Desert

    USGS Publications Warehouse

    Davis, Frank W.; Kreitler, Jason R.; Soong, Oliver; Stoms, David M.; Dashiell, Stephanie; Hannah, Lee; Wilkinson, Whitney; Dingman, John

    2013-01-01

    This project developed analytical approaches, tools and geospatial data to support conservation planning for renewable energy development in the California deserts. Research focused on geographical analysis to avoid, minimize and mitigate the cumulative biological effects of utility-scale solar energy development. A hierarchical logic model was created to map the compatibility of new solar energy projects with current biological conservation values. The research indicated that the extent of compatible areas is much greater than the estimated land area required to achieve 2040 greenhouse gas reduction goals. Species distribution models were produced for 65 animal and plant species that were of potential conservation significance to the Desert Renewable Energy Conservation Plan process. These models mapped historical and projected future habitat suitability using 270 meter resolution climate grids. The results were integrated into analytical frameworks to locate potential sites for offsetting project impacts and evaluating the cumulative effects of multiple solar energy projects. Examples applying these frameworks in the Western Mojave Desert ecoregion show the potential of these publicly-available tools to assist regional planning efforts. Results also highlight the necessity to explicitly consider projected land use change and climate change when prioritizing areas for conservation and mitigation offsets. Project data, software and model results are all available online.

  3. Representation of the Coulomb Matrix Elements by Means of Appell Hypergeometric Function F 2

    NASA Astrophysics Data System (ADS)

    Bentalha, Zine el abidine

    2018-06-01

    Exact analytical representation for the Coulomb matrix elements by means of Appell's double series F 2 is derived. The finite sum obtained for the Appell function F 2 allows us to evaluate explicitly the matrix elements of the two-body Coulomb interaction in the lowest Landau level. An application requiring the matrix elements of Coulomb potential in quantum Hall effect regime is presented.

  4. Subsurface Electromagnetic Induction Imaging for Unexploded Ordnance Detection

    DTIC Science & Technology

    2012-01-01

    Baum, 1999; Pasion and Oldenburg, 2001). The EMI- response problem has been solved analytically for spheroids (Ao et al., 2002; Barrowes et al., 2004...components. We also have made explicit the fact that the polarizabilities are always positive ( Pasion et al., 2008); we impose this constraint in the...Wiley-Blackwell, Chichester, UK. Pasion , L.R., Oldenburg, D.W., 2001. A discrimination algorithm for UXO using time- domain electromagnetic induction

  5. Solutions for the diurnally forced advection-diffusion equation to estimate bulk fluid velocity and diffusivity in streambeds from temperature time series

    Treesearch

    Charles H. Luce; Daniele Tonina; Frank Gariglio; Ralph Applebee

    2013-01-01

    Work over the last decade has documented methods for estimating fluxes between streams and streambeds from time series of temperature at two depths in the streambed. We present substantial extension to the existing theory and practice of using temperature time series to estimate streambed water fluxes and thermal properties, including (1) a new explicit analytical...

  6. Fluctuations in time intervals of financial data from the view point of the Gini index

    NASA Astrophysics Data System (ADS)

    Sazuka, Naoya; Inoue, Jun-ichi

    2007-09-01

    We propose an approach to explain fluctuations in time intervals of financial markets data from the view-point of the Gini index. We show the explicit form of the Gini index for a Weibull distribution: A good candidate to describe the first passage time of foreign exchange rate. The analytical expression of the Gini index compares well with the value obtained from empirical data.

  7. Using Multiple Lenses to Examine the Development of Beginning Biology Teachers' Pedagogical Content Knowledge for Teaching Natural Selection Simulations

    NASA Astrophysics Data System (ADS)

    Sickel, Aaron J.; Friedrichsen, Patricia

    2018-02-01

    Pedagogical content knowledge (PCK) has become a useful construct to examine science teacher learning. Yet, researchers conceptualize PCK development in different ways. The purpose of this longitudinal study was to use three analytic lenses to understand the development of three beginning biology teachers' PCK for teaching natural selection simulations. We observed three early-career biology teachers as they taught natural selection in their respective school contexts over two consecutive years. Data consisted of six interviews with each participant. Using the PCK model developed by Magnusson et al. (1999), we examined topic-specific PCK development utilizing three different lenses: (1) expansion of knowledge within an individual knowledge base, (2) integration of knowledge across knowledge bases, and (3) knowledge that explicitly addressed core concepts of natural selection. We found commonalities across the participants, yet each lens was also useful to understand the influence of different factors (e.g., orientation, subject matter preparation, and the idiosyncratic nature of teacher knowledge) on PCK development. This multi-angle approach provides implications for considering the quality of beginning science teachers' knowledge and future research on PCK development. We conclude with an argument that explicitly communicating lenses used to understand PCK development will help the research community compare analytic approaches and better understand the nature of science teacher learning.

  8. Numerically stable formulas for a particle-based explicit exponential integrator

    NASA Astrophysics Data System (ADS)

    Nadukandi, Prashanth

    2015-05-01

    Numerically stable formulas are presented for the closed-form analytical solution of the X-IVAS scheme in 3D. This scheme is a state-of-the-art particle-based explicit exponential integrator developed for the particle finite element method. Algebraically, this scheme involves two steps: (1) the solution of tangent curves for piecewise linear vector fields defined on simplicial meshes and (2) the solution of line integrals of piecewise linear vector-valued functions along these tangent curves. Hence, the stable formulas presented here have general applicability, e.g. exact integration of trajectories in particle-based (Lagrangian-type) methods, flow visualization and computer graphics. The Newton form of the polynomial interpolation definition is used to express exponential functions of matrices which appear in the analytical solution of the X-IVAS scheme. The divided difference coefficients in these expressions are defined in a piecewise manner, i.e. in a prescribed neighbourhood of removable singularities their series approximations are computed. An optimal series approximation of divided differences is presented which plays a critical role in this methodology. At least ten significant decimal digits in the formula computations are guaranteed to be exact using double-precision floating-point arithmetic. The worst case scenarios occur in the neighbourhood of removable singularities found in fourth-order divided differences of the exponential function.

  9. Energy and energy gradient matrix elements with N-particle explicitly correlated complex Gaussian basis functions with L =1

    NASA Astrophysics Data System (ADS)

    Bubin, Sergiy; Adamowicz, Ludwik

    2008-03-01

    In this work we consider explicitly correlated complex Gaussian basis functions for expanding the wave function of an N-particle system with the L =1 total orbital angular momentum. We derive analytical expressions for various matrix elements with these basis functions including the overlap, kinetic energy, and potential energy (Coulomb interaction) matrix elements, as well as matrix elements of other quantities. The derivatives of the overlap, kinetic, and potential energy integrals with respect to the Gaussian exponential parameters are also derived and used to calculate the energy gradient. All the derivations are performed using the formalism of the matrix differential calculus that facilitates a way of expressing the integrals in an elegant matrix form, which is convenient for the theoretical analysis and the computer implementation. The new method is tested in calculations of two systems: the lowest P state of the beryllium atom and the bound P state of the positronium molecule (with the negative parity). Both calculations yielded new, lowest-to-date, variational upper bounds, while the number of basis functions used was significantly smaller than in previous studies. It was possible to accomplish this due to the use of the analytic energy gradient in the minimization of the variational energy.

  10. Energy and energy gradient matrix elements with N-particle explicitly correlated complex Gaussian basis functions with L=1.

    PubMed

    Bubin, Sergiy; Adamowicz, Ludwik

    2008-03-21

    In this work we consider explicitly correlated complex Gaussian basis functions for expanding the wave function of an N-particle system with the L=1 total orbital angular momentum. We derive analytical expressions for various matrix elements with these basis functions including the overlap, kinetic energy, and potential energy (Coulomb interaction) matrix elements, as well as matrix elements of other quantities. The derivatives of the overlap, kinetic, and potential energy integrals with respect to the Gaussian exponential parameters are also derived and used to calculate the energy gradient. All the derivations are performed using the formalism of the matrix differential calculus that facilitates a way of expressing the integrals in an elegant matrix form, which is convenient for the theoretical analysis and the computer implementation. The new method is tested in calculations of two systems: the lowest P state of the beryllium atom and the bound P state of the positronium molecule (with the negative parity). Both calculations yielded new, lowest-to-date, variational upper bounds, while the number of basis functions used was significantly smaller than in previous studies. It was possible to accomplish this due to the use of the analytic energy gradient in the minimization of the variational energy.

  11. Euclidean mirrors: enhanced vacuum decay from reflected instantons

    NASA Astrophysics Data System (ADS)

    Akal, Ibrahim; Moortgat-Pick, Gudrid

    2018-05-01

    We study the tunnelling of virtual matter–antimatter pairs from the quantum vacuum in the presence of a spatially uniform, time-dependent electric background composed of a strong, slow field superimposed with a weak, rapid field. After analytic continuation to Euclidean spacetime, we obtain from the instanton equations two critical points. While one of them is the closing point of the instanton path, the other serves as an Euclidean mirror which reflects and squeezes the instanton. It is this reflection and shrinking which is responsible for an enormous enhancement of the vacuum pair production rate. We discuss how important features of two different mechanisms can be analysed and understood via such a rotation in the complex plane. (a) Consistent with previous studies, we first discuss the standard assisted mechanism with a static strong field and certain weak fields with a distinct pole structure in order to show that the reflection takes place exactly at the poles. We also discuss the effect of possible sub-cycle structures. We extend this reflection picture then to weak fields which have no poles present and illustrate the effective reflections with explicit examples. An additional field strength dependence for the rate occurs in such cases. We analytically compute the characteristic threshold for the assisted mechanism given by the critical combined Keldysh parameter. We discuss significant differences between these two types of fields. For various backgrounds, we present the contributing instantons and perform analytical computations for the corresponding rates treating both fields nonperturbatively. (b) In addition, we also study the case with a nonstatic strong field which gives rise to the assisted dynamical mechanism. For different strong field profiles we investigate the impact on the critical combined Keldysh parameter. As an explicit example, we analytically compute the rate by employing the exact reflection points. The validity of the predictions for both mechanisms is confirmed by numerical computations.

  12. Growth of nano-dots on the grazing incidence mirror surface under FEL irradiation: analytic approach to modeling

    NASA Astrophysics Data System (ADS)

    Kozhevnikov, I. V.; Buzmakov, A. V.; Siewert, F.; Tiedtke, K.; Störmer, M.; Samoylova, L.; Sinn, H.

    2017-05-01

    Simple analytic equation is deduced to explain new physical phenomenon detected experimentally: growth of nano-dots (40-55 nm diameter, 8-13 nm height, 9.4 dots/μm2 surface density) on the grazing incidence mirror surface under the three years irradiation by the free electron laser FLASH (5-45 nm wavelength, 3 degrees grazing incidence angle). The growth model is based on the assumption that the growth of nano-dots is caused by polymerization of incoming hydrocarbon molecules under the action of incident photons directly or photoelectrons knocked out from a mirror surface. The key feature of our approach consists in that we take into account the radiation intensity variation nearby a mirror surface in an explicit form, because the polymerization probability is proportional to it. We demonstrate that the simple analytic approach allows to explain all phenomena observed in experiment and to predict new effects. In particular, we show that the nano-dots growth depends crucially on the grazing angle of incoming beam and its intensity: growth of nano-dots is observed in the limited from above and below intervals of the grazing angle and the radiation intensity. Decrease in the grazing angle by 1 degree only (from 3 to 2 degree) may result in a strong suppression of nanodots growth and their total disappearing. Similarly, decrease in the radiation intensity by several times (replacement of free electron laser by synchrotron) results also in disappearing of nano-dots growth.

  13. Asymptotic solutions for flow in microchannels with ridged walls and arbitrary meniscus protrusion

    NASA Astrophysics Data System (ADS)

    Kirk, Toby

    2017-11-01

    Flow over structured surfaces exhibiting apparent slip, such as parallel ridges, have received much attention experimentally and numerically, but analytical and asymptotic solutions that account for the microstructure have so far been limited to unbounded geometries such as shear-driven flows. Analysis for channel flows has been limited to (close to) flat interfaces spanning the grooves between ridges, but in applications the interfaces (menisci) can highly protrude and have a significant impact on the apparent slip. In this presentation, we consider pressure-driven flow through a microchannel with longitudinal ridges patterning one or both walls. With no restriction on the meniscus protrusion, we develop explicit formulae for the slip length using a formal matched asymptotic expansion. Assuming the ratio of channel height to ridge period is large, the periodicity is confined to an inner layer close to the ridges, and the expansion is found to all algebraic orders. As a result, the error is exponentially small and, under a further ``diluteness'' assumption, the explicit formulae are compared to finite element solutions. They are found to have a very wide range of validity in channel height (even when the menisci can touch the opposing wall) and so are useful for practitioners.

  14. Computational Prediction of Shock Ignition Thresholds and Ignition Probability of Polymer-Bonded Explosives

    NASA Astrophysics Data System (ADS)

    Wei, Yaochi; Kim, Seokpum; Horie, Yasuyuki; Zhou, Min

    2017-06-01

    A computational approach is developed to predict the probabilistic ignition thresholds of polymer-bonded explosives (PBXs). The simulations explicitly account for microstructure, constituent properties, and interfacial responses and capture processes responsible for the development of hotspots and damage. The specific damage mechanisms considered include viscoelasticity, viscoplasticity, fracture, post-fracture contact, frictional heating, and heat conduction. The probabilistic analysis uses sets of statistically similar microstructure samples to mimic relevant experiments for statistical variations of material behavior due to inherent material heterogeneities. The ignition thresholds and corresponding ignition probability maps are predicted for PBX 9404 and PBX 9501 for the impact loading regime of Up = 200 --1200 m/s. James and Walker-Wasley relations are utilized to establish explicit analytical expressions for the ignition probability as a function of load intensities. The predicted results are in good agreement with available experimental measurements. The capability to computationally predict the macroscopic response out of material microstructures and basic constituent properties lends itself to the design of new materials and the analysis of existing materials. The authors gratefully acknowledge the support from Air Force Office of Scientific Research (AFOSR) and the Defense Threat Reduction Agency (DTRA).

  15. A Statistical Physicist's Approach to Biological Motion: From the the Kinesin Walk to Muscle Contraction

    NASA Astrophysics Data System (ADS)

    Vicsek, Tamas

    1997-03-01

    It is demonstrated that a wide range of experimental results on biological motion can be successfully interpreted in terms of statistical physics motivated models taking into account the relevant microscopic details of motor proteins and allowing analytic solutions. Two important examples are considered, i) the motion of a single kinesin molecule along microtubules inside individual cells and ii) muscle contraction which is a macroscopic phenomenon due to the collective action of a large number of myosin heads along actin filaments. i) Recently individual two-headed kinesin molecules have been studied in in vitro motility assays revealing a number of their peculiar transport properties. Here we propose a simple and robust model for the kinesin stepping process with elastically coupled Brownian heads showing all of these properties. The analytic treatment of our model results in a very good fit to the experimental data and practically has no free parameters. ii) Myosin is an ATPase enzyme that converts the chemical energy stored in ATP molecules into mechanical work. During muscle contraction, the myosin cross-bridges attach to the actin filaments and exert force on them yielding a relative sliding of the actin and myosin filaments. In this paper we present a simple mechanochemical model for the cross-bridge interaction involving the relevant kinetic data and providing simple analytic solutions for the mechanical properties of muscle contraction, such as the force-velocity relationship or the relative number of the attached cross-bridges. So far the only analytic formula which could be fitted to the measured force-velocity curves has been the well known Hill equation containing parameters lacking clear microscopic origin. The main advantages of our new approach are that it explicitly connects the mechanical data with the kinetic data and the concentration of the ATP and ATPase products and as such it leads to new analytic solutions which agree extremely well with a wide range of experimental curves, while the parameters of the corresponding expressions have well defined microscopic meaning.

  16. Reaction Force of Micro-scale Liquid Droplets Constrained Between Parallel Plates through CFD

    NASA Astrophysics Data System (ADS)

    Free, Robert; Hekiri, Haider; Hawa, Takumi

    2012-02-01

    Micro-scale liquid droplets responding to depression between parallel plates are investigated analytically and numerically. The functional dependence of the reaction force accrued in such droplets on droplet size, surface tension, depression amount, and contact angle is explored. For both the 2D and 3D case, an analytical model is developed based on first principles. Computational fluid dynamics is then utilized to evaluate the validity of these models. The reaction force is highly nonlinear, initially increasing very slowly with increasing depression of the droplet, but eventually moving asymptotically to infinity. The force scales linearly with both the droplet free radius and surface tension of the liquid, but has a much more complicated dependence on the contact angle and depression. Explicit expressions for the reaction force have been determined, showing these dependencies. The 3D model has been largely supported by the CFD results. It very accurately predicts the reaction force on the upper plate as the droplet is crushed, accounting for the effect of contact angle, surface tension, and droplet size.

  17. Travelling waves and their bifurcations in the Lorenz-96 model

    NASA Astrophysics Data System (ADS)

    van Kekem, Dirk L.; Sterk, Alef E.

    2018-03-01

    In this paper we study the dynamics of the monoscale Lorenz-96 model using both analytical and numerical means. The bifurcations for positive forcing parameter F are investigated. The main analytical result is the existence of Hopf or Hopf-Hopf bifurcations in any dimension n ≥ 4. Exploiting the circulant structure of the Jacobian matrix enables us to reduce the first Lyapunov coefficient to an explicit formula from which it can be determined when the Hopf bifurcation is sub- or supercritical. The first Hopf bifurcation for F > 0 is always supercritical and the periodic orbit born at this bifurcation has the physical interpretation of a travelling wave. Furthermore, by unfolding the codimension two Hopf-Hopf bifurcation it is shown to act as an organising centre, explaining dynamics such as quasi-periodic attractors and multistability, which are observed in the original Lorenz-96 model. Finally, the region of parameter values beyond the first Hopf bifurcation value is investigated numerically and routes to chaos are described using bifurcation diagrams and Lyapunov exponents. The observed routes to chaos are various but without clear pattern as n → ∞.

  18. Eigenvalues of normalized Laplacian matrices of fractal trees and dendrimers: Analytical results and applications

    NASA Astrophysics Data System (ADS)

    Julaiti, Alafate; Wu, Bin; Zhang, Zhongzhi

    2013-05-01

    The eigenvalues of the normalized Laplacian matrix of a network play an important role in its structural and dynamical aspects associated with the network. In this paper, we study the spectra and their applications of normalized Laplacian matrices of a family of fractal trees and dendrimers modeled by Cayley trees, both of which are built in an iterative way. For the fractal trees, we apply the spectral decimation approach to determine analytically all the eigenvalues and their corresponding multiplicities, with the eigenvalues provided by a recursive relation governing the eigenvalues of networks at two successive generations. For Cayley trees, we show that all their eigenvalues can be obtained by computing the roots of several small-degree polynomials defined recursively. By using the relation between normalized Laplacian spectra and eigentime identity, we derive the explicit solution to the eigentime identity for random walks on the two treelike networks, the leading scalings of which follow quite different behaviors. In addition, we corroborate the obtained eigenvalues and their degeneracies through the link between them and the number of spanning trees.

  19. Electron acceleration in combined intense laser fields and self-consistent quasistatic fields in plasma

    NASA Astrophysics Data System (ADS)

    Qiao, Bin; He, X. T.; Zhu, Shao-ping; Zheng, C. Y.

    2005-08-01

    The acceleration of plasma electron in intense laser-plasma interaction is investigated analytically and numerically, where the conjunct effect of laser fields and self-consistent spontaneous fields (including quasistatic electric field Esl, azimuthal quasistatic magnetic field Bsθ and the axial one Bsz) is completely considered for the first time. An analytical relativistic electron fluid model using test-particle method has been developed to give an explicit analysis about the effects of each quasistatic fields. The ponderomotive accelerating and scattering effects on electrons are partly offset by Esl, furthermore, Bsθ pinches and Bsz collimates electrons along the laser axis. The dependences of energy gain and scattering angle of electron on its initial radial position, plasma density, and laser intensity are, respectively, studied. The qualities of the relativistic electron beam (REB), such as energy spread, beam divergence, and emitting (scattering) angle, generated by both circularly polarized (CP) and linearly polarized (LP) lasers are studied. Results show CP laser is of clear advantage comparing to LP laser for it can generate a better REB in collimation and stabilization.

  20. Finite Element Simulation of Three Full-Scale Crash Tests for Cessna 172 Aircraft

    NASA Technical Reports Server (NTRS)

    Mason, Brian H.; Warren, Jerry E., Jr.

    2017-01-01

    The NASA Emergency Locator Transmitter Survivability and Reliability (ELT-SAR) project was initiated in 2013 to assess the crash performance standards for the next generation of emergency locator transmitter (ELT) systems. Three Cessna 172 aircraft were acquired to perform crash testing at NASA Langley Research Center's Landing and Impact Research Facility. Full-scale crash tests were conducted in the summer of 2015 and each test article was subjected to severe, but survivable, impact conditions including a flare-to-stall during emergency landing, and two controlled-flight-into-terrain scenarios. Full-scale finite element analyses were performed using a commercial explicit solver, ABAQUS. The first test simulated impacting a concrete surface represented analytically by a rigid plane. Tests 2 and 3 simulated impacting a dirt surface represented analytically by an Eulerian grid of brick elements using a Mohr-Coulomb material model. The objective of this paper is to summarize the test and analysis results for the three full-scale crash tests. Simulation models of the airframe which correlate well with the tests are needed for future studies of alternate ELT mounting configurations.

  1. Investigation of the three-dimensional flow field within a transonic fan rotor: Experiment and analysis

    NASA Technical Reports Server (NTRS)

    Pierzga, M. J.; Wood, J. R.

    1984-01-01

    An experimental investigation of the three dimensional flow field through a low aspect ratio, transonic, axial flow fan rotor has been conducted using an advanced laser anemometer (LA) system. Laser velocimeter measurements of the rotor flow field at the design operating speed and over a range of through flow conditions are compared to analytical solutions. The numerical technique used herein yields the solution to the full, three dimensional, unsteady Euler equations using an explicit time marching, finite volume approach. The numerical analysis, when coupled with a simplified boundary layer calculation, generally yields good agreement with the experimental data. The test rotor has an aspect ratio of 1.56, a design total pressure ratio of 1.629 and a tip relative Mach number of 1.38. The high spatial resolution of the LA data matrix (9 radial by 30 axial by 50 blade to blade) permits details of the transonic flow field such as shock location, turning distribution and blade loading levels to be investigated and compared to analytical results.

  2. Fully Anisotropic Rotational Diffusion Tensor from Molecular Dynamics Simulations.

    PubMed

    Linke, Max; Köfinger, Jürgen; Hummer, Gerhard

    2018-05-31

    We present a method to calculate the fully anisotropic rotational diffusion tensor from molecular dynamics simulations. Our approach is based on fitting the time-dependent covariance matrix of the quaternions that describe the rigid-body rotational dynamics. Explicit analytical expressions have been derived for the covariances by Favro, which are valid irrespective of the degree of anisotropy. We use these expressions to determine an optimal rotational diffusion tensor from trajectory data. The molecular structures are aligned against a reference by optimal rigid-body superposition. The quaternion covariances can then be obtained directly from the rotation matrices used in the alignment. The rotational diffusion tensor is determined by a fit to the time-dependent quaternion covariances, or directly by Laplace transformation and matrix diagonalization. To quantify uncertainties in the fit, we derive analytical expressions and compare them with the results of Brownian dynamics simulations of anisotropic rotational diffusion. We apply the method to microsecond long trajectories of the Dickerson-Drew B-DNA dodecamer and of horse heart myoglobin. The anisotropic rotational diffusion tensors calculated from simulations agree well with predictions from hydrodynamics.

  3. Low velocity impact analysis of composite laminated plates

    NASA Astrophysics Data System (ADS)

    Zheng, Daihua

    2007-12-01

    In the past few decades polymer composites have been utilized more in structures where high strength and light weight are major concerns, e.g., aircraft, high-speed boats and sports supplies. It is well known that they are susceptible to damage resulting from lateral impact by foreign objects, such as dropped tools, hail and debris thrown up from the runway. The impact response of the structures depends not only on the material properties but also on the dynamic behavior of the impacted structure. Although commercial software is capable of analyzing such impact processes, it often requires extensive expertise and rigorous training for design and analysis. Analytical models are useful as they allow parametric studies and provide a foundation for validating the numerical results from large-scale commercial software. Therefore, it is necessary to develop analytical or semi-analytical models to better understand the behaviors of composite structures under impact and their associated failure process. In this study, several analytical models are proposed in order to analyze the impact response of composite laminated plates. Based on Meyer's Power Law, a semi-analytical model is obtained for small mass impact response of infinite composite laminates by the method of asymptotic expansion. The original nonlinear second-order ordinary differential equation is transformed into two linear ordinary differential equations. This is achieved by neglecting high-order terms in the asymptotic expansion. As a result, the semi-analytical solution of the overall impact response can be applied to contact laws with varying coefficients. Then an analytical model accounting for permanent deformation based on an elasto-plastic contact law is proposed to obtain the closed-form solutions of the wave-controlled impact responses of composite laminates. The analytical model is also used to predict the threshold velocity for delamination onset by combining with an existing quasi-static delamination criterion. The predictions are compared with experimental data and explicit finite element LS-DYNA simulation. The comparisons show reasonable agreement. Furthermore, an analytical model is developed to evaluate the combined effects of prestresses and permanent deformation based on the linearized elasto-plastic contact law and the Laplace Transform technique. It is demonstrated that prestresses do not have noticeable effects on the time history of contact force and strains, but they have significant consequences on the plate central displacement. For a impacted composite laminate with the presence of prestresses, the contact force increases with the increasing of the mass of impactor, thickness and interlaminar shear strength of the laminate. The combined analytical and numerical investigations provide validated models for elastic and elasto-plastic impact analysis of composite structures and shed light on the design of impact-resistant composite systems.

  4. Tutorial in medical decision modeling incorporating waiting lines and queues using discrete event simulation.

    PubMed

    Jahn, Beate; Theurl, Engelbert; Siebert, Uwe; Pfeiffer, Karl-Peter

    2010-01-01

    In most decision-analytic models in health care, it is assumed that there is treatment without delay and availability of all required resources. Therefore, waiting times caused by limited resources and their impact on treatment effects and costs often remain unconsidered. Queuing theory enables mathematical analysis and the derivation of several performance measures of queuing systems. Nevertheless, an analytical approach with closed formulas is not always possible. Therefore, simulation techniques are used to evaluate systems that include queuing or waiting, for example, discrete event simulation. To include queuing in decision-analytic models requires a basic knowledge of queuing theory and of the underlying interrelationships. This tutorial introduces queuing theory. Analysts and decision-makers get an understanding of queue characteristics, modeling features, and its strength. Conceptual issues are covered, but the emphasis is on practical issues like modeling the arrival of patients. The treatment of coronary artery disease with percutaneous coronary intervention including stent placement serves as an illustrative queuing example. Discrete event simulation is applied to explicitly model resource capacities, to incorporate waiting lines and queues in the decision-analytic modeling example.

  5. Some key features in the evolution of self psychology and psychoanalysis.

    PubMed

    Fosshage, James L

    2009-04-01

    Psychoanalysis, as every science and its application, has continued to evolve over the past century, especially accelerating over the last 30 years. Self psychology has played a constitutive role in that evolution and has continued to change itself. These movements have been supported and augmented by a wide range of emergent research and theory, especially that of cognitive psychology, infant and attachment research, rapid eye movement and dream research, psychotherapy research, and neuroscience. I present schematically some of what I consider to be the key features of the evolution of self psychology and their interconnection with that of psychoanalysis at large, including the revolutionary paradigm changes, the new epistemology, listening/experiencing perspectives, from narcissism to the development of the self, the new organization model of transference, the new organization model of dreams, and the implicit and explicit dimensions of analytic work. I conclude with a focus on the radical ongoing extension of the analyst's participation in the analytic relationship, using, as an example, the co-creation of analytic love, and providing several brief clinical illustrations. The leading edge question guiding my discussion is "How does analytic change occur?"

  6. Optimum design of structures subject to general periodic loads

    NASA Technical Reports Server (NTRS)

    Reiss, Robert; Qian, B.

    1989-01-01

    A simplified version of Icerman's problem regarding the design of structures subject to a single harmonic load is discussed. The nature of the restrictive conditions that must be placed on the design space in order to ensure an analytic optimum are discussed in detail. Icerman's problem is then extended to include multiple forcing functions with different driving frequencies. And the conditions that now must be placed upon the design space to ensure an analytic optimum are again discussed. An important finding is that all solutions to the optimality condition (analytic stationary design) are local optima, but the global optimum may well be non-analytic. The more general problem of distributing the fixed mass of a linear elastic structure subject to general periodic loads in order to minimize some measure of the steady state deflection is also considered. This response is explicitly expressed in terms of Green's functional and the abstract operators defining the structure. The optimality criterion is derived by differentiating the response with respect to the design parameters. The theory is applicable to finite element as well as distributed parameter models.

  7. Convergence analysis of two-node CMFD method for two-group neutron diffusion eigenvalue problem

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

    Jeong, Yongjin; Park, Jinsu; Lee, Hyun Chul

    2015-12-01

    In this paper, the nonlinear coarse-mesh finite difference method with two-node local problem (CMFD2N) is proven to be unconditionally stable for neutron diffusion eigenvalue problems. The explicit current correction factor (CCF) is derived based on the two-node analytic nodal method (ANM2N), and a Fourier stability analysis is applied to the linearized algorithm. It is shown that the analytic convergence rate obtained by the Fourier analysis compares very well with the numerically measured convergence rate. It is also shown that the theoretical convergence rate is only governed by the converged second harmonic buckling and the mesh size. It is also notedmore » that the convergence rate of the CCF of the CMFD2N algorithm is dependent on the mesh size, but not on the total problem size. This is contrary to expectation for eigenvalue problem. The novel points of this paper are the analytical derivation of the convergence rate of the CMFD2N algorithm for eigenvalue problem, and the convergence analysis based on the analytic derivations.« less

  8. A semi-analytical description of protein folding that incorporates detailed geometrical information

    PubMed Central

    Suzuki, Yoko; Noel, Jeffrey K.; Onuchic, José N.

    2011-01-01

    Much has been done to study the interplay between geometric and energetic effects on the protein folding energy landscape. Numerical techniques such as molecular dynamics simulations are able to maintain a precise geometrical representation of the protein. Analytical approaches, however, often focus on the energetic aspects of folding, including geometrical information only in an average way. Here, we investigate a semi-analytical expression of folding that explicitly includes geometrical effects. We consider a Hamiltonian corresponding to a Gaussian filament with structure-based interactions. The model captures local features of protein folding often averaged over by mean-field theories, for example, loop contact formation and excluded volume. We explore the thermodynamics and folding mechanisms of beta-hairpin and alpha-helical structures as functions of temperature and Q, the fraction of native contacts formed. Excluded volume is shown to be an important component of a protein Hamiltonian, since it both dominates the cooperativity of the folding transition and alters folding mechanisms. Understanding geometrical effects in analytical formulae will help illuminate the consequences of the approximations required for the study of larger proteins. PMID:21721664

  9. The legal and ethical concerns that arise from using complex predictive analytics in health care.

    PubMed

    Cohen, I Glenn; Amarasingham, Ruben; Shah, Anand; Xie, Bin; Lo, Bernard

    2014-07-01

    Predictive analytics, or the use of electronic algorithms to forecast future events in real time, makes it possible to harness the power of big data to improve the health of patients and lower the cost of health care. However, this opportunity raises policy, ethical, and legal challenges. In this article we analyze the major challenges to implementing predictive analytics in health care settings and make broad recommendations for overcoming challenges raised in the four phases of the life cycle of a predictive analytics model: acquiring data to build the model, building and validating it, testing it in real-world settings, and disseminating and using it more broadly. For instance, we recommend that model developers implement governance structures that include patients and other stakeholders starting in the earliest phases of development. In addition, developers should be allowed to use already collected patient data without explicit consent, provided that they comply with federal regulations regarding research on human subjects and the privacy of health information. Project HOPE—The People-to-People Health Foundation, Inc.

  10. Judicial and legislative viewpoints on physician misestimation of patient dysutilities: a problem for decision analysts.

    PubMed

    Mazur, D J

    1990-01-01

    Appellate courts, state legislatures, and ethicists have recently (post-1972) been interested-through the evolving court doctrine of informed consent-in patient-physician joint decision making. Yet these professional groups' approaches differ markedly from that of decision analysis, failing to include an explicit role for patients' rational processing of information in informed consent. In addition, these groups charge that decision analysts are misestimating patient dysutilities. This paper examines three issues: 1) in what sense(s), if any, is decision-analytic work in individualized medical decision making misestimating patient dysutilities, 2) if this misestimation is real, whether it is an example of the normative-descriptive tensions that exist in medical decision making, and 3) in what ways do the relationships between decision-analytic and judicial decision making change when informed consent is viewed in terms of contract law as opposed to tort law. This paper argues that a key link dividing these professional groups is the differing weights given to the "value of information" by decision-analytic vs. non-decision-analytic frameworks.

  11. From the fundamental rule to the analysing situation.

    PubMed

    Donnet, J L

    2001-02-01

    The analytic method relies on the mental capacity to produce an associative sequence, and, afterwards, to discern its unconscious logic; within the social practice of the analytic cure, the method presents itself as the mastered enactment of the condition through which free association proves to be possible, interpretable and beneficial. There is a contradiction between the necessity of relying on a former theorisation and that of willingly suspending a knowledge that might serve the authenticity of the experience. The author reminds us of the structural links between the fundamental rule and the defined situations within which the analytic process of transformative investigation can take place. He raises the problems that it is suggested arise with the initial objectivation method by acknowledging the transference as the created-found object of interpretation. He shows how the transformation of the patient into analysand implies the functional introjection of the various elements contained by the analytic site. The meaning given to the expression 'analysing situation' is made explicit. The crucial value of the process of enunciation is illustrated by a brief example.

  12. Shape dependence of holographic Rényi entropy in general dimensions

    DOE PAGES

    Bianchi, Lorenzo; Chapman, Shira; Dong, Xi; ...

    2016-11-29

    We present a holographic method for computing the response of Rényi entropies in conformal field theories to small shape deformations around a flat (or spherical) entangling surface. Our strategy employs the stress tensor one-point function in a deformed hyperboloid background and relates it to the coefficient in the two-point function of the displacement operator. We obtain explicit numerical results for d = 3, · · · , 6 spacetime dimensions, and also evaluate analytically the limits where the Rényi index approaches 1 and 0 in general dimensions. We use our results to extend the work of 1602.08493 and disprove amore » set of conjectures in the literature regarding the relation between the Rényi shape dependence and the conformal weight of the twist operator. As a result, we also extend our analysis beyond leading order in derivatives in the bulk theory by studying Gauss-Bonnet gravity.« less

  13. Magnon edge states in the hardcore- Bose-Hubbard model.

    PubMed

    Owerre, S A

    2016-11-02

    Quantum Monte Carlo (QMC) simulation has uncovered nonzero Berry curvature and bosonic edge states in the hardcore-Bose-Hubbard model on the gapped honeycomb lattice. The competition between the chemical potential and staggered onsite potential leads to an interesting quantum phase diagram comprising the superfluid phase, Mott insulator, and charge density wave insulator. In this paper, we present a semiclassical perspective of this system by mapping to a spin-1/2 quantum XY model. We give an explicit analytical origin of the quantum phase diagram, the Berry curvatures, and the edge states using semiclassical approximations. We find very good agreement between the semiclassical analyses and the QMC results. Our results show that the topological properties of the hardcore-Bose-Hubbard model are the same as those of magnon in the corresponding quantum spin system. Our results are applicable to systems of ultracold bosonic atoms trapped in honeycomb optical lattices.

  14. On the numerical solution of the dynamically loaded hydrodynamic lubrication of the point contact problem

    NASA Technical Reports Server (NTRS)

    Lim, Sang G.; Brewe, David E.; Prahl, Joseph M.

    1990-01-01

    The transient analysis of hydrodynamic lubrication of a point-contact is presented. A body-fitted coordinate system is introduced to transform the physical domain to a rectangular computational domain, enabling the use of the Newton-Raphson method for determining pressures and locating the cavitation boundary, where the Reynolds boundary condition is specified. In order to obtain the transient solution, an explicit Euler method is used to effect a time march. The transient dynamic load is a sinusoidal function of time with frequency, fractional loading, and mean load as parameters. Results include the variation of the minimum film thickness and phase-lag with time as functions of excitation frequency. The results are compared with the analytic solution to the transient step bearing problem with the same dynamic loading function. The similarities of the results suggest an approximate model of the point contact minimum film thickness solution.

  15. A new solution method for wheel/rail rolling contact.

    PubMed

    Yang, Jian; Song, Hua; Fu, Lihua; Wang, Meng; Li, Wei

    2016-01-01

    To solve the problem of wheel/rail rolling contact of nonlinear steady-state curving, a three-dimensional transient finite element (FE) model is developed by the explicit software ANSYS/LS-DYNA. To improve the solving speed and efficiency, an explicit-explicit order solution method is put forward based on analysis of the features of implicit and explicit algorithm. The solution method was first applied to calculate the pre-loading of wheel/rail rolling contact with explicit algorithm, and then the results became the initial conditions in solving the dynamic process of wheel/rail rolling contact with explicit algorithm as well. Simultaneously, the common implicit-explicit order solution method is used to solve the FE model. Results show that the explicit-explicit order solution method has faster operation speed and higher efficiency than the implicit-explicit order solution method while the solution accuracy is almost the same. Hence, the explicit-explicit order solution method is more suitable for the wheel/rail rolling contact model with large scale and high nonlinearity.

  16. Quantum State Tomography via Linear Regression Estimation

    PubMed Central

    Qi, Bo; Hou, Zhibo; Li, Li; Dong, Daoyi; Xiang, Guoyong; Guo, Guangcan

    2013-01-01

    A simple yet efficient state reconstruction algorithm of linear regression estimation (LRE) is presented for quantum state tomography. In this method, quantum state reconstruction is converted into a parameter estimation problem of a linear regression model and the least-squares method is employed to estimate the unknown parameters. An asymptotic mean squared error (MSE) upper bound for all possible states to be estimated is given analytically, which depends explicitly upon the involved measurement bases. This analytical MSE upper bound can guide one to choose optimal measurement sets. The computational complexity of LRE is O(d4) where d is the dimension of the quantum state. Numerical examples show that LRE is much faster than maximum-likelihood estimation for quantum state tomography. PMID:24336519

  17. Note on the coefficient of variations of neuronal spike trains.

    PubMed

    Lengler, Johannes; Steger, Angelika

    2017-08-01

    It is known that many neurons in the brain show spike trains with a coefficient of variation (CV) of the interspike times of approximately 1, thus resembling the properties of Poisson spike trains. Computational studies have been able to reproduce this phenomenon. However, the underlying models were too complex to be examined analytically. In this paper, we offer a simple model that shows the same effect but is accessible to an analytic treatment. The model is a random walk model with a reflecting barrier; we give explicit formulas for the CV in the regime of excess inhibition. We also analyze the effect of probabilistic synapses in our model and show that it resembles previous findings that were obtained by simulation.

  18. Analytical Solutions, Moments, and Their Asymptotic Behaviors for the Time-Space Fractional Cable Equation

    NASA Astrophysics Data System (ADS)

    Li, Can; Deng, Wei-Hua

    2014-07-01

    Following the fractional cable equation established in the letter [B.I. Henry, T.A.M. Langlands, and S.L. Wearne, Phys. Rev. Lett. 100 (2008) 128103], we present the time-space fractional cable equation which describes the anomalous transport of electrodiffusion in nerve cells. The derivation is based on the generalized fractional Ohm's law; and the temporal memory effects and spatial-nonlocality are involved in the time-space fractional model. With the help of integral transform method we derive the analytical solutions expressed by the Green's function; the corresponding fractional moments are calculated; and their asymptotic behaviors are discussed. In addition, the explicit solutions of the considered model with two different external current injections are also presented.

  19. The High-Resolution Wave-Propagation Method Applied to Meso- and Micro-Scale Flows

    NASA Technical Reports Server (NTRS)

    Ahmad, Nashat N.; Proctor, Fred H.

    2012-01-01

    The high-resolution wave-propagation method for computing the nonhydrostatic atmospheric flows on meso- and micro-scales is described. The design and implementation of the Riemann solver used for computing the Godunov fluxes is discussed in detail. The method uses a flux-based wave decomposition in which the flux differences are written directly as the linear combination of the right eigenvectors of the hyperbolic system. The two advantages of the technique are: 1) the need for an explicit definition of the Roe matrix is eliminated and, 2) the inclusion of source term due to gravity does not result in discretization errors. The resulting flow solver is conservative and able to resolve regions of large gradients without introducing dispersion errors. The methodology is validated against exact analytical solutions and benchmark cases for non-hydrostatic atmospheric flows.

  20. Solving the Self-Interaction Problem in Kohn-Sham Density Functional Theory. Application to Atoms

    DOE PAGES

    Daene, M.; Gonis, A.; Nicholson, D. M.; ...

    2014-10-14

    Previously, we proposed a computational methodology that addresses the elimination of the self-interaction error from the Kohn–Sham formulation of the density functional theory. We demonstrated how the exchange potential can be obtained, and presented results of calculations for atomic systems up to Kr carried out within a Cartesian coordinate system. In our paper, we provide complete details of this self-interaction free method formulated in spherical coordinates based on the explicit equidensity basis ansatz. We also prove analytically that derivatives obtained using this method satisfy the Virial theorem for spherical orbitals, where the problem can be reduced to one dimension. Wemore » present the results of calculations of ground-state energies of atomic systems throughout the periodic table carried out within the exchange-only mode.« less

  1. Comparison of Virtual Oscillator and Droop Control: Preprint

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

    Johnson, Brian B; Rodriguez, Miguel; Dhople, Sairaj

    Virtual oscillator control and droop control are two techniques that can be used to ensure synchronization and power sharing of parallel inverters in islanded operation. VOC relies on the implementation of non-linear Van der Pol oscillator equations in the control system of the inverter, acting upon the time-domain instantaneous inverter current and terminal voltage. On the other hand, DC explicitly computes active and reactive power produced by the inverter and relies on limited bandwidth low-pass filters. Even though both methods can be engineered to produce the same steady-state characteristics, their dynamic performances are significantly different. This paper presents analytical andmore » experimental results that aim to compare both methods. It is shown that VOC is inherently faster and enables minimizing the circulating currents. The results are verified using three 120V, 1kW inverters.« less

  2. Exact relations between homoclinic and periodic orbit actions in chaotic systems

    NASA Astrophysics Data System (ADS)

    Li, Jizhou; Tomsovic, Steven

    2018-02-01

    Homoclinic and unstable periodic orbits in chaotic systems play central roles in various semiclassical sum rules. The interferences between terms are governed by the action functions and Maslov indices. In this article, we identify geometric relations between homoclinic and unstable periodic orbits, and derive exact formulas expressing the periodic orbit classical actions in terms of corresponding homoclinic orbit actions plus certain phase space areas. The exact relations provide a basis for approximations of the periodic orbit actions as action differences between homoclinic orbits with well-estimated errors. This enables an explicit study of relations between periodic orbits, which results in an analytic expression for the action differences between long periodic orbits and their shadowing decomposed orbits in the cycle expansion.

  3. Asymptotic approximations to posterior distributions via conditional moment equations

    USGS Publications Warehouse

    Yee, J.L.; Johnson, W.O.; Samaniego, F.J.

    2002-01-01

    We consider asymptotic approximations to joint posterior distributions in situations where the full conditional distributions referred to in Gibbs sampling are asymptotically normal. Our development focuses on problems where data augmentation facilitates simpler calculations, but results hold more generally. Asymptotic mean vectors are obtained as simultaneous solutions to fixed point equations that arise naturally in the development. Asymptotic covariance matrices flow naturally from the work of Arnold & Press (1989) and involve the conditional asymptotic covariance matrices and first derivative matrices for conditional mean functions. When the fixed point equations admit an analytical solution, explicit formulae are subsequently obtained for the covariance structure of the joint limiting distribution, which may shed light on the use of the given statistical model. Two illustrations are given. ?? 2002 Biometrika Trust.

  4. Optimal solutions for the evolution of a social obesity epidemic model

    NASA Astrophysics Data System (ADS)

    Sikander, Waseem; Khan, Umar; Mohyud-Din, Syed Tauseef

    2017-06-01

    In this work, a novel modification in the traditional homotopy perturbation method (HPM) is proposed by embedding an auxiliary parameter in the boundary condition. The scheme is used to carry out a mathematical evaluation of the social obesity epidemic model. The incidence of excess weight and obesity in adulthood population and prediction of its behavior in the coming years is analyzed by using a modified algorithm. The proposed method increases the convergence of the approximate analytical solution over the domain of the problem. Furthermore, a convenient way is considered for choosing an optimal value of auxiliary parameters via minimizing the total residual error. The graphical comparison of the obtained results with the standard HPM explicitly reveals the accuracy and efficiency of the developed scheme.

  5. Phase transitions in coupled map lattices and in associated probabilistic cellular automata.

    PubMed

    Just, Wolfram

    2006-10-01

    Analytical tools are applied to investigate piecewise linear coupled map lattices in terms of probabilistic cellular automata. The so-called disorder condition of probabilistic cellular automata is closely related with attracting sets in coupled map lattices. The importance of this condition for the suppression of phase transitions is illustrated by spatially one-dimensional systems. Invariant densities and temporal correlations are calculated explicitly. Ising type phase transitions are found for one-dimensional coupled map lattices acting on repelling sets and for a spatially two-dimensional Miller-Huse-like system with stable long time dynamics. Critical exponents are calculated within a finite size scaling approach. The relevance of detailed balance of the resulting probabilistic cellular automaton for the critical behavior is pointed out.

  6. LSD (Landing System Development) Impact Simulation

    NASA Astrophysics Data System (ADS)

    Ullio, R.; Riva, N.; Pellegrino, P.; Deloo, P.

    2012-07-01

    In the frame of the Exploration Programs, a soft landing on the planet surface is foreseen. To ensure a successful final landing phase, a landing system by using leg tripod design landing legs with adequate crushable damping system was selected, capable of absorbing the residual velocities (vertical, horizontal and angular) at touch- down, insuring stability. TAS-I developed a numerical non linear dynamic methodology for the landing impact simulation of the Lander system by using a commercial explicit finite element analysis code (i.e. Altair RADIOSS). In this paper the most significant FE modeling approaches and results of the analytical simulation of landing impact are reported, especially with respect to the definition of leg dimensioning loads and the design update of selected parts (if necessary).

  7. A cubic spline approximation for problems in fluid mechanics

    NASA Technical Reports Server (NTRS)

    Rubin, S. G.; Graves, R. A., Jr.

    1975-01-01

    A cubic spline approximation is presented which is suited for many fluid-mechanics problems. This procedure provides a high degree of accuracy, even with a nonuniform mesh, and leads to an accurate treatment of derivative boundary conditions. The truncation errors and stability limitations of several implicit and explicit integration schemes are presented. For two-dimensional flows, a spline-alternating-direction-implicit method is evaluated. The spline procedure is assessed, and results are presented for the one-dimensional nonlinear Burgers' equation, as well as the two-dimensional diffusion equation and the vorticity-stream function system describing the viscous flow in a driven cavity. Comparisons are made with analytic solutions for the first two problems and with finite-difference calculations for the cavity flow.

  8. Explicit solution techniques for impact with contact constraints

    NASA Technical Reports Server (NTRS)

    Mccarty, Robert E.

    1993-01-01

    Modern military aircraft transparency systems, windshields and canopies, are complex systems which must meet a large and rapidly growing number of requirements. Many of these transparency system requirements are conflicting, presenting difficult balances which must be achieved. One example of a challenging requirements balance or trade is shaping for stealth versus aircrew vision. The large number of requirements involved may be grouped in a variety of areas including man-machine interface; structural integration with the airframe; combat hazards; environmental exposures; and supportability. Some individual requirements by themselves pose very difficult, severely nonlinear analysis problems. One such complex problem is that associated with the dynamic structural response resulting from high energy bird impact. An improved analytical capability for soft-body impact simulation was developed.

  9. Explicit solution techniques for impact with contact constraints

    NASA Astrophysics Data System (ADS)

    McCarty, Robert E.

    1993-08-01

    Modern military aircraft transparency systems, windshields and canopies, are complex systems which must meet a large and rapidly growing number of requirements. Many of these transparency system requirements are conflicting, presenting difficult balances which must be achieved. One example of a challenging requirements balance or trade is shaping for stealth versus aircrew vision. The large number of requirements involved may be grouped in a variety of areas including man-machine interface; structural integration with the airframe; combat hazards; environmental exposures; and supportability. Some individual requirements by themselves pose very difficult, severely nonlinear analysis problems. One such complex problem is that associated with the dynamic structural response resulting from high energy bird impact. An improved analytical capability for soft-body impact simulation was developed.

  10. Computation of leaky guided waves dispersion spectrum using vibroacoustic analyses and the Matrix Pencil Method: a validation study for immersed rectangular waveguides.

    PubMed

    Mazzotti, M; Bartoli, I; Castellazzi, G; Marzani, A

    2014-09-01

    The paper aims at validating a recently proposed Semi Analytical Finite Element (SAFE) formulation coupled with a 2.5D Boundary Element Method (2.5D BEM) for the extraction of dispersion data in immersed waveguides of generic cross-section. To this end, three-dimensional vibroacoustic analyses are carried out on two waveguides of square and rectangular cross-section immersed in water using the commercial Finite Element software Abaqus/Explicit. Real wavenumber and attenuation dispersive data are extracted by means of a modified Matrix Pencil Method. It is demonstrated that the results obtained using the two techniques are in very good agreement. Copyright © 2014 Elsevier B.V. All rights reserved.

  11. A Petri-net coordination model for an intelligent mobile robot

    NASA Technical Reports Server (NTRS)

    Wang, F.-Y.; Kyriakopoulos, K. J.; Tsolkas, A.; Saridis, G. N.

    1990-01-01

    The authors present a Petri net model of the coordination level of an intelligent mobile robot system (IMRS). The purpose of this model is to specify the integration of the individual efforts on path planning, supervisory motion control, and vision systems that are necessary for the autonomous operation of the mobile robot in a structured dynamic environment. This is achieved by analytically modeling the various units of the system as Petri net transducers and explicitly representing the task precedence and information dependence among them. The model can also be used to simulate the task processing and to evaluate the efficiency of operations and the responsibility of decisions in the coordination level of the IMRS. Some simulation results on the task processing and learning are presented.

  12. Mixed Initiative Visual Analytics Using Task-Driven Recommendations

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

    Cook, Kristin A.; Cramer, Nicholas O.; Israel, David

    2015-12-07

    Visual data analysis is composed of a collection of cognitive actions and tasks to decompose, internalize, and recombine data to produce knowledge and insight. Visual analytic tools provide interactive visual interfaces to data to support tasks involved in discovery and sensemaking, including forming hypotheses, asking questions, and evaluating and organizing evidence. Myriad analytic models can be incorporated into visual analytic systems, at the cost of increasing complexity in the analytic discourse between user and system. Techniques exist to increase the usability of interacting with such analytic models, such as inferring data models from user interactions to steer the underlying modelsmore » of the system via semantic interaction, shielding users from having to do so explicitly. Such approaches are often also referred to as mixed-initiative systems. Researchers studying the sensemaking process have called for development of tools that facilitate analytic sensemaking through a combination of human and automated activities. However, design guidelines do not exist for mixed-initiative visual analytic systems to support iterative sensemaking. In this paper, we present a candidate set of design guidelines and introduce the Active Data Environment (ADE) prototype, a spatial workspace supporting the analytic process via task recommendations invoked by inferences on user interactions within the workspace. ADE recommends data and relationships based on a task model, enabling users to co-reason with the system about their data in a single, spatial workspace. This paper provides an illustrative use case, a technical description of ADE, and a discussion of the strengths and limitations of the approach.« less

  13. Nonlinear field equations for aligning self-propelled rods.

    PubMed

    Peshkov, Anton; Aranson, Igor S; Bertin, Eric; Chaté, Hugues; Ginelli, Francesco

    2012-12-28

    We derive a set of minimal and well-behaved nonlinear field equations describing the collective properties of self-propelled rods from a simple microscopic starting point, the Vicsek model with nematic alignment. Analysis of their linear and nonlinear dynamics shows good agreement with the original microscopic model. In particular, we derive an explicit expression for density-segregated, banded solutions, allowing us to develop a more complete analytic picture of the problem at the nonlinear level.

  14. Multiple soliton production and the Korteweg-de Vries equation.

    NASA Technical Reports Server (NTRS)

    Hershkowitz, N.; Romesser, T.; Montgomery, D.

    1972-01-01

    Compressive square-wave pulses are launched in a double-plasma device. Their evolution is interpreted according to the Korteweg-de Vries description of Washimi and Taniuti. Square-wave pulses are an excitation for which an explicit solution of the Schrodinger equation permits an analytical prediction of the number and amplitude of emergent solitons. Bursts of energetic particles (pseudowaves) appear above excitation voltages greater than an electron thermal energy, and may be mistaken for solitons.

  15. Remanent Magnetization: Signature of Many-Body Localization in Quantum Antiferromagnets

    NASA Astrophysics Data System (ADS)

    Ros, V.; Müller, M.

    2017-06-01

    We study the remanent magnetization in antiferromagnetic, many-body localized quantum spin chains, initialized in a fully magnetized state. Its long time limit is an order parameter for the localization transition, which is readily accessible by standard experimental probes in magnets. We analytically calculate its value in the strong-disorder regime exploiting the explicit construction of quasilocal conserved quantities of the localized phase. We discuss analogies in cold atomic systems.

  16. The underdamped Brownian duet and stochastic linear irreversible thermodynamics

    NASA Astrophysics Data System (ADS)

    Proesmans, Karel; Van den Broeck, Christian

    2017-10-01

    Building on our earlier work [Proesmans et al., Phys. Rev. X 6, 041010 (2016)], we introduce the underdamped Brownian duet as a prototype model of a dissipative system or of a work-to-work engine. Several recent advances from the theory of stochastic thermodynamics are illustrated with explicit analytic calculations and corresponding Langevin simulations. In particular, we discuss the Onsager-Casimir symmetry, the trade-off relations between power, efficiency and dissipation, and stochastic efficiency.

  17. Pressure-coupled combustion response model for solid propellants based on Zeldovich-Novozhilov approach

    NASA Technical Reports Server (NTRS)

    Harstad, K. G.; Strand, L. D.

    1987-01-01

    An exact analytical solution is given to the problem of long-time propellant thermal response to a specified pressure oscillation. Coupling to the gas phase is made using the quasisteady Zeldovich-Novozhilov approximation. Explicit linear and lowest order (quadratic) nonlinear expressions for propellant response are obtained from the implicit nonlinear solutions. Using these expressions, response curves are presented for an ammonium perchlorate composite propellant and HMX monopropellant.

  18. A Study on Flexural Properties of Sandwich Structures with Fiber/Metal Laminate Face Sheets

    NASA Astrophysics Data System (ADS)

    Dariushi, S.; Sadighi, M.

    2013-10-01

    In this work, a new family of sandwich structures with fiber metal laminate (FML) faces is investigated. FMLs have benefits over both metal and fiber reinforced composites. To investigate the bending properties of sandwich beams with FML faces and compare with similar sandwich beams with fibrous composite faces, 6 groups of specimen with different layer arrangements were made and tested. Results show that FML faces have good resistance against transverse local loads and minimize stress concentration and local deformations of skin and core under the loading tip. In addition, FML faces have a good integrity even after plateau region of foam cores and prevent from catastrophic failures, which cannot be seen in fibrous composite faces. Also, FML faces are lighter than metal faces and have better connection with foam cores. Sandwich beams with FML faces have a larger elastic region because of simultaneous deformation of top and bottom faces and larger failure strain thanks to good durability of FMLs. A geometrical nonlinear classical theory is used to predict force-deflection behavior. In this model an explicit formula between symmetrical sandwich beams deflections and applied force which can be useful for designers, is derived. Good agreement is obtained between the analytical predictions and experimental results. Also, analytical results are compared with small deformation solution in a parametric study, and the effects of geometric parameters on difference between linear and nonlinear results are discussed.

  19. Trait-based assessment of borderline personality disorder using the NEO Five-Factor Inventory: Phenotypic and genetic support

    PubMed Central

    Few, Lauren R.; Miller, Joshua D.; Grant, Julia D.; Maples, Jessica; Trull, Timothy J.; Nelson, Elliot C.; Oltmanns, Thomas F.; Martin, Nicholas G.; Lynskey, Michael T.; Agrawal, Arpana

    2015-01-01

    The aim of the current study was to examine the reliability and validity of a trait-based assessment of borderline personality disorder (BPD) using the NEO Five-Factor Inventory. Correlations between the Five-Factor Inventory-BPD composite (FFI-BPD) and explicit measures of BPD were examined across six samples, including undergraduate, community, and clinical samples. The median correlation was .60, which was nearly identical to the correlation between measures of BPD and a BPD composite generated from the full Revised NEO Personality Inventory (i.e., NEO-BPD; r =.61). Correlations between FFI-BPD and relevant measures of psychiatric symptomatology and etiology (e.g., childhood abuse, drug use, depression, and personality disorders) were also examined and compared to those generated using explicit measures of BPD and NEO-BPD. As expected, the FFI-BPD composite correlated most strongly with measures associated with high levels of Neuroticism, such as depression, anxiety, and emotion dysregulation, and the pattern of correlations generated using the FFI-BPD was highly similar to those generated using explicit measures of BPD and NEO-BPD. Finally, genetic analyses estimated that FFI-BPD is 44% heritable, which is comparable to meta-analytic research examining genetics associated with BPD, and revealed that 71% of the genetic influences are shared between FFI-BPD and a self-report measure assessing BPD (Personality Assessment Inventory – Borderline subscale; Morey, 1991). Generally, these results support the use of FFI-BPD as a reasonable proxy for BPD, which has considerable implications, particularly for potential gene-finding efforts in large, epidemiological datasets that include the NEO FFI. PMID:25984635

  20. On non-autonomous dynamical systems

    NASA Astrophysics Data System (ADS)

    Anzaldo-Meneses, A.

    2015-04-01

    In usual realistic classical dynamical systems, the Hamiltonian depends explicitly on time. In this work, a class of classical systems with time dependent nonlinear Hamiltonians is analyzed. This type of problems allows to find invariants by a family of Veronese maps. The motivation to develop this method results from the observation that the Poisson-Lie algebra of monomials in the coordinates and momenta is clearly defined in terms of its brackets and leads naturally to an infinite linear set of differential equations, under certain circumstances. To perform explicit analytic and numerical calculations, two examples are presented to estimate the trajectories, the first given by a nonlinear problem and the second by a quadratic Hamiltonian with three time dependent parameters. In the nonlinear problem, the Veronese approach using jets is shown to be equivalent to a direct procedure using elliptic functions identities, and linear invariants are constructed. For the second example, linear and quadratic invariants as well as stability conditions are given. Explicit solutions are also obtained for stepwise constant forces. For the quadratic Hamiltonian, an appropriated set of coordinates relates the geometric setting to that of the three dimensional manifold of central conic sections. It is shown further that the quantum mechanical problem of scattering in a superlattice leads to mathematically equivalent equations for the wave function, if the classical time is replaced by the space coordinate along a superlattice. The mathematical method used to compute the trajectories for stepwise constant parameters can be applied to both problems. It is the standard method in quantum scattering calculations, as known for locally periodic systems including a space dependent effective mass.

  1. Counting Cats: Spatially Explicit Population Estimates of Cheetah (Acinonyx jubatus) Using Unstructured Sampling Data

    PubMed Central

    Broekhuis, Femke; Gopalaswamy, Arjun M.

    2016-01-01

    Many ecological theories and species conservation programmes rely on accurate estimates of population density. Accurate density estimation, especially for species facing rapid declines, requires the application of rigorous field and analytical methods. However, obtaining accurate density estimates of carnivores can be challenging as carnivores naturally exist at relatively low densities and are often elusive and wide-ranging. In this study, we employ an unstructured spatial sampling field design along with a Bayesian sex-specific spatially explicit capture-recapture (SECR) analysis, to provide the first rigorous population density estimates of cheetahs (Acinonyx jubatus) in the Maasai Mara, Kenya. We estimate adult cheetah density to be between 1.28 ± 0.315 and 1.34 ± 0.337 individuals/100km2 across four candidate models specified in our analysis. Our spatially explicit approach revealed ‘hotspots’ of cheetah density, highlighting that cheetah are distributed heterogeneously across the landscape. The SECR models incorporated a movement range parameter which indicated that male cheetah moved four times as much as females, possibly because female movement was restricted by their reproductive status and/or the spatial distribution of prey. We show that SECR can be used for spatially unstructured data to successfully characterise the spatial distribution of a low density species and also estimate population density when sample size is small. Our sampling and modelling framework will help determine spatial and temporal variation in cheetah densities, providing a foundation for their conservation and management. Based on our results we encourage other researchers to adopt a similar approach in estimating densities of individually recognisable species. PMID:27135614

  2. Counting Cats: Spatially Explicit Population Estimates of Cheetah (Acinonyx jubatus) Using Unstructured Sampling Data.

    PubMed

    Broekhuis, Femke; Gopalaswamy, Arjun M

    2016-01-01

    Many ecological theories and species conservation programmes rely on accurate estimates of population density. Accurate density estimation, especially for species facing rapid declines, requires the application of rigorous field and analytical methods. However, obtaining accurate density estimates of carnivores can be challenging as carnivores naturally exist at relatively low densities and are often elusive and wide-ranging. In this study, we employ an unstructured spatial sampling field design along with a Bayesian sex-specific spatially explicit capture-recapture (SECR) analysis, to provide the first rigorous population density estimates of cheetahs (Acinonyx jubatus) in the Maasai Mara, Kenya. We estimate adult cheetah density to be between 1.28 ± 0.315 and 1.34 ± 0.337 individuals/100km2 across four candidate models specified in our analysis. Our spatially explicit approach revealed 'hotspots' of cheetah density, highlighting that cheetah are distributed heterogeneously across the landscape. The SECR models incorporated a movement range parameter which indicated that male cheetah moved four times as much as females, possibly because female movement was restricted by their reproductive status and/or the spatial distribution of prey. We show that SECR can be used for spatially unstructured data to successfully characterise the spatial distribution of a low density species and also estimate population density when sample size is small. Our sampling and modelling framework will help determine spatial and temporal variation in cheetah densities, providing a foundation for their conservation and management. Based on our results we encourage other researchers to adopt a similar approach in estimating densities of individually recognisable species.

  3. Technical Note: Effect of explicit M and N-shell atomic transitions on a low-energy x-ray source

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

    Watson, Peter G. F., E-mail: peter.watson@mail.mcgill.ca; Seuntjens, Jan

    Purpose: In EGSnrc, atomic transitions to and from the M and N-shells are treated in an average way by default. This approach is justified in which the energy difference between explicit and average M and N-shell binding energies is less than 1 keV, and for most applications can be considered negligible. However, for simulations of low energy x-ray sources on thin, high-Z targets, characteristic x-rays can make up a significant portion of the source spectra. As of release V4-2.4.0, EGSnrc has included an option to enable a more complete algorithm of all atomic transitions available in the EADL compilation. Inmore » this paper, the effect of M and N-shell averaging on the calculation of half-value layer (HVL) and relative depth dose (RDD) curve of a 50 kVp intraoperative x-ray tube with a thin gold target was investigated. Methods: A 50 kVp miniature x-ray source with a gold target (The INTRABEAM System, Carl Zeiss, Germany) was modeled with the EGSnrc user code cavity, both with and without M and N-shell averaging. From photon fluence spectra simulations, the source HVLs were determined analytically. The same source model was then used with egs-chamber to calculate RDD curves in water. Results: A 4% increase of HVL was reported when accounting for explicit M and N-shell transitions, and up to a 9% decrease in local relative dose for normalization at 3 mm depth in water. Conclusions: The EGSnrc default of using averaged M and N-shell binding energies has an observable effect on the HVL and RDD of a low energy x-ray source with high-Z target. For accurate modeling of this class of devices, explicit atomic transitions should be included.« less

  4. The Soil Foam Drainage Equation - an alternative model for unsaturated flow in porous media

    NASA Astrophysics Data System (ADS)

    Assouline, Shmuel; Lehmann, Peter; Hoogland, Frouke; Or, Dani

    2017-04-01

    The analogy between the geometry and dynamics of wet foam drainage and gravity drainage of unsaturated porous media expands modeling capabilities for capillary flows and supplements the standard Richards equation representation. The governing equation for draining foam (or a soil variant termed the soil foam drainage equation - SFDE) obviates the need for macroscopic unsaturated hydraulic conductivity function by an explicit account of diminishing flow pathway sizes as the medium gradually drains. Potential advantages of the proposed drainage foam formalism include direct description of transient flow without requiring constitutive functions; evolution of capillary cross sections that provides consistent description of self-regulating internal fluxes (e.g., towards field capacity); and a more intuitive geometrical picture of capillary flow across textural boundaries. We will present new and simple analytical expressions for drainage rates and volumes from unsaturated porous media subjected to different boundary conditions that are in good agreement with the numerical solution of the SFDE and experimental results. The foam drainage methodology expands the range of tools available for describing and quantifying unsaturated flows and provides geometrically tractable links between evolution of liquid configuration and flow dynamics in unsaturated porous media. The resulting geometrical representation of capillary drainage could improve understanding of colloid and pathogen transport. The explicit geometrical interpretation of flow pathways underlying the hydraulic functions used by the Richards equation offers new insights that benefit both approaches.

  5. Relations between the single-pass and double-pass transition probabilities in quantum systems with two and three states

    NASA Astrophysics Data System (ADS)

    Vitanov, Nikolay V.

    2018-05-01

    In the experimental determination of the population transfer efficiency between discrete states of a coherently driven quantum system it is often inconvenient to measure the population of the target state. Instead, after the interaction that transfers the population from the initial state to the target state, a second interaction is applied which brings the system back to the initial state, the population of which is easy to measure and normalize. If the transition probability is p in the forward process, then classical intuition suggests that the probability to return to the initial state after the backward process should be p2. However, this classical expectation is generally misleading because it neglects interference effects. This paper presents a rigorous theoretical analysis based on the SU(2) and SU(3) symmetries of the propagators describing the evolution of quantum systems with two and three states, resulting in explicit analytic formulas that link the two-step probabilities to the single-step ones. Explicit examples are given with the popular techniques of rapid adiabatic passage and stimulated Raman adiabatic passage. The present results suggest that quantum-mechanical probabilities degrade faster in repeated processes than classical probabilities. Therefore, the actual single-pass efficiencies in various experiments, calculated from double-pass probabilities, might have been greater than the reported values.

  6. Use of evidence in a categorization task: analytic and holistic processing modes.

    PubMed

    Greco, Alberto; Moretti, Stefania

    2017-11-01

    Category learning performance can be influenced by many contextual factors, but the effects of these factors are not the same for all learners. The present study suggests that these differences can be due to the different ways evidence is used, according to two main basic modalities of processing information, analytically or holistically. In order to test the impact of the information provided, an inductive rule-based task was designed, in which feature salience and comparison informativeness between examples of two categories were manipulated during the learning phases, by introducing and progressively reducing some perceptual biases. To gather data on processing modalities, we devised the Active Feature Composition task, a production task that does not require classifying new items but reproducing them by combining features. At the end, an explicit rating task was performed, which entailed assessing the accuracy of a set of possible categorization rules. A combined analysis of the data collected with these two different tests enabled profiling participants in regard to the kind of processing modality, the structure of representations and the quality of categorial judgments. Results showed that despite the fact that the information provided was the same for all participants, those who adopted analytic processing better exploited evidence and performed more accurately, whereas with holistic processing categorization is perfectly possible but inaccurate. Finally, the cognitive implications of the proposed procedure, with regard to involved processes and representations, are discussed.

  7. Complete set of homogeneous isotropic analytic solutions in scalar-tensor cosmology with radiation and curvature

    NASA Astrophysics Data System (ADS)

    Bars, Itzhak; Chen, Shih-Hung; Steinhardt, Paul J.; Turok, Neil

    2012-10-01

    We study a model of a scalar field minimally coupled to gravity, with a specific potential energy for the scalar field, and include curvature and radiation as two additional parameters. Our goal is to obtain analytically the complete set of configurations of a homogeneous and isotropic universe as a function of time. This leads to a geodesically complete description of the Universe, including the passage through the cosmological singularities, at the classical level. We give all the solutions analytically without any restrictions on the parameter space of the model or initial values of the fields. We find that for generic solutions the Universe goes through a singular (zero-size) bounce by entering a period of antigravity at each big crunch and exiting from it at the following big bang. This happens cyclically again and again without violating the null-energy condition. There is a special subset of geodesically complete nongeneric solutions which perform zero-size bounces without ever entering the antigravity regime in all cycles. For these, initial values of the fields are synchronized and quantized but the parameters of the model are not restricted. There is also a subset of spatial curvature-induced solutions that have finite-size bounces in the gravity regime and never enter the antigravity phase. These exist only within a small continuous domain of parameter space without fine-tuning the initial conditions. To obtain these results, we identified 25 regions of a 6-parameter space in which the complete set of analytic solutions are explicitly obtained.

  8. Highly accurate analytic formulae for projectile motion subjected to quadratic drag

    NASA Astrophysics Data System (ADS)

    Turkyilmazoglu, Mustafa

    2016-05-01

    The classical phenomenon of motion of a projectile fired (thrown) into the horizon through resistive air charging a quadratic drag onto the object is revisited in this paper. No exact solution is known that describes the full physical event under such an exerted resistance force. Finding elegant analytical approximations for the most interesting engineering features of dynamical behavior of the projectile is the principal target. Within this purpose, some analytical explicit expressions are derived that accurately predict the maximum height, its arrival time as well as the flight range of the projectile at the highest ascent. The most significant property of the proposed formulas is that they are not restricted to the initial speed and firing angle of the object, nor to the drag coefficient of the medium. In combination with the available approximations in the literature, it is possible to gain information about the flight and complete the picture of a trajectory with high precision, without having to numerically simulate the full governing equations of motion.

  9. A combined analytical formulation and genetic algorithm to analyze the nonlinear damage responses of continuous fiber toughened composites

    NASA Astrophysics Data System (ADS)

    Jeon, Haemin; Yu, Jaesang; Lee, Hunsu; Kim, G. M.; Kim, Jae Woo; Jung, Yong Chae; Yang, Cheol-Min; Yang, B. J.

    2017-09-01

    Continuous fiber-reinforced composites are important materials that have the highest commercialized potential in the upcoming future among existing advanced materials. Despite their wide use and value, their theoretical mechanisms have not been fully established due to the complexity of the compositions and their unrevealed failure mechanisms. This study proposes an effective three-dimensional damage modeling of a fibrous composite by combining analytical micromechanics and evolutionary computation. The interface characteristics, debonding damage, and micro-cracks are considered to be the most influential factors on the toughness and failure behaviors of composites, and a constitutive equation considering these factors was explicitly derived in accordance with the micromechanics-based ensemble volume averaged method. The optimal set of various model parameters in the analytical model were found using modified evolutionary computation that considers human-induced error. The effectiveness of the proposed formulation was validated by comparing a series of numerical simulations with experimental data from available studies.

  10. Combined structures-controls optimization of lattice trusses

    NASA Technical Reports Server (NTRS)

    Balakrishnan, A. V.

    1991-01-01

    The role that distributed parameter model can play in CSI is demonstrated, in particular in combined structures controls optimization problems of importance in preliminary design. Closed form solutions can be obtained for performance criteria such as rms attitude error, making possible analytical solutions of the optimization problem. This is in contrast to the need for numerical computer solution involving the inversion of large matrices in traditional finite element model (FEM) use. Another advantage of the analytic solution is that it can provide much needed insight into phenomena that can otherwise be obscured or difficult to discern from numerical computer results. As a compromise in level of complexity between a toy lab model and a real space structure, the lattice truss used in the EPS (Earth Pointing Satellite) was chosen. The optimization problem chosen is a generic one: of minimizing the structure mass subject to a specified stability margin and to a specified upper bond on the rms attitude error, using a co-located controller and sensors. Standard FEM treating each bar as a truss element is used, while the continuum model is anisotropic Timoshenko beam model. Performance criteria are derived for each model, except that for the distributed parameter model, explicit closed form solutions was obtained. Numerical results obtained by the two model show complete agreement.

  11. Capture zones for simple aquifers

    USGS Publications Warehouse

    McElwee, Carl D.

    1991-01-01

    Capture zones showing the area influenced by a well within a certain time are useful for both aquifer protection and cleanup. If hydrodynamic dispersion is neglected, a deterministic curve defines the capture zone. Analytical expressions for the capture zones can be derived for simple aquifers. However, the capture zone equations are transcendental and cannot be explicitly solved for the coordinates of the capture zone boundary. Fortunately, an iterative scheme allows the solution to proceed quickly and efficiently even on a modest personal computer. Three forms of the analytical solution must be used in an iterative scheme to cover the entire region of interest, after the extreme values of the x coordinate are determined by an iterative solution. The resulting solution is a discrete one, and usually 100-1000 intervals along the x-axis are necessary for a smooth definition of the capture zone. The presented program is written in FORTRAN and has been used in a variety of computing environments. No graphics capability is included with the program; it is assumed the user has access to a commercial package. The superposition of capture zones for multiple wells is expected to be satisfactory if the spacing is not too close. Because this program deals with simple aquifers, the results rarely will be the final word in a real application.

  12. Analytical Solutions for an Escape Problem in a Disc with an Arbitrary Distribution of Exit Holes Along Its Boundary

    NASA Astrophysics Data System (ADS)

    Marshall, J. S.

    2016-12-01

    We analytically construct solutions for the mean first-passage time and splitting probabilities for the escape problem of a particle moving with continuous Brownian motion in a confining planar disc with an arbitrary distribution (i.e., of any number, size and spacing) of exit holes/absorbing sections along its boundary. The governing equations for these quantities are Poisson's equation with a (non-zero) constant forcing term and Laplace's equation, respectively, and both are subject to a mixture of homogeneous Neumann and Dirichlet boundary conditions. Our solutions are expressed as explicit closed formulae written in terms of a parameterising variable via a conformal map, using special transcendental functions that are defined in terms of an associated Schottky group. They are derived by exploiting recent results for a related problem of fluid mechanics that describes a unidirectional flow over "no-slip/no-shear" surfaces, as well as results from potential theory, all of which were themselves derived using the same theory of Schottky groups. They are exact up to the determination of a finite set of mapping parameters, which is performed numerically. Their evaluation also requires the numerical inversion of the parameterising conformal map. Computations for a series of illustrative examples are also presented.

  13. Analytical model of threshold voltage degradation due to localized charges in gate material engineered Schottky barrier cylindrical GAA MOSFETs

    NASA Astrophysics Data System (ADS)

    Kumar, Manoj; Haldar, Subhasis; Gupta, Mridula; Gupta, R. S.

    2016-10-01

    The threshold voltage degradation due to the hot carrier induced localized charges (LC) is a major reliability concern for nanoscale Schottky barrier (SB) cylindrical gate all around (GAA) metal-oxide-semiconductor field-effect transistors (MOSFETs). The degradation physics of gate material engineered (GME)-SB-GAA MOSFETs due to LC is still unexplored. An explicit threshold voltage degradation model for GME-SB-GAA-MOSFETs with the incorporation of localized charges (N it) is developed. To accurately model the threshold voltage the minimum channel carrier density has been taken into account. The model renders how +/- LC affects the device subthreshold performance. One-dimensional (1D) Poisson’s and 2D Laplace equations have been solved for two different regions (fresh and damaged) with two different gate metal work-functions. LCs are considered at the drain side with low gate metal work-function as N it is more vulnerable towards the drain. For the reduction of carrier mobility degradation, a lightly doped channel has been considered. The proposed model also includes the effect of barrier height lowering at the metal-semiconductor interface. The developed model results have been verified using numerical simulation data obtained by the ATLAS-3D device simulator and excellent agreement is observed between analytical and simulation results.

  14. A first-principles analytical theory for 2D magnetic reconnection in electron and Hall MHD.

    NASA Astrophysics Data System (ADS)

    Zocco, A.; Simakov, A. N.; Chacon, L.

    2007-11-01

    While the relevance of two-fluid effects in fast magnetic reconnection is well-known,ootnotetextJ. Birn et al., J. Geophys. Res., 106 (A3), pp. 3715--3719 (2001) a first-principles theory --akin to Sweet and Parker's in resistive MHD-- has been elusive. Here, we present such a first principles steady-state theory for electron MHD,ootnotetextL. Chac'on, A. N. Simakov, A. Zocco, Phys. Rev. Lett., submitted and its extension to Hall.ootnotetextA. N. Simakov, L. Chac'on, in preparation The theory discretizes the extended MHD equations at the reconnection site, leading to a set of time-dependent ODEs. Their steady-state analysis provides predictions for the scaling of relevant quantities with the dissipation coefficients (e.g, resistivity and hyper-resistivity) and other relevant parameters. In particular, we will show that EMHD admits both elongated and open-X point configurations of the reconnection region, and that the reconnection rate Ez can be shown not to scale explicitly with the dissipation parameters. This analytic result confirms earlier computational work on the possibility of fast (dissipation-independent) magnetic reconnection in EMHD. We have extended the EMHD results to Hall MHD, and have found a general scaling law for the reconnection rate (and associated length scales) that bridges the gap between resistive and EMHD.

  15. Reactant conversion in homogeneous turbulence: Mathematical modeling, computational validations and practical applications

    NASA Technical Reports Server (NTRS)

    Madnia, C. K.; Frankel, S. H.; Givi, P.

    1992-01-01

    Closed form analytical expressions are obtained for predicting the limited rate of reactant conversion in a binary reaction of the type F + rO yields (1 + r) Product in unpremixed homogeneous turbulence. These relations are obtained by means of a single point Probability Density Function (PDF) method based on the Amplitude Mapping Closure. It is demonstrated that with this model, the maximum rate of the reactants' decay can be conveniently expressed in terms of definite integrals of the Parabolic Cylinder Functions. For the cases with complete initial segregation, it is shown that the results agree very closely with those predicted by employing a Beta density of the first kind for an appropriately defined Shvab-Zeldovich scalar variable. With this assumption, the final results can also be expressed in terms of closed form analytical expressions which are based on the Incomplete Beta Functions. With both models, the dependence of the results on the stoichiometric coefficient and the equivalence ratio can be expressed in an explicit manner. For a stoichiometric mixture, the analytical results simplify significantly. In the mapping closure, these results are expressed in terms of simple trigonometric functions. For the Beta density model, they are in the form of Gamma Functions. In all the cases considered, the results are shown to agree well with data generated by Direct Numerical Simulations (DNS). Due to the simplicity of these expressions and because of nice mathematical features of the Parabolic Cylinder and the Incomplete Beta Functions, these models are recommended for estimating the limiting rate of reactant conversion in homogeneous reacting flows. These results also provide useful insights in assessing the extent of validity of turbulence closures in the modeling of unpremixed reacting flows. Some discussions are provided on the extension of the model for treating more complicated reacting systems including realistic kinetics schemes and multi-scalar mixing with finite rate chemical reactions in more complex configurations.

  16. Complementary optical rogue waves in parametric three-wave mixing.

    PubMed

    Chen, Shihua; Cai, Xian-Ming; Grelu, Philippe; Soto-Crespo, J M; Wabnitz, Stefan; Baronio, Fabio

    2016-03-21

    We investigate the resonant interaction of two optical pulses of the same group velocity with a pump pulse of different velocity in a weakly dispersive quadratic medium and report on the complementary rogue wave dynamics which are unique to such a parametric three-wave mixing. Analytic rogue wave solutions up to the second order are explicitly presented and their robustness is confirmed by numerical simulations, in spite of the onset of modulation instability activated by quantum noise.

  17. On the orthogonal dissipative lax-phillips scattering theory

    NASA Astrophysics Data System (ADS)

    Neidhardt, Hagen

    1988-08-01

    The paper is devoted to the so-called orthogonal dissipative Lax-Phillips scattering theory. A parametrization of all possible orthogonal dissipative Lax-Phillips scattering theories is obtained in terms of ordered 6-tuples consisting of unilateral shifts and contractions which can be, roughly speaking, freely chosen. In this parametrization the wave and scattering operators as well as the scattering matrix are explicitly calculated. Moreover, a description of all analytical contraction-valued functions admitting a Darlington synthesis is found.

  18. An exact solution to the relativistic equation of motion of a charged particle driven by a linearly polarized electromagnetic wave

    NASA Technical Reports Server (NTRS)

    Shebalin, John V.

    1988-01-01

    An exact analytic solution is found for a basic electromagnetic wave-charged particle interaction by solving the nonlinear equations of motion. The particle position, velocity, and corresponding time are found to be explicit functions of the total phase of the wave. Particle position and velocity are thus implicit functions of time. Applications include describing the motion of a free electron driven by an intense laser beam..

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

    Wallace Tyner

    The project had three main objectives: to build and incorporate an explicit biomass energy sector within the GTAP analytical framework and data base; to provide an analysis of the impact of renewable fuel standards and other policies in the U.S. and E.U, as well as alternative biofuel policies in other parts of the world, on changes in production, prices, consumption, trade and poverty; and to evaluate environmental impacts of alternative policies for bioenergy development. Progress and outputs related to each objective are reported.

  20. Comparative-effectiveness research to aid population decision making by relating clinical outcomes and quality-adjusted life years.

    PubMed

    Campbell, Jonathan D; Zerzan, Judy; Garrison, Louis P; Libby, Anne M

    2013-04-01

    Comparative-effectiveness research (CER) at the population level is missing standardized approaches to quantify and weigh interventions in terms of their clinical risks, benefits, and uncertainty. We proposed an adapted CER framework for population decision making, provided example displays of the outputs, and discussed the implications for population decision makers. Building on decision-analytical modeling but excluding cost, we proposed a 2-step approach to CER that explicitly compared interventions in terms of clinical risks and benefits and linked this evidence to the quality-adjusted life year (QALY). The first step was a traditional intervention-specific evidence synthesis of risks and benefits. The second step was a decision-analytical model to simulate intervention-specific progression of disease over an appropriate time. The output was the ability to compare and quantitatively link clinical outcomes with QALYs. The outputs from these CER models include clinical risks, benefits, and QALYs over flexible and relevant time horizons. This approach yields an explicit, structured, and consistent quantitative framework to weigh all relevant clinical measures. Population decision makers can use this modeling framework and QALYs to aid in their judgment of the individual and collective risks and benefits of the alternatives over time. Future research should study effective communication of these domains for stakeholders. Copyright © 2013 Elsevier HS Journals, Inc. All rights reserved.

  1. The Electrostatic Instability for Realistic Pair Distributions in Blazar/EBL Cascades

    NASA Astrophysics Data System (ADS)

    Vafin, S.; Rafighi, I.; Pohl, M.; Niemiec, J.

    2018-04-01

    This work revisits the electrostatic instability for blazar-induced pair beams propagating through the intergalactic medium (IGM) using linear analysis and PIC simulations. We study the impact of the realistic distribution function of pairs resulting from the interaction of high-energy gamma-rays with the extragalactic background light. We present analytical and numerical calculations of the linear growth rate of the instability for the arbitrary orientation of wave vectors. Our results explicitly demonstrate that the finite angular spread of the beam dramatically affects the growth rate of the waves, leading to the fastest growth for wave vectors quasi-parallel to the beam direction and a growth rate at oblique directions that is only a factor of 2–4 smaller compared to the maximum. To study the nonlinear beam relaxation, we performed PIC simulations that take into account a realistic wide-energy distribution of beam particles. The parameters of the simulated beam-plasma system provide an adequate physical picture that can be extrapolated to realistic blazar-induced pairs. In our simulations, the beam looses only 1% of its energy, and we analytically estimate that the beam would lose its total energy over about 100 simulation times. An analytical scaling is then used to extrapolate the parameters of realistic blazar-induced pair beams. We find that they can dissipate their energy slightly faster by the electrostatic instability than through inverse-Compton scattering. The uncertainties arising from, e.g., details of the primary gamma-ray spectrum are too large to make firm statements for individual blazars, and an analysis based on their specific properties is required.

  2. Generalized Born Models of Macromolecular Solvation Effects

    NASA Astrophysics Data System (ADS)

    Bashford, Donald; Case, David A.

    2000-10-01

    It would often be useful in computer simulations to use a simple description of solvation effects, instead of explicitly representing the individual solvent molecules. Continuum dielectric models often work well in describing the thermodynamic aspects of aqueous solvation, and approximations to such models that avoid the need to solve the Poisson equation are attractive because of their computational efficiency. Here we give an overview of one such approximation, the generalized Born model, which is simple and fast enough to be used for molecular dynamics simulations of proteins and nucleic acids. We discuss its strengths and weaknesses, both for its fidelity to the underlying continuum model and for its ability to replace explicit consideration of solvent molecules in macromolecular simulations. We focus particularly on versions of the generalized Born model that have a pair-wise analytical form, and therefore fit most naturally into conventional molecular mechanics calculations.

  3. Pesticide risk assessment in free-ranging bees is weather and landscape dependent.

    PubMed

    Henry, Mickaël; Bertrand, Colette; Le Féon, Violette; Requier, Fabrice; Odoux, Jean-François; Aupinel, Pierrick; Bretagnolle, Vincent; Decourtye, Axel

    2014-07-10

    The risk assessment of plant protection products on pollinators is currently based on the evaluation of lethal doses through repeatable lethal toxicity laboratory trials. Recent advances in honeybee toxicology have, however, raised interest on assessing sublethal effects in free-ranging individuals. Here, we show that the sublethal effects of a neonicotinoid pesticide are modified in magnitude by environmental interactions specific to the landscape and time of exposure events. Field sublethal assessment is therefore context dependent and should be addressed in a temporally and spatially explicit way, especially regarding weather and landscape physiognomy. We further develop an analytical Effective Dose (ED) framework to help disentangle context-induced from treatment-induced effects and thus to alleviate uncertainty in field studies. Although the ED framework involves trials at concentrations above the expected field exposure levels, it allows to explicitly delineating the climatic and landscape contexts that should be targeted for in-depth higher tier risk assessment.

  4. On the representation of many-body interactions in water

    DOE PAGES

    Medders, Gregory R.; Gotz, Andreas W.; Morales, Miguel A.; ...

    2015-09-09

    Our recent work has shown that the many-body expansion of the interactionenergy can be used to develop analytical representations of global potential energy surfaces (PESs) for water. In this study, the role of short- and long-range interactions at different orders is investigated by analyzing water potentials that treat the leading terms of the many-body expansion through implicit (i.e., TTM3-F and TTM4-F PESs) and explicit (i.e., WHBB and MB-pol PESs) representations. Moreover, it is found that explicit short-range representations of 2-body and 3-body interactions along with a physically correct incorporation of short- and long-range contributions are necessary for an accurate representationmore » of the waterinteractions from the gas to the condensed phase. Likewise, a complete many-body representation of the dipole moment surface is found to be crucial to reproducing the correct intensities of the infrared spectrum of liquid water.« less

  5. Quantum thermal diode based on two interacting spinlike systems under different excitations.

    PubMed

    Ordonez-Miranda, Jose; Ezzahri, Younès; Joulain, Karl

    2017-02-01

    We demonstrate that two interacting spinlike systems characterized by different excitation frequencies and coupled to a thermal bath each, can be used as a quantum thermal diode capable of efficiently rectifying the heat current. This is done by deriving analytical expressions for both the heat current and rectification factor of the diode, based on the solution of a master equation for the density matrix. Higher rectification factors are obtained for lower heat currents, whose magnitude takes their maximum values for a given interaction coupling proportional to the temperature of the hotter thermal bath. It is shown that the rectification ability of the diode increases with the excitation frequencies difference, which drives the asymmetry of the heat current, when the temperatures of the thermal baths are inverted. Furthermore, explicit conditions for the optimization of the rectification factor and heat current are explicitly found.

  6. GPU-accelerated simulations of isolated black holes

    NASA Astrophysics Data System (ADS)

    Lewis, Adam G. M.; Pfeiffer, Harald P.

    2018-05-01

    We present a port of the numerical relativity code SpEC which is capable of running on NVIDIA GPUs. Since this code must be maintained in parallel with SpEC itself, a primary design consideration is to perform as few explicit code changes as possible. We therefore rely on a hierarchy of automated porting strategies. At the highest level we use TLoops, a C++ library of our design, to automatically emit CUDA code equivalent to tensorial expressions written into C++ source using a syntax similar to analytic calculation. Next, we trace out and cache explicit matrix representations of the numerous linear transformations in the SpEC code, which allows these to be performed on the GPU using pre-existing matrix-multiplication libraries. We port the few remaining important modules by hand. In this paper we detail the specifics of our port, and present benchmarks of it simulating isolated black hole spacetimes on several generations of NVIDIA GPU.

  7. Improved Subcell Model for the Prediction of Braided Composite Response

    NASA Technical Reports Server (NTRS)

    Cater, Christopher R.; Xinran, Xiao; Goldberg, Robert K.; Kohlman, Lee W.

    2013-01-01

    In this work, the modeling of triaxially braided composites was explored through a semi-analytical discretization. Four unique subcells, each approximated by a "mosaic" stacking of unidirectional composite plies, were modeled through the use of layered-shell elements within the explicit finite element code LS-DYNA. Two subcell discretizations were investigated: a model explicitly capturing pure matrix regions, and a novel model which absorbed pure matrix pockets into neighboring tow plies. The in-plane stiffness properties of both models, computed using bottom-up micromechanics, correlated well to experimental data. The absorbed matrix model, however, was found to best capture out-of- plane flexural properties by comparing numerical simulations of the out-of-plane displacements from single-ply tension tests to experimental full field data. This strong correlation of out-of-plane characteristics supports the current modeling approach as a viable candidate for future work involving impact simulations.

  8. Designing a Double-Pole Nanoscale Relay Based on a Carbon Nanotube: A Theoretical Study

    NASA Astrophysics Data System (ADS)

    Mu, Weihua; Ou-Yang, Zhong-can; Dresselhaus, Mildred S.

    2017-08-01

    We theoretically investigate a novel and powerful double-pole nanoscale relay based on a carbon nanotube, which is one of the nanoelectromechanical switches being able to work under the strong nuclear radiation, and analyze the physical mechanism of the operating stages in the operation, including "pull in," "connection," and "pull back," as well as the key factors influencing the efficiency of the devices. We explicitly provide the analytical expression of the two important operation voltages, Vpull in and Vpull back , therefore clearly showing the dependence of the material properties and geometry of the present devices by the analytical method from basic physics, avoiding complex numerical calculations. Our method is easy to use in preparing the design guide for fabricating the present device and other nanoelectromechanical devices.

  9. Leading multi-soft limits from scattering equations

    NASA Astrophysics Data System (ADS)

    Zlotnikov, Michael

    2017-10-01

    A Cachazo-He-Yuan (CHY) type formula is derived for the leading gluon, bi-adjoint scalar ϕ 3, Yang-Mills-scalar and non-linear sigma model m-soft factors S m in arbitrary dimension. The general formula is used to evaluate explicit examples for up to three soft legs analytically and up to four soft legs numerically via comparison with amplitude ratios under soft kinematics. A structural pattern for gluon m-soft factor is inferred and a simpler formula for its calculation is conjectured. In four dimensions, a Cachazo-Svrček-Witten (CSW) recursive procedure producing the leading m-soft gluon factor in spinor helicity formalism is developed as an alternative, and Britto-Cachazo-Feng-Witten (BCFW) recursion is used to obtain the leading four-soft gluon factor for all analytically distinct helicity configurations.

  10. Tornado model for a magnetised plasma

    NASA Astrophysics Data System (ADS)

    Onishchenko, O. G.; Fedun, V.; Smolyakov, A.; Horton, W.; Pokhotelov, O. A.; Verth, G.

    2018-05-01

    A new analytical model of axially-symmetric magnetic vortices with both a twisted fluid flow and a magnetic field is proposed. The exact solution for the three-dimensional structure of the fluid velocity and the magnetic field is obtained within the framework of the ideal magnetohydrodynamic equations for an incompressible fluid in a gravitational field. A quasi-stationary localised vortex arises when the radial flow that tends to concentrate vorticity in a narrow column around the axis of symmetry is balanced by the vertical vortex advection in the axial direction. The explicit expressions for the velocity and magnetic field components are obtained. The proposed analytic model may be used to parameterise the observed solar tornadoes and can provide a new indirect way for estimating magnetic twist from the observed azimuthal velocity profiles.

  11. Analytical inversions in remote sensing of particle size distributions. IV - Comparison of Fymat and Box-McKellar solutions in the anomalous diffraction approximation

    NASA Technical Reports Server (NTRS)

    Fymat, A. L.; Smith, C. B.

    1979-01-01

    It is shown that the inverse analytical solutions, provided separately by Fymat and Box-McKellar, for reconstructing particle size distributions from remote spectral transmission measurements under the anomalous diffraction approximation can be derived using a cosine and a sine transform, respectively. Sufficient conditions of validity of the two formulas are established. Their comparison shows that the former solution is preferable to the latter in that it requires less a priori information (knowledge of the particle number density is not needed) and has wider applicability. For gamma-type distributions, and either a real or a complex refractive index, explicit expressions are provided for retrieving the distribution parameters; such expressions are, interestingly, proportional to the geometric area of the polydispersion.

  12. Analytical close-to-source investigation for an isotropic point source in an unbounded, anisotropically scattering medium

    NASA Astrophysics Data System (ADS)

    Rinzema, Kees; ten Bosch, Jaap J.; Ferwerda, Hedzer A.; Hoenders, Bernhard J.

    1995-01-01

    The diffusion approximation, which is often used to describe the propagation of light in biological tissues, is only good at a sufficient distance from sources and boundaries. Light- tissue interaction is however most intense in the region close to the source. It would therefore be interesting to study this region more closely. Although scattering in biological tissues is predominantly forward peaked, explicit solutions to the transport equation have only been obtained in the case of isotropic scattering. Particularly, for the case of an isotropic point source in an unbounded, isotropically scattering medium the solution is well known. We show that this problem can also be solved analytically if the scattering is no longer isotropic, while everything else remains the same.

  13. Exact solutions of the population balance equation including particle transport, using group analysis

    NASA Astrophysics Data System (ADS)

    Lin, Fubiao; Meleshko, Sergey V.; Flood, Adrian E.

    2018-06-01

    The population balance equation (PBE) has received an unprecedented amount of attention in recent years from both academics and industrial practitioners because of its long history, widespread use in engineering, and applicability to a wide variety of particulate and discrete-phase processes. However it is typically impossible to obtain analytical solutions, although in almost every case a numerical solution of the PBEs can be obtained. In this article, the symmetries of PBEs with homogeneous coagulation kernels involving aggregation, breakage and growth processes and particle transport in one dimension are found by direct solving the determining equations. Using the optimal system of one and two-dimensional subalgebras, all invariant solutions and reduced equations are obtained. In particular, an explicit analytical physical solution is also presented.

  14. An analytic solution of the radiative transfer equation for a gray scattering atmosphere in motion

    NASA Astrophysics Data System (ADS)

    Pistinner, Shlomi; Shaviv, Giora

    1994-12-01

    We provide a formal analytic solution of the radiative transfer equation for a gray moving atmosphere in a plane parallel geometry. A formal solution in the diffusion and the free-streaming limit is also provided in the case of a spherically extended atmosphere. The formal solutions are written explicitly for scattering atmospheres in which the density and the velocity fields are given by a power law. A self-consistent temperature profile accurate to O(Beta = v/c) is provided for the case in which the absorption or the scattering are temperature independent. The gray extinction temperature profile is considerably simplified in the case of a scattering atmosphere. Steady state flow and homologous expansion are special cases that are considered in detail.

  15. An analytic solution of the radiative transfer equation for a gray scattering atmosphere in motion

    NASA Technical Reports Server (NTRS)

    Pistinner, Shlomi; Shaviv, Giora

    1994-01-01

    We provide a formal analytic solution of the radiative transfer equation for a gray moving atmosphere in a plane parallel geometry. A formal solution in the diffusion and the free-streaming limit is also provided in the case of a spherically extended atmosphere. The formal solutions are written explicitly for scattering atmospheres in which the density and the velocity fields are given by a power law. A self-consistent temperature profile accurate to O(Beta = v/c) is provided for the case in which the absorption or the scattering are temperature independent. The gray extinction temperature profile is considerably simplified in the case of a scattering atmosphere. Steady state flow and homologous expansion are special cases that are considered in detail.

  16. Non-collinear magnetism with analytic Bond-Order Potentials

    NASA Astrophysics Data System (ADS)

    Ford, Michael E.; Pettifor, D. G.; Drautz, Ralf

    2015-03-01

    The theory of analytic Bond-Order Potentials as applied to non-collinear magnetic structures of transition metals is extended to take into account explicit rotations of Hamiltonian and local moment matrix elements between locally and globally defined spin-coordinate systems. Expressions for the gradients of the energy with respect to the Hamiltonian matrix elements, the interatomic forces and the magnetic torques are derived. The method is applied to simulations of the rotation of magnetic moments in α iron, as well as α and β manganese, based on d-valent orthogonal tight-binding parametrizations of the electronic structure. A new weighted-average terminator is introduced to improve the convergence of the Bond-Order Potential energies and torques with respect to tight-binding reference values, although the general behavior is qualitatively correct for low-moment expansions.

  17. Geomorphology and landscape organization of a northern peatland complex

    NASA Astrophysics Data System (ADS)

    Richardson, M. C.

    2012-12-01

    The geomorphic evolution of northern peatlands is governed by complex ecohydrological feedback mechanisms and associated hydro-climatic drivers. For example, prevailing models of bog development (i.e. Ingram's groundwater mounding hypothesis and variants) attempt to explicitly link bog dome characteristics to the regional climate based on analytical and numerical models of lateral groundwater flow and the first-order control of water table position on rates of peat accumulation. In this talk I will present new results from quantitative geomorphic analyses of a northern peatland complex at the De Beers Victor diamond mine site in the Hudson Bay Lowlands of northern Ontario. This work capitalizes on spatially-extensive, high-resolution topographic (LiDAR) data to rigorously test analytical and numerical models of bog dome development in this landscape. The analysis and discussion are then expanded beyond individual bog formations to more broadly consider ecohydrological drivers of landscape organization, with implications for understanding and modeling catchment-scale runoff response. Results show that in this landscape, drainage patterns exhibit relatively well-organized characteristics consistent with observed runoff responses in six gauged research catchments. Interpreted together, the results of these geomorphic and hydrologic analyses help refine our understanding of water balance partitioning among different landcover types within northern peatland complexes. These findings can be used to help guide the development of appropriate numerical model structures for hydrologic prediction in ungauged peatland basins of northern Canada.

  18. Predicting organic food consumption: A meta-analytic structural equation model based on the theory of planned behavior.

    PubMed

    Scalco, Andrea; Noventa, Stefano; Sartori, Riccardo; Ceschi, Andrea

    2017-05-01

    During the last decade, the purchase of organic food within a sustainable consumption context has gained momentum. Consequently, the amount of research in the field has increased, leading in some cases to discrepancies regarding both methods and results. The present review examines those works that applied the theory of planned behavior (TPB; Ajzen, 1991) as a theoretical framework in order to understand and predict consumers' motivation to buy organic food. A meta-analysis has been conducted to assess the strength of the relationships between attitude, subjective norms, perceived behavioral control, and intention, as well as between intention and behavior. Results confirm the major role played by individual attitude in shaping buying intention, followed by subjective norms and perceived behavioral control. Intention-behavior shows a large effect size, few studies however explicitly reported such an association. Furthermore, starting from a pooled correlation matrix, a meta-analytic structural equation model has been applied to jointly evaluate the strength of the relationships among the factors of the original model. Results suggest the robustness of the TPB model. In addition, mediation analysis indicates a potential direct effect from subjective norms to individual attitude in the present context. Finally, some issues regarding methodological aspects of the application of the TPB within the context of organic food are discussed for further research developments. Copyright © 2017 Elsevier Ltd. All rights reserved.

  19. Forces and torques on rigid inclusions in an elastic environment: Resulting matrix-mediated interactions, displacements, and rotations

    NASA Astrophysics Data System (ADS)

    Puljiz, Mate; Menzel, Andreas M.

    2017-05-01

    Embedding rigid inclusions into elastic matrix materials is a procedure of high practical relevance, for instance, for the fabrication of elastic composite materials. We theoretically analyze the following situation. Rigid spherical inclusions are enclosed by a homogeneous elastic medium under stick boundary conditions. Forces and torques are directly imposed from outside onto the inclusions or are externally induced between them. The inclusions respond to these forces and torques by translations and rotations against the surrounding elastic matrix. This leads to elastic matrix deformations, and in turn results in mutual long-ranged matrix-mediated interactions between the inclusions. Adapting a well-known approach from low-Reynolds-number hydrodynamics, we explicitly calculate the displacements and rotations of the inclusions from the externally imposed or induced forces and torques. Analytical expressions are presented as a function of the inclusion configuration in terms of displaceability and rotateability matrices. The role of the elastic environment is implicitly included in these relations. That is, the resulting expressions allow a calculation of the induced displacements and rotations directly from the inclusion configuration, without having to explicitly determine the deformations of the elastic environment. In contrast to the hydrodynamic case, compressibility of the surrounding medium is readily taken into account. We present the complete derivation based on the underlying equations of linear elasticity theory. In the future, the method will, for example, be helpful to characterize the behavior of externally tunable elastic composite materials, to accelerate numerical approaches, as well as to improve the quantitative interpretation of microrheological results.

  20. Operator assistant systems - An experimental approach using a telerobotics application

    NASA Technical Reports Server (NTRS)

    Boy, Guy A.; Mathe, Nathalie

    1993-01-01

    This article presents a knowledge-based system methodology for developing operator assistant (OA) systems in dynamic and interactive environments. This is a problem both of training and design, which is the subject of this article. Design includes both design of the system to be controlled and design of procedures for operating this system. A specific knowledge representation is proposed for representing the corresponding system and operational knowledge. This representation is based on the situation recognition and analytical reasoning paradigm. It tries to make explicit common factors involved in both human and machine intelligence, including perception and reasoning. An OA system based on this representation has been developed for space telerobotics. Simulations have been carried out with astronauts and the resulting protocols have been analyzed. Results show the relevance of the approach and have been used for improving the knowledge representation and the OA architecture.

  1. Information of Complex Systems and Applications in Agent Based Modeling.

    PubMed

    Bao, Lei; Fritchman, Joseph C

    2018-04-18

    Information about a system's internal interactions is important to modeling the system's dynamics. This study examines the finer categories of the information definition and explores the features of a type of local information that describes the internal interactions of a system. Based on the results, a dual-space agent and information modeling framework (AIM) is developed by explicitly distinguishing an information space from the material space. The two spaces can evolve both independently and interactively. The dual-space framework can provide new analytic methods for agent based models (ABMs). Three examples are presented including money distribution, individual's economic evolution, and artificial stock market. The results are analyzed in the dual-space, which more clearly shows the interactions and evolutions within and between the information and material spaces. The outcomes demonstrate the wide-ranging applicability of using the dual-space AIMs to model and analyze a broad range of interactive and intelligent systems.

  2. Entanglement negativity after a local quantum quench in conformal field theories

    NASA Astrophysics Data System (ADS)

    Wen, Xueda; Chang, Po-Yao; Ryu, Shinsei

    2015-08-01

    We study the time evolution of the entanglement negativity after a local quantum quench in (1 + 1)-dimensional conformal field theories (CFTs), which we introduce by suddenly joining two initially decoupled CFTs at their end points. We calculate the negativity evolution for both adjacent intervals and disjoint intervals explicitly. For two adjacent intervals, the entanglement negativity grows logarithmically in time right after the quench. After developing a plateau-like feature, the entanglement negativity drops to the ground-state value. For the case of two spatially separated intervals, a light-cone behavior is observed in the negativity evolution; in addition, a long-range entanglement, which is independent of the distance between two intervals, can be created. Our results agree with the heuristic picture that quasiparticles, which carry entanglement, are emitted from the joining point and propagate freely through the system. Our analytical results are confirmed by numerical calculations based on a critical harmonic chain.

  3. Semiclassical evaluation of quantum fidelity

    NASA Astrophysics Data System (ADS)

    Vaníček, Jiří; Heller, Eric J.

    2003-11-01

    We present a numerically feasible semiclassical (SC) method to evaluate quantum fidelity decay (Loschmidt echo) in a classically chaotic system. It was thought that such evaluation would be intractable, but instead we show that a uniform SC expression not only is tractable but it also gives remarkably accurate numerical results for the standard map in both the Fermi-golden-rule and Lyapunov regimes. Because it allows Monte Carlo evaluation, the uniform expression is accurate at times when there are 1070 semiclassical contributions. Remarkably, it also explicitly contains the “building blocks” of analytical theories of recent literature, and thus permits a direct test of the approximations made by other authors in these regimes, rather than an a posteriori comparison with numerical results. We explain in more detail the extended validity of the classical perturbation approximation and show that within this approximation, the so-called “diagonal approximation” is automatic and does not require ensemble averaging.

  4. Numerical solution of the full potential equation using a chimera grid approach

    NASA Technical Reports Server (NTRS)

    Holst, Terry L.

    1995-01-01

    A numerical scheme utilizing a chimera zonal grid approach for solving the full potential equation in two spatial dimensions is described. Within each grid zone a fully-implicit approximate factorization scheme is used to advance the solution one interaction. This is followed by the explicit advance of all common zonal grid boundaries using a bilinear interpolation of the velocity potential. The presentation is highlighted with numerical results simulating the flow about a two-dimensional, nonlifting, circular cylinder. For this problem, the flow domain is divided into two parts: an inner portion covered by a polar grid and an outer portion covered by a Cartesian grid. Both incompressible and compressible (transonic) flow solutions are included. Comparisons made with an analytic solution as well as single grid results indicate that the chimera zonal grid approach is a viable technique for solving the full potential equation.

  5. A Combined FEM/MoM/GTD Technique To Analyze Elliptically Polarized Cavity-Backed Antennas With Finite Ground Plane

    NASA Technical Reports Server (NTRS)

    Reddy, C. J.; Deshpande, M. D.; Fralick, D. T.; Cockrell, C. R.; Beck, F. B.

    1996-01-01

    Radiation pattern prediction analysis of elliptically polarized cavity-backed aperture antennas in a finite ground plane is performed using a combined Finite Element Method/Method of Moments/Geometrical Theory of Diffraction (FEM/MoM/GTD) technique. The magnetic current on the cavity-backed aperture in an infinite ground plane is calculated using the combined FEM/MoM analysis. GTD, including the slope diffraction contribution, is used to calculate the diffracted fields caused by both soft and hard polarizations at the edges of the finite ground plane. Explicit expressions for regular diffraction coefficients and slope diffraction coefficients are presented. The slope of the incident magnetic field at the diffraction points is derived and analytical expressions are presented. Numerical results for the radiation patterns of a cavity-backed circular spiral microstrip patch antenna excited by a coaxial probe in a finite rectangular ground plane are computed and compared with experimental results.

  6. Coaxial rotatory-freestanding triboelectric nanogenerator for effective energy scavenging from wind

    NASA Astrophysics Data System (ADS)

    Ren, Xiaohu; Fan, Huiqing; Wang, Chao; Ma, Jiangwei; Zhao, Nan

    2018-06-01

    Ambient mechanical energy is one of the most abundant energy sources around us. It is a promising approach to solve the problem of energy and environment by harvesting such energy due to its cost-effectiveness, environmental friendliness and sustainability. Recently, triboelectric nanogenerator (TENG) has been proposed as an effective and promising technology for harvesting ambient mechanical energy. Herein, a coaxial rotatory-freestanding TENG (CRF-TENG) was developed and its theoretical model was constructed. An approximate V–Q–α relationship was derived and the explicit analytical solutions of the transferred charge, output current, voltage and average power are obtained from numerically calculation. Finally, to verify the theoretical results, the real output performances of as-fabricated CRF-TENG were measured. The experimental results are consistent with the theoretical ones. The newly developed TENG mode greatly expands the applicability of TENGs for harvesting energy from ambient rotating mechanical motion.

  7. Coherent control of molecular alignment of homonuclear diatomic molecules by analytically designed laser pulses.

    PubMed

    Zou, Shiyang; Sanz, Cristina; Balint-Kurti, Gabriel G

    2008-09-28

    We present an analytic scheme for designing laser pulses to manipulate the field-free molecular alignment of a homonuclear diatomic molecule. The scheme is based on the use of a generalized pulse-area theorem and makes use of pulses constructed around two-photon resonant frequencies. In the proposed scheme, the populations and relative phases of the rovibrational states of the molecule are independently controlled utilizing changes in the laser intensity and in the carrier-envelope phase difference, respectively. This allows us to create the correct coherent superposition of rovibrational states needed to achieve optimal molecular alignment. The validity and efficiency of the scheme are demonstrated by explicit application to the H(2) molecule. The analytically designed laser pulses are tested by exact numerical solutions of the time-dependent Schrodinger equation including laser-molecule interactions to all orders of the field strength. The design of a sequence of pulses to further enhance molecular alignment is also discussed and tested. It is found that the rotating wave approximation used in the analytic design of the laser pulses leads to small errors in the prediction of the relative phase of the rotational states. It is further shown how these errors may be easily corrected.

  8. Kinetic corrections from analytic non-Maxwellian distribution functions in magnetized plasmas

    NASA Astrophysics Data System (ADS)

    Izacard, Olivier

    2016-08-01

    In magnetized plasma physics, almost all developed analytic theories assume a Maxwellian distribution function (MDF) and in some cases small deviations are described using the perturbation theory. The deviations with respect to the Maxwellian equilibrium, called kinetic effects, are required to be taken into account especially for fusion reactor plasmas. Generally, because the perturbation theory is not consistent with observed steady-state non-Maxwellians, these kinetic effects are numerically evaluated by very central processing unit (CPU)-expensive codes, avoiding the analytic complexity of velocity phase space integrals. We develop here a new method based on analytic non-Maxwellian distribution functions constructed from non-orthogonal basis sets in order to (i) use as few parameters as possible, (ii) increase the efficiency to model numerical and experimental non-Maxwellians, (iii) help to understand unsolved problems such as diagnostics discrepancies from the physical interpretation of the parameters, and (iv) obtain analytic corrections due to kinetic effects given by a small number of terms and removing the numerical error of the evaluation of velocity phase space integrals. This work does not attempt to derive new physical effects even if it could be possible to discover one from the better understandings of some unsolved problems, but here we focus on the analytic prediction of kinetic corrections from analytic non-Maxwellians. As applications, examples of analytic kinetic corrections are shown for the secondary electron emission, the Langmuir probe characteristic curve, and the entropy. This is done by using three analytic representations of the distribution function: the Kappa distribution function, the bi-modal or a new interpreted non-Maxwellian distribution function (INMDF). The existence of INMDFs is proved by new understandings of the experimental discrepancy of the measured electron temperature between two diagnostics in JET. As main results, it is shown that (i) the empirical formula for the secondary electron emission is not consistent with a MDF due to the presence of super-thermal particles, (ii) the super-thermal particles can replace a diffusion parameter in the Langmuir probe current formula, and (iii) the entropy can explicitly decrease in presence of sources only for the introduced INMDF without violating the second law of thermodynamics. Moreover, the first order entropy of an infinite number of super-thermal tails stays the same as the entropy of a MDF. The latter demystifies the Maxwell's demon by statistically describing non-isolated systems.

  9. Kinetic corrections from analytic non-Maxwellian distribution functions in magnetized plasmas

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

    Izacard, Olivier, E-mail: izacard@llnl.gov

    In magnetized plasma physics, almost all developed analytic theories assume a Maxwellian distribution function (MDF) and in some cases small deviations are described using the perturbation theory. The deviations with respect to the Maxwellian equilibrium, called kinetic effects, are required to be taken into account especially for fusion reactor plasmas. Generally, because the perturbation theory is not consistent with observed steady-state non-Maxwellians, these kinetic effects are numerically evaluated by very central processing unit (CPU)-expensive codes, avoiding the analytic complexity of velocity phase space integrals. We develop here a new method based on analytic non-Maxwellian distribution functions constructed from non-orthogonal basismore » sets in order to (i) use as few parameters as possible, (ii) increase the efficiency to model numerical and experimental non-Maxwellians, (iii) help to understand unsolved problems such as diagnostics discrepancies from the physical interpretation of the parameters, and (iv) obtain analytic corrections due to kinetic effects given by a small number of terms and removing the numerical error of the evaluation of velocity phase space integrals. This work does not attempt to derive new physical effects even if it could be possible to discover one from the better understandings of some unsolved problems, but here we focus on the analytic prediction of kinetic corrections from analytic non-Maxwellians. As applications, examples of analytic kinetic corrections are shown for the secondary electron emission, the Langmuir probe characteristic curve, and the entropy. This is done by using three analytic representations of the distribution function: the Kappa distribution function, the bi-modal or a new interpreted non-Maxwellian distribution function (INMDF). The existence of INMDFs is proved by new understandings of the experimental discrepancy of the measured electron temperature between two diagnostics in JET. As main results, it is shown that (i) the empirical formula for the secondary electron emission is not consistent with a MDF due to the presence of super-thermal particles, (ii) the super-thermal particles can replace a diffusion parameter in the Langmuir probe current formula, and (iii) the entropy can explicitly decrease in presence of sources only for the introduced INMDF without violating the second law of thermodynamics. Moreover, the first order entropy of an infinite number of super-thermal tails stays the same as the entropy of a MDF. The latter demystifies the Maxwell's demon by statistically describing non-isolated systems.« less

  10. A model-based approach to determine the long-term effects of multiple interacting stressors on coral reefs.

    PubMed

    Blackwood, Julie C; Hastings, Alan; Mumby, Peter J

    2011-10-01

    The interaction between multiple stressors on Caribbean coral reefs, namely, fishing effort and hurricane impacts, is a key element in the future sustainability of reefs. We develop an analytic model of coral-algal interactions and explicitly consider grazing by herbivorous reef fish. Further, we consider changes in structural complexity, or rugosity, in addition to the direct impacts of hurricanes, which are implemented as stochastic jump processes. The model simulations consider various levels of fishing effort corresponding to' several hurricane frequencies and impact levels dependent on geographic location. We focus on relatively short time scales so we do not explicitly include changes in ocean temperature, chemistry, or sea level rise. The general features of our approach would, however, apply to these other stressors and to the management of other systems in the face of multiple stressors. It is determined that the appropriate management policy, either local reef restoration or fisheries management, greatly depends on hurricane frequency and impact level. For sufficiently low hurricane impact and macroalgal growth rate, our results indicate that regions with lower-frequency hurricanes require stricter fishing regulations, whereas management in regions with higher-frequency hurricanes might be less concerned with enhancing grazing and instead consider whether local-scale restorative activities to increase vertical structure are cost-effective.

  11. Stability switches of arbitrary high-order consensus in multiagent networks with time delays.

    PubMed

    Yang, Bo

    2013-01-01

    High-order consensus seeking, in which individual high-order dynamic agents share a consistent view of the objectives and the world in a distributed manner, finds its potential broad applications in the field of cooperative control. This paper presents stability switches analysis of arbitrary high-order consensus in multiagent networks with time delays. By employing a frequency domain method, we explicitly derive analytical equations that clarify a rigorous connection between the stability of general high-order consensus and the system parameters such as the network topology, communication time-delays, and feedback gains. Particularly, our results provide a general and a fairly precise notion of how increasing communication time-delay causes the stability switches of consensus. Furthermore, under communication constraints, the stability and robustness problems of consensus algorithms up to third order are discussed in details to illustrate our central results. Numerical examples and simulation results for fourth-order consensus are provided to demonstrate the effectiveness of our theoretical results.

  12. Dynamic stabilization of Rayleigh-Taylor instability in an ablation front

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

    Piriz, A. R.; Di Lucchio, L.; Rodriguez Prieto, G.

    2011-01-15

    Dynamic stabilization of Rayleigh-Taylor instability in an ablation front is studied by considering a modulation in the acceleration that consists of sequences of Dirac deltas. This allows obtaining explicit analytical expressions for the instability growth rate as well as for the boundaries of the stability region. As a general rule, it is found that it is possible to stabilize all wave numbers above a certain minimum value k{sub m}, but the requirements in the modulation amplitude and frequency become more exigent with smaller k{sub m}. The essential role of compressibility is phenomenologically addressed in order to find the constraint itmore » imposes on the stability region. The results for some different wave forms of the acceleration modulation are also presented.« less

  13. All two-loop maximally helicity-violating amplitudes in multi-Regge kinematics from applied symbology

    NASA Astrophysics Data System (ADS)

    Prygarin, Alexander; Spradlin, Marcus; Vergu, Cristian; Volovich, Anastasia

    2012-04-01

    Recent progress on scattering amplitudes has benefited from the mathematical technology of symbols for efficiently handling the types of polylogarithm functions which frequently appear in multiloop computations. The symbol for all two-loop maximally helicity violating amplitudes in planar supersymmetric Yang-Mills theory is known, but explicit analytic formulas for the amplitudes are hard to come by except in special limits where things simplify, such as multi-Regge kinematics. By applying symbology we obtain a formula for the leading behavior of the imaginary part (the Mandelstam cut contribution) of this amplitude in multi-Regge kinematics for any number of gluons. Our result predicts a simple recursive structure which agrees with a direct Balitsky-Fadin-Kuraev-Lipatov computation carried out in a parallel publication.

  14. Exact results for models of multichannel quantum nonadiabatic transitions

    DOE PAGES

    Sinitsyn, N. A.

    2014-12-11

    We consider nonadiabatic transitions in explicitly time-dependent systems with Hamiltonians of the form Hˆ(t)=Aˆ+Bˆt+Cˆ/t, where t is time and Aˆ,Bˆ,Cˆ are Hermitian N × N matrices. We show that in any model of this type, scattering matrix elements satisfy nontrivial exact constraints that follow from the absence of the Stokes phenomenon for solutions with specific conditions at t→–∞. This allows one to continue such solutions analytically to t→+∞, and connect their asymptotic behavior at t→–∞ and t→+∞. This property becomes particularly useful when a model shows additional discrete symmetries. Specifically, we derive a number of simple exact constraints and explicitmore » expressions for scattering probabilities in such systems.« less

  15. Application of Soft Computing in Coherent Communications Phase Synchronization

    NASA Technical Reports Server (NTRS)

    Drake, Jeffrey T.; Prasad, Nadipuram R.

    2000-01-01

    The use of soft computing techniques in coherent communications phase synchronization provides an alternative to analytical or hard computing methods. This paper discusses a novel use of Adaptive Neuro-Fuzzy Inference Systems (ANFIS) for phase synchronization in coherent communications systems utilizing Multiple Phase Shift Keying (MPSK) modulation. A brief overview of the M-PSK digital communications bandpass modulation technique is presented and it's requisite need for phase synchronization is discussed. We briefly describe the hybrid platform developed by Jang that incorporates fuzzy/neural structures namely the, Adaptive Neuro-Fuzzy Interference Systems (ANFIS). We then discuss application of ANFIS to phase estimation for M-PSK. The modeling of both explicit, and implicit phase estimation schemes for M-PSK symbols with unknown structure are discussed. Performance results from simulation of the above scheme is presented.

  16. Criticality and Connectivity in Macromolecular Charge Complexation

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

    Qin, Jian; de Pablo, Juan J.

    We examine the role of molecular connectivity and architecture on the complexation of ionic macromolecules (polyelectrolytes) of finite size. A unified framework is developed and applied to evaluate the electrostatic correlation free energy for point-like, rod-like, and coil-like molecules. That framework is generalized to molecules of variable fractal dimensions, including dendrimers. Analytical expressions for the free energy, correlation length, and osmotic pressure are derived, thereby enabling consideration of the effects of charge connectivity, fractal dimension, and backbone stiffness on the complexation behavior of a wide range of polyelectrolytes. Results are presented for regions in the immediate vicinity of the criticalmore » region and far from it. A transparent and explicit expression for the coexistence curve is derived in order to facilitate analysis of experimentally observed phase diagrams.« less

  17. Nonsingular solutions and instabilities in Einstein-scalar-Gauss-Bonnet cosmology

    NASA Astrophysics Data System (ADS)

    Sberna, Laura; Pani, Paolo

    2017-12-01

    It is generically believed that higher-order curvature corrections to the Einstein-Hilbert action might cure the curvature singularities that plague general relativity. Here we consider Einstein-scalar-Gauss-Bonnet gravity, the only four-dimensional, ghost-free theory with quadratic curvature terms. For any choice of the coupling function and of the scalar potential, we show that the theory does not allow for bouncing solutions in the flat and open Friedmann universe. For the case of a closed universe, using a reverse-engineering method, we explicitly provide a bouncing solution which is nevertheless linearly unstable in the scalar gravitational sector. Moreover, we show that the expanding, singularity-free, early-time cosmologies allowed in the theory are unstable. These results rely only on analyticity and finiteness of cosmological variables at early times.

  18. Conductivity of Weakly Disordered Metals Close to a "Ferromagnetic" Quantum Critical Point

    NASA Astrophysics Data System (ADS)

    Kastrinakis, George

    2018-05-01

    We calculate analytically the conductivity of weakly disordered metals close to a "ferromagnetic" quantum critical point in the low-temperature regime. Ferromagnetic in the sense that the effective carrier potential V(q,ω ), due to critical fluctuations, is peaked at zero momentum q=0. Vertex corrections, due to both critical fluctuations and impurity scattering, are explicitly considered. We find that only the vertex corrections due to impurity scattering, combined with the self-energy, generate appreciable effects as a function of the temperature T and the control parameter a, which measures the proximity to the critical point. Our results are consistent with resistivity experiments in several materials displaying typical Fermi liquid behaviour, but with a diverging prefactor of the T^2 term for small a.

  19. Human motion planning based on recursive dynamics and optimal control techniques

    NASA Technical Reports Server (NTRS)

    Lo, Janzen; Huang, Gang; Metaxas, Dimitris

    2002-01-01

    This paper presents an efficient optimal control and recursive dynamics-based computer animation system for simulating and controlling the motion of articulated figures. A quasi-Newton nonlinear programming technique (super-linear convergence) is implemented to solve minimum torque-based human motion-planning problems. The explicit analytical gradients needed in the dynamics are derived using a matrix exponential formulation and Lie algebra. Cubic spline functions are used to make the search space for an optimal solution finite. Based on our formulations, our method is well conditioned and robust, in addition to being computationally efficient. To better illustrate the efficiency of our method, we present results of natural looking and physically correct human motions for a variety of human motion tasks involving open and closed loop kinematic chains.

  20. Coherent States for Kronecker Products of Non Compact Groups: Formulation and Applications

    NASA Technical Reports Server (NTRS)

    Bambah, Bindu A.; Agarwal, Girish S.

    1996-01-01

    We introduce and study the properties of a class of coherent states for the group SU(1,1) X SU(1,1) and derive explicit expressions for these using the Clebsch-Gordan algebra for the SU(1,1) group. We restrict ourselves to the discrete series representations of SU(1,1). These are the generalization of the 'Barut Girardello' coherent states to the Kronecker Product of two non-compact groups. The resolution of the identity and the analytic phase space representation of these states is presented. This phase space representation is based on the basis of products of 'pair coherent states' rather than the standard number state canonical basis. We discuss the utility of the resulting 'bi-pair coherent states' in the context of four-mode interactions in quantum optics.

  1. First and second sound in cylindrically trapped gases.

    PubMed

    Bertaina, G; Pitaevskii, L; Stringari, S

    2010-10-08

    We investigate the propagation of density and temperature waves in a cylindrically trapped gas with radial harmonic confinement. Starting from two-fluid hydrodynamic theory we derive effective 1D equations for the chemical potential and the temperature which explicitly account for the effects of viscosity and thermal conductivity. Differently from quantum fluids confined by rigid walls, the harmonic confinement allows for the propagation of both first and second sound in the long wavelength limit. We provide quantitative predictions for the two sound velocities of a superfluid Fermi gas at unitarity. For shorter wavelengths we discover a new surprising class of excitations continuously spread over a finite interval of frequencies. This results in a nondissipative damping in the response function which is analytically calculated in the limiting case of a classical ideal gas.

  2. Uncertainty propagation in life cycle assessment of biodiesel versus diesel: global warming and non-renewable energy.

    PubMed

    Hong, Jinglan

    2012-06-01

    Uncertainty information is essential for the proper use of life cycle assessment and environmental assessments in decision making. To investigate the uncertainties of biodiesel and determine the level of confidence in the assertion that biodiesel is more environmentally friendly than diesel, an explicit analytical approach based on the Taylor series expansion for lognormal distribution was applied in the present study. A biodiesel case study demonstrates the probability that biodiesel has a lower global warming and non-renewable energy score than diesel, that is 92.3% and 93.1%, respectively. The results indicate the level of confidence in the assertion that biodiesel is more environmentally friendly than diesel based on the global warming and non-renewable energy scores. Copyright © 2011 Elsevier Ltd. All rights reserved.

  3. Analytical Modelling of the Spread of Disease in Confined and Crowded Spaces

    NASA Astrophysics Data System (ADS)

    Goscé, Lara; Barton, David A. W.; Johansson, Anders

    2014-05-01

    Since 1927 and until recently, most models describing the spread of disease have been of compartmental type, based on the assumption that populations are homogeneous and well-mixed. Recent models have utilised agent-based models and complex networks to explicitly study heterogeneous interaction patterns, but this leads to an increasing computational complexity. Compartmental models are appealing because of their simplicity, but their parameters, especially the transmission rate, are complex and depend on a number of factors, which makes it hard to predict how a change of a single environmental, demographic, or epidemiological factor will affect the population. Therefore, in this contribution we propose a middle ground, utilising crowd-behaviour research to improve compartmental models in crowded situations. We show how both the rate of infection as well as the walking speed depend on the local crowd density around an infected individual. The combined effect is that the rate of infection at a population scale has an analytically tractable non-linear dependency on crowd density. We model the spread of a hypothetical disease in a corridor and compare our new model with a typical compartmental model, which highlights the regime in which current models may not produce credible results.

  4. From wrinkling to global buckling of a ring on a curved substrate

    NASA Astrophysics Data System (ADS)

    Lagrange, R.; López Jiménez, F.; Terwagne, D.; Brojan, M.; Reis, P. M.

    2016-04-01

    We present a combined analytical approach and numerical study on the stability of a ring bound to an annular elastic substrate, which contains a circular cavity. The system is loaded by depressurizing the inner cavity. The ring is modeled as an Euler-Bernoulli beam and its equilibrium equations are derived from the mechanical energy which takes into account both stretching and bending contributions. The curvature of the substrate is considered explicitly to model the work done by its reaction force on the ring. We distinguish two different instabilities: periodic wrinkling of the ring or global buckling of the structure. Our model provides an expression for the critical pressure, as well as a phase diagram that rationalizes the transition between instability modes. Towards assessing the role of curvature, we compare our results for the critical stress and the wrinkling wavelength to their planar counterparts. We show that the critical stress is insensitive to the curvature of the substrate, while the wavelength is only affected due to the permissible discrete values of the azimuthal wavenumber imposed by the geometry of the problem. Throughout, we contrast our analytical predictions against finite element simulations.

  5. Single molecule diffusion and the solution of the spherically symmetric residence time equation.

    PubMed

    Agmon, Noam

    2011-06-16

    The residence time of a single dye molecule diffusing within a laser spot is propotional to the total number of photons emitted by it. With this application in mind, we solve the spherically symmetric "residence time equation" (RTE) to obtain the solution for the Laplace transform of the mean residence time (MRT) within a d-dimensional ball, as a function of the initial location of the particle and the observation time. The solutions for initial conditions of potential experimental interest, starting in the center, on the surface or uniformly within the ball, are explicitly presented. Special cases for dimensions 1, 2, and 3 are obtained, which can be Laplace inverted analytically for d = 1 and 3. In addition, the analytic short- and long-time asymptotic behaviors of the MRT are derived and compared with the exact solutions for d = 1, 2, and 3. As a demonstration of the simplification afforded by the RTE, the Appendix obtains the residence time distribution by solving the Feynman-Kac equation, from which the MRT is obtained by differentiation. Single-molecule diffusion experiments could be devised to test the results for the MRT presented in this work. © 2011 American Chemical Society

  6. Inclusion of Topological Measurements into Analytic Estimates of Effective Permeability in Fractured Media

    NASA Astrophysics Data System (ADS)

    Sævik, P. N.; Nixon, C. W.

    2017-11-01

    We demonstrate how topology-based measures of connectivity can be used to improve analytical estimates of effective permeability in 2-D fracture networks, which is one of the key parameters necessary for fluid flow simulations at the reservoir scale. Existing methods in this field usually compute fracture connectivity using the average fracture length. This approach is valid for ideally shaped, randomly distributed fractures, but is not immediately applicable to natural fracture networks. In particular, natural networks tend to be more connected than randomly positioned fractures of comparable lengths, since natural fractures often terminate in each other. The proposed topological connectivity measure is based on the number of intersections and fracture terminations per sampling area, which for statistically stationary networks can be obtained directly from limited outcrop exposures. To evaluate the method, numerical permeability upscaling was performed on a large number of synthetic and natural fracture networks, with varying topology and geometry. The proposed method was seen to provide much more reliable permeability estimates than the length-based approach, across a wide range of fracture patterns. We summarize our results in a single, explicit formula for the effective permeability.

  7. A micromechanics-based strength prediction methodology for notched metal matrix composites

    NASA Technical Reports Server (NTRS)

    Bigelow, C. A.

    1992-01-01

    An analytical micromechanics based strength prediction methodology was developed to predict failure of notched metal matrix composites. The stress-strain behavior and notched strength of two metal matrix composites, boron/aluminum (B/Al) and silicon-carbide/titanium (SCS-6/Ti-15-3), were predicted. The prediction methodology combines analytical techniques ranging from a three dimensional finite element analysis of a notched specimen to a micromechanical model of a single fiber. In the B/Al laminates, a fiber failure criteria based on the axial and shear stress in the fiber accurately predicted laminate failure for a variety of layups and notch-length to specimen-width ratios with both circular holes and sharp notches when matrix plasticity was included in the analysis. For the SCS-6/Ti-15-3 laminates, a fiber failure based on the axial stress in the fiber correlated well with experimental results for static and post fatigue residual strengths when fiber matrix debonding and matrix cracking were included in the analysis. The micromechanics based strength prediction methodology offers a direct approach to strength prediction by modeling behavior and damage on a constituent level, thus, explicitly including matrix nonlinearity, fiber matrix debonding, and matrix cracking.

  8. A micromechanics-based strength prediction methodology for notched metal-matrix composites

    NASA Technical Reports Server (NTRS)

    Bigelow, C. A.

    1993-01-01

    An analytical micromechanics-based strength prediction methodology was developed to predict failure of notched metal matrix composites. The stress-strain behavior and notched strength of two metal matrix composites, boron/aluminum (B/Al) and silicon-carbide/titanium (SCS-6/Ti-15-3), were predicted. The prediction methodology combines analytical techniques ranging from a three-dimensional finite element analysis of a notched specimen to a micromechanical model of a single fiber. In the B/Al laminates, a fiber failure criteria based on the axial and shear stress in the fiber accurately predicted laminate failure for a variety of layups and notch-length to specimen-width ratios with both circular holes and sharp notches when matrix plasticity was included in the analysis. For the SCS-6/Ti-15-3 laminates, a fiber failure based on the axial stress in the fiber correlated well with experimental results for static and postfatigue residual strengths when fiber matrix debonding and matrix cracking were included in the analysis. The micromechanics-based strength prediction methodology offers a direct approach to strength prediction by modeling behavior and damage on a constituent level, thus, explicitly including matrix nonlinearity, fiber matrix debonding, and matrix cracking.

  9. Asymptotic theory of time-varying social networks with heterogeneous activity and tie allocation.

    PubMed

    Ubaldi, Enrico; Perra, Nicola; Karsai, Márton; Vezzani, Alessandro; Burioni, Raffaella; Vespignani, Alessandro

    2016-10-24

    The dynamic of social networks is driven by the interplay between diverse mechanisms that still challenge our theoretical and modelling efforts. Amongst them, two are known to play a central role in shaping the networks evolution, namely the heterogeneous propensity of individuals to i) be socially active and ii) establish a new social relationships with their alters. Here, we empirically characterise these two mechanisms in seven real networks describing temporal human interactions in three different settings: scientific collaborations, Twitter mentions, and mobile phone calls. We find that the individuals' social activity and their strategy in choosing ties where to allocate their social interactions can be quantitatively described and encoded in a simple stochastic network modelling framework. The Master Equation of the model can be solved in the asymptotic limit. The analytical solutions provide an explicit description of both the system dynamic and the dynamical scaling laws characterising crucial aspects about the evolution of the networks. The analytical predictions match with accuracy the empirical observations, thus validating the theoretical approach. Our results provide a rigorous dynamical system framework that can be extended to include other processes shaping social dynamics and to generate data driven predictions for the asymptotic behaviour of social networks.

  10. Commentary: Fundamental problems with candidate gene-by-environment interaction studies - reflections on Moore and Thoemmes (2016).

    PubMed

    Border, Richard; Keller, Matthew C

    2017-03-01

    Moore and Thoemmes elaborate on one particular source of difficulty in the study of candidate gene-by-environment interactions (cG × E): how different biologically plausible configurations of gene-environment covariation can bias estimates of cG × E when not explicitly modeled. However, even if cG × E investigators were able to account for the sources of bias Moore and Thoemmes elaborate, it is unlikely that conventional approaches would yield reliable results. Published cG × E findings to date have generally employed inadequate analytic procedures, have relied on samples orders of magnitude too small to detect plausible effects, and have relied on a particular candidate gene approach that has been unfruitful and largely jettisoned in mainstream genetic analyses of complex traits. Analytic procedures for the study of gene-environment interplay must evolve to meet the challenges that the genetic architecture of complex traits presents, and investigators must collaborate on grander scales if we hope to begin to understand how specific genes and environments combine to affect behavior. © 2017 Association for Child and Adolescent Mental Health.

  11. On wiping the interior walls of 37-mm closed-face cassettes: an OSHA perspective.

    PubMed

    Hendricks, Warren; Stones, Fern; Lillquist, Dean

    2009-12-01

    As early as 1976, Occupational Safety and Health Administration (OSHA) methods for analyzing metal samples collected using 37-mm polystyrene closed-face cassettes specified that any loose dust be transferred from the cassette to the digestion vessel, that the cassette be rinsed, and that, if necessary, the cassette be wiped out to help ensure that all particles that enter the cassette are included along with the filter as part of the sample for analysis. OSHA analytical methods for metal analysis were recently revised to explicitly require cassette wiping for all metal samples. This change was based on policy that any material entering the collection device constitutes part of the sample and on OSHA Salt Lake Technical Center research showing that invisible residue on the cassette walls can significantly contribute to the total sample results reported. OSHA procedures are consistent with guidance given in the NIOSH Manual of Analytical Methods. This guidance concludes that internal deposits in sampling cassettes should be included in the analysis and that one way to accomplish this would be to wipe or wash the internal surfaces of the cassette and include the material along with the filter for analysis.

  12. Asymptotic theory of time-varying social networks with heterogeneous activity and tie allocation

    NASA Astrophysics Data System (ADS)

    Ubaldi, Enrico; Perra, Nicola; Karsai, Márton; Vezzani, Alessandro; Burioni, Raffaella; Vespignani, Alessandro

    2016-10-01

    The dynamic of social networks is driven by the interplay between diverse mechanisms that still challenge our theoretical and modelling efforts. Amongst them, two are known to play a central role in shaping the networks evolution, namely the heterogeneous propensity of individuals to i) be socially active and ii) establish a new social relationships with their alters. Here, we empirically characterise these two mechanisms in seven real networks describing temporal human interactions in three different settings: scientific collaborations, Twitter mentions, and mobile phone calls. We find that the individuals’ social activity and their strategy in choosing ties where to allocate their social interactions can be quantitatively described and encoded in a simple stochastic network modelling framework. The Master Equation of the model can be solved in the asymptotic limit. The analytical solutions provide an explicit description of both the system dynamic and the dynamical scaling laws characterising crucial aspects about the evolution of the networks. The analytical predictions match with accuracy the empirical observations, thus validating the theoretical approach. Our results provide a rigorous dynamical system framework that can be extended to include other processes shaping social dynamics and to generate data driven predictions for the asymptotic behaviour of social networks.

  13. A behavior analytic analogue of learning to use synonyms, syntax, and parts of speech.

    PubMed

    Chase, Philip N; Ellenwood, David W; Madden, Gregory

    2008-01-01

    Matching-to-sample and sequence training procedures were used to develop responding to stimulus classes that were considered analogous to 3 aspects of verbal behavior: identifying synonyms and parts of speech, and using syntax. Matching-to-sample procedures were used to train 12 paired associates from among 24 stimuli. These pairs were analogous to synonyms. Then, sequence characteristics were trained to 6 of the stimuli. The result was the formation of 3 classes of 4 stimuli, with the classes controlling a sequence response analogous to a simple ordering syntax: first, second, and third. Matching-to-sample procedures were then used to add 4 stimuli to each class. These stimuli, without explicit sequence training, also began to control the same sequence responding as the other members of their class. Thus, three 8-member functionally equivalent sequence classes were formed. These classes were considered to be analogous to parts of speech. Further testing revealed three 8-member equivalence classes and 512 different sequences of first, second, and third. The study indicated that behavior analytic procedures may be used to produce some generative aspects of verbal behavior related to simple syntax and semantics.

  14. MOCCA-SURVEY Database. I. Eccentric Black Hole Mergers during Binary–Single Interactions in Globular Clusters

    NASA Astrophysics Data System (ADS)

    Samsing, Johan; Askar, Abbas; Giersz, Mirek

    2018-03-01

    We estimate the population of eccentric gravitational wave (GW) binary black hole (BBH) mergers forming during binary–single interactions in globular clusters (GCs), using ∼800 GC models that were evolved using the MOCCA code for star cluster simulations as part of the MOCCA-Survey Database I project. By re-simulating BH binary–single interactions extracted from this set of GC models using an N-body code that includes GW emission at the 2.5 post-Newtonian level, we find that ∼10% of all the BBHs assembled in our GC models that merge at present time form during chaotic binary–single interactions, and that about half of this sample have an eccentricity >0.1 at 10 Hz. We explicitly show that this derived rate of eccentric mergers is ∼100 times higher than one would find with a purely Newtonian N-body code. Furthermore, we demonstrate that the eccentric fraction can be accurately estimated using a simple analytical formalism when the interacting BHs are of similar mass, a result that serves as the first successful analytical description of eccentric GW mergers forming during three-body interactions in realistic GCs.

  15. Formulation and application of optimal homotopty asymptotic method to coupled differential-difference equations.

    PubMed

    Ullah, Hakeem; Islam, Saeed; Khan, Ilyas; Shafie, Sharidan; Fiza, Mehreen

    2015-01-01

    In this paper we applied a new analytic approximate technique Optimal Homotopy Asymptotic Method (OHAM) for treatment of coupled differential-difference equations (DDEs). To see the efficiency and reliability of the method, we consider Relativistic Toda coupled nonlinear differential-difference equation. It provides us a convenient way to control the convergence of approximate solutions when it is compared with other methods of solution found in the literature. The obtained solutions show that OHAM is effective, simpler, easier and explicit.

  16. Formulation and Application of Optimal Homotopty Asymptotic Method to Coupled Differential - Difference Equations

    PubMed Central

    Ullah, Hakeem; Islam, Saeed; Khan, Ilyas; Shafie, Sharidan; Fiza, Mehreen

    2015-01-01

    In this paper we applied a new analytic approximate technique Optimal Homotopy Asymptotic Method (OHAM) for treatment of coupled differential- difference equations (DDEs). To see the efficiency and reliability of the method, we consider Relativistic Toda coupled nonlinear differential-difference equation. It provides us a convenient way to control the convergence of approximate solutions when it is compared with other methods of solution found in the literature. The obtained solutions show that OHAM is effective, simpler, easier and explicit. PMID:25874457

  17. Probabilistic Cloning of Three Real States with Optimal Success Probabilities

    NASA Astrophysics Data System (ADS)

    Rui, Pin-shu

    2017-06-01

    We investigate the probabilistic quantum cloning (PQC) of three real states with average probability distribution. To get the analytic forms of the optimal success probabilities we assume that the three states have only two pairwise inner products. Based on the optimal success probabilities, we derive the explicit form of 1 →2 PQC for cloning three real states. The unitary operation needed in the PQC process is worked out too. The optimal success probabilities are also generalized to the M→ N PQC case.

  18. Exponential localization of Wannier functions in insulators.

    PubMed

    Brouder, Christian; Panati, Gianluca; Calandra, Matteo; Mourougane, Christophe; Marzari, Nicola

    2007-01-26

    The exponential localization of Wannier functions in two or three dimensions is proven for all insulators that display time-reversal symmetry, settling a long-standing conjecture. Our proof relies on the equivalence between the existence of analytic quasi-Bloch functions and the nullity of the Chern numbers (or of the Hall current) for the system under consideration. The same equivalence implies that Chern insulators cannot display exponentially localized Wannier functions. An explicit condition for the reality of the Wannier functions is identified.

  19. Enhancing robustness and immunization in geographical networks

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

    Huang Liang; Department of Physics, Lanzhou University, Lanzhou 730000; Yang Kongqing

    2007-03-15

    We find that different geographical structures of networks lead to varied percolation thresholds, although these networks may have similar abstract topological structures. Thus, strategies for enhancing robustness and immunization of a geographical network are proposed. Using the generating function formalism, we obtain an explicit form of the percolation threshold q{sub c} for networks containing arbitrary order cycles. For three-cycles, the dependence of q{sub c} on the clustering coefficients is ascertained. The analysis substantiates the validity of the strategies with analytical evidence.

  20. Theory of ion-matrix-sheath dynamics

    NASA Astrophysics Data System (ADS)

    Kos, L.; Tskhakaya, D. D.

    2018-01-01

    The time evolution of a one-dimensional, uni-polar ion sheath (an "ion matrix sheath") is investigated. The analytical solutions for the ion-fluid and Poisson's equations are found for an arbitrary time dependence of the wall-applied negative potential. In the case that the wall potential is large and remains constant after its ramp-up application, the explicit time dependencies of the sheath's parameters during the initial stage of the process are given. The characteristic rate of approaching the stationary state, satisfying the Child-Langmuir law, is determined.

  1. Invariant Tori in the Secular Motions of the Three-body Planetary Systems

    NASA Astrophysics Data System (ADS)

    Locatelli, Ugo; Giorgilli, Antonio

    We consider the problem of the applicability of KAM theorem to a realistic problem of three bodies. In the framework of the averaged dynamics over the fast angles for the Sun-Jupiter-Saturn system we can prove the perpetual stability of the orbit. The proof is based on semi-numerical algorithms requiring both explicit algebraic manipulations of series and analytical estimates. The proof is made rigorous by using interval arithmetics in order to control the numerical errors.

  2. Numerical Algorithm for Delta of Asian Option

    PubMed Central

    Zhang, Boxiang; Yu, Yang; Wang, Weiguo

    2015-01-01

    We study the numerical solution of the Greeks of Asian options. In particular, we derive a close form solution of Δ of Asian geometric option and use this analytical form as a control to numerically calculate Δ of Asian arithmetic option, which is known to have no explicit close form solution. We implement our proposed numerical method and compare the standard error with other classical variance reduction methods. Our method provides an efficient solution to the hedging strategy with Asian options. PMID:26266271

  3. Tides and tidal stress: Applications to Europa

    NASA Astrophysics Data System (ADS)

    Hurford, Terry Anthony, Jr.

    A review of analytical techniques and documentation of previously inaccessible mathematical formulations is applied to study of Jupiter's satellite Europa. Compared with numerical codes that are commonly used to model global tidal effects, analytical models of tidal deformation give deeper insight into the mechanics of tides, and can better reveal the nature of the dependence of observable effects on key parameters. I develop analytical models for tidal deformation of multi-layered bodies. Previous studies of Europa, based on numerical computation, only to show isolated examples from parameter space. My results show a systematic dependence of tidal response on the thicknesses and material parameters of Europa's core, rocky mantle, liquid water ocean, and outer layer of ice. As in the earlier work, I restrict these studies to incompressible materials. Any set of Love numbers h 2 and k 2 which describe a planet's tidal deformation, could be fit by a range of ice thickness values, by adjusting other parameters such as mantle rigidity or core size, an important result for mission planning. Inclusion of compression into multilayer models has been addressed analytically, uncovering several issues that are not explicit in the literature. Full evaluation with compression is here restricted to a uniform sphere. A set of singularities in the classical solution, which correspond to instabilities due to self-gravity has been identified and mapped in parameter space. The analytical models of tidal response yield the stresses anywhere within the body, including on its surface. Crack patterns (such as cycloids) on Europa are probably controlled by these stresses. However, in contrast to previous studies which used a thin shell approximation of the tidal stress, I consider how other tidal models compare with the observed tectonic features. In this way the relationship between Europa's surface tectonics and the global tidal distortion can be constrained. While large-scale tidal deformations probe internal structure deep within a body, small-scale deformations can probe internal structure at shallower depths. I have used photoclinometry to obtain topographic profiles across terrain adjacent to Europan ridges to detect the effects of loading on the lithosphere. Lithospheric thicknesses have been determined and correlated with types and ages of terrain.

  4. Properties of interaction networks underlying the minority game.

    PubMed

    Caridi, Inés

    2014-11-01

    The minority game is a well-known agent-based model with no explicit interaction among its agents. However, it is known that they interact through the global magnitudes of the model and through their strategies. In this work we have attempted to formalize the implicit interactions among minority game agents as if they were links on a complex network. We have defined the link between two agents by quantifying the similarity between them. This link definition is based on the information of the instance of the game (the set of strategies assigned to each agent at the beginning) without any dynamic information on the game and brings about a static, unweighed and undirected network. We have analyzed the structure of the resulting network for different parameters, such as the number of agents (N) and the agent's capacity to process information (m), always taking into account games with two strategies per agent. In the region of crowd effects of the model, the resulting networks structure is a small-world network, whereas in the region where the behavior of the minority game is the same as in a game of random decisions, networks become a random network of Erdos-Renyi. The transition between these two types of networks is slow, without any peculiar feature of the network in the region of the coordination among agents. Finally, we have studied the resulting static networks for the full strategy minority game model, a maximal instance of the minority game in which all possible agents take part in the game. We have explicitly calculated the degree distribution of the full strategy minority game network and, on the basis of this analytical result, we have estimated the degree distribution of the minority game network, which is in accordance with computational results.

  5. Life cycle thinking in impact assessment—Current practice and LCA gains

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

    Bidstrup, Morten, E-mail: Bidstrup@plan.aau.dk

    It has been advocated that life cycle thinking (LCT) should be applied in impact assessment (IA) to a greater extent, since some development proposals pose a risk of significant impacts throughout the interconnected activities of product systems. Multiple authors have proposed the usage of life cycle assessment (LCA) for such analytical advancement, but little to no research on this tool application has been founded in IA practice so far. The aim of this article is to elaborate further on the gains assigned to application of LCA. The research builds on a review of 85 Danish IA reports, which were analysedmore » for analytical appropriateness and application of LCT. Through a focus on the non-technical summary, the conclusion and the use of specific search words, passages containing LCT were searched for in each IA report. These passages were then analysed with a generic framework. The results reveal that LCT is appropriate for most of the IAs, but that LCA is rarely applied to provide such a perspective. Without LCA, the IAs show mixed performance in regard to LCT. Most IAs do consider the product provision of development proposals, but they rarely relate impacts to this function explicitly. Many IAs do consider downstream impacts, but assessments of upstream, distant impacts are generally absent. It is concluded that multiple analytical gains can be attributed to greater application of LCA in IA practice, though some level of LCT already exists. - Highlights: • Life cycle thinking is appropriate across the types and topics of impact assessment. • Yet, life cycle assessment is rarely used for adding such perspective. • Impact assessment practice does apply some degree of life cycle thinking. • However, application of life cycle assessment could bring analytical gains.« less

  6. Quantitative Analysis of Fullerene Nanomaterials in Environmental Systems: A Critical Review

    PubMed Central

    Isaacson, Carl W.; Kleber, Markus; Field, Jennifer A.

    2009-01-01

    The increasing production and use of fullerene nanomaterials has led to calls for more information regarding the potential impacts that releases of these materials may have on human and environmental health. Fullerene nanomaterials, which are comprised of both fullerenes and surface-functionalized fullerenes, are used in electronic, optic, medical and cosmetic applications. Measuring fullerene nanomaterial concentrations in natural environments is difficult because they exhibit a duality of physical and chemical characteristics as they transition from hydrophobic to polar forms upon exposure to water. In aqueous environments, this is expressed as their tendency to initially (i) self assemble into aggregates of appreciable size and hydrophobicity, and subsequently (ii) interact with the surrounding water molecules and other chemical constituents in natural environments thereby acquiring negative surface charge. Fullerene nanomaterials may therefore deceive the application of any single analytical method that is applied with the assumption that fullerenes have but one defining characteristic (e.g., hydrophobicity). [1] We find that analytical procedures are needed to account for the potentially transitory nature of fullerenes in natural environments through the use of approaches that provide chemically-explicit information including molecular weight and the number and identity of surface functional groups. [2] We suggest that sensitive and mass-selective detection, such as that offered by mass spectrometry when combined with optimized extraction procedures, offers the greatest potential to achieve this goal. [3] With this review, we show that significant improvements in analytical rigor would result from an increased availability of well characterized authentic standards, reference materials, and isotopically-labeled internal standards. Finally, the benefits of quantitative and validated analytical methods for advancing the knowledge on fullerene occurrence, fate, and behavior are indicated. PMID:19764203

  7. Methods for the thematic synthesis of qualitative research in systematic reviews

    PubMed Central

    Thomas, James; Harden, Angela

    2008-01-01

    Background There is a growing recognition of the value of synthesising qualitative research in the evidence base in order to facilitate effective and appropriate health care. In response to this, methods for undertaking these syntheses are currently being developed. Thematic analysis is a method that is often used to analyse data in primary qualitative research. This paper reports on the use of this type of analysis in systematic reviews to bring together and integrate the findings of multiple qualitative studies. Methods We describe thematic synthesis, outline several steps for its conduct and illustrate the process and outcome of this approach using a completed review of health promotion research. Thematic synthesis has three stages: the coding of text 'line-by-line'; the development of 'descriptive themes'; and the generation of 'analytical themes'. While the development of descriptive themes remains 'close' to the primary studies, the analytical themes represent a stage of interpretation whereby the reviewers 'go beyond' the primary studies and generate new interpretive constructs, explanations or hypotheses. The use of computer software can facilitate this method of synthesis; detailed guidance is given on how this can be achieved. Results We used thematic synthesis to combine the studies of children's views and identified key themes to explore in the intervention studies. Most interventions were based in school and often combined learning about health benefits with 'hands-on' experience. The studies of children's views suggested that fruit and vegetables should be treated in different ways, and that messages should not focus on health warnings. Interventions that were in line with these suggestions tended to be more effective. Thematic synthesis enabled us to stay 'close' to the results of the primary studies, synthesising them in a transparent way, and facilitating the explicit production of new concepts and hypotheses. Conclusion We compare thematic synthesis to other methods for the synthesis of qualitative research, discussing issues of context and rigour. Thematic synthesis is presented as a tried and tested method that preserves an explicit and transparent link between conclusions and the text of primary studies; as such it preserves principles that have traditionally been important to systematic reviewing. PMID:18616818

  8. Extended artificial neural networks: incorporation of a priori chemical knowledge enables use of ion selective electrodes for in-situ measurement of ions at environmentally relevant levels.

    PubMed

    Mueller, Amy V; Hemond, Harold F

    2013-12-15

    A novel artificial neural network (ANN) architecture is proposed which explicitly incorporates a priori system knowledge, i.e., relationships between output signals, while preserving the unconstrained non-linear function estimator characteristics of the traditional ANN. A method is provided for architecture layout, disabling training on a subset of neurons, and encoding system knowledge into the neuron structure. The novel architecture is applied to raw readings from a chemical sensor multi-probe (electric tongue), comprised of off-the-shelf ion selective electrodes (ISEs), to estimate individual ion concentrations in solutions at environmentally relevant concentrations and containing environmentally representative ion mixtures. Conductivity measurements and the concept of charge balance are incorporated into the ANN structure, resulting in (1) removal of estimation bias typically seen with use of ISEs in mixtures of unknown composition and (2) improvement of signal estimation by an order of magnitude or more for both major and minor constituents relative to use of ISEs as stand-alone sensors and error reduction by 30-50% relative to use of standard ANN models. This method is suggested as an alternative to parameterization of traditional models (e.g., Nikolsky-Eisenman), for which parameters are strongly dependent on both analyte concentration and temperature, and to standard ANN models which have no mechanism for incorporation of system knowledge. Network architecture and weighting are presented for the base case where the dot product can be used to relate ion concentrations to both conductivity and charge balance as well as for an extension to log-normalized data where the model can no longer be represented in this manner. While parameterization in this case study is analyte-dependent, the architecture is generalizable, allowing application of this method to other environmental problems for which mathematical constraints can be explicitly stated. © 2013 Elsevier B.V. All rights reserved.

  9. Implicit and explicit self-esteem in currently depressed individuals with and without suicidal ideation.

    PubMed

    Franck, Erik; De Raedt, Rudi; Dereu, Mieke; Van den Abbeele, Dirk

    2007-03-01

    In the present study, we have further explored implicit self-esteem in currently depressed individuals. Since suicidal ideation is associated with lower self-esteem in depressed individuals, we measured both implicit and explicit self-esteem in a population of currently depressed (CD) individuals, with and without suicidal ideation (SI), and in a group of non-depressed controls (ND). The results indicate that only CD individuals with SI show a discrepancy between their implicit and explicit self-esteem: that is, they exhibit high implicit and low explicit self-esteem. CD individuals without SI exhibit both low implicit and low explicit self-esteem; and ND controls exhibit both normal implicit and normal explicit self-esteem. These results provide new insights in the study of implicit self-esteem and the combination of implicit and explicit self-esteem in depression.

  10. A GIS based spatially-explicit sensitivity and uncertainty analysis approach for multi-criteria decision analysis.

    PubMed

    Feizizadeh, Bakhtiar; Jankowski, Piotr; Blaschke, Thomas

    2014-03-01

    GIS multicriteria decision analysis (MCDA) techniques are increasingly used in landslide susceptibility mapping for the prediction of future hazards, land use planning, as well as for hazard preparedness. However, the uncertainties associated with MCDA techniques are inevitable and model outcomes are open to multiple types of uncertainty. In this paper, we present a systematic approach to uncertainty and sensitivity analysis. We access the uncertainty of landslide susceptibility maps produced with GIS-MCDA techniques. A new spatially-explicit approach and Dempster-Shafer Theory (DST) are employed to assess the uncertainties associated with two MCDA techniques, namely Analytical Hierarchical Process (AHP) and Ordered Weighted Averaging (OWA) implemented in GIS. The methodology is composed of three different phases. First, weights are computed to express the relative importance of factors (criteria) for landslide susceptibility. Next, the uncertainty and sensitivity of landslide susceptibility is analyzed as a function of weights using Monte Carlo Simulation and Global Sensitivity Analysis. Finally, the results are validated using a landslide inventory database and by applying DST. The comparisons of the obtained landslide susceptibility maps of both MCDA techniques with known landslides show that the AHP outperforms OWA. However, the OWA-generated landslide susceptibility map shows lower uncertainty than the AHP-generated map. The results demonstrate that further improvement in the accuracy of GIS-based MCDA can be achieved by employing an integrated uncertainty-sensitivity analysis approach, in which the uncertainty of landslide susceptibility model is decomposed and attributed to model's criteria weights.

  11. A GIS based spatially-explicit sensitivity and uncertainty analysis approach for multi-criteria decision analysis☆

    PubMed Central

    Feizizadeh, Bakhtiar; Jankowski, Piotr; Blaschke, Thomas

    2014-01-01

    GIS multicriteria decision analysis (MCDA) techniques are increasingly used in landslide susceptibility mapping for the prediction of future hazards, land use planning, as well as for hazard preparedness. However, the uncertainties associated with MCDA techniques are inevitable and model outcomes are open to multiple types of uncertainty. In this paper, we present a systematic approach to uncertainty and sensitivity analysis. We access the uncertainty of landslide susceptibility maps produced with GIS-MCDA techniques. A new spatially-explicit approach and Dempster–Shafer Theory (DST) are employed to assess the uncertainties associated with two MCDA techniques, namely Analytical Hierarchical Process (AHP) and Ordered Weighted Averaging (OWA) implemented in GIS. The methodology is composed of three different phases. First, weights are computed to express the relative importance of factors (criteria) for landslide susceptibility. Next, the uncertainty and sensitivity of landslide susceptibility is analyzed as a function of weights using Monte Carlo Simulation and Global Sensitivity Analysis. Finally, the results are validated using a landslide inventory database and by applying DST. The comparisons of the obtained landslide susceptibility maps of both MCDA techniques with known landslides show that the AHP outperforms OWA. However, the OWA-generated landslide susceptibility map shows lower uncertainty than the AHP-generated map. The results demonstrate that further improvement in the accuracy of GIS-based MCDA can be achieved by employing an integrated uncertainty–sensitivity analysis approach, in which the uncertainty of landslide susceptibility model is decomposed and attributed to model's criteria weights. PMID:25843987

  12. A GIS based spatially-explicit sensitivity and uncertainty analysis approach for multi-criteria decision analysis

    NASA Astrophysics Data System (ADS)

    Feizizadeh, Bakhtiar; Jankowski, Piotr; Blaschke, Thomas

    2014-03-01

    GIS multicriteria decision analysis (MCDA) techniques are increasingly used in landslide susceptibility mapping for the prediction of future hazards, land use planning, as well as for hazard preparedness. However, the uncertainties associated with MCDA techniques are inevitable and model outcomes are open to multiple types of uncertainty. In this paper, we present a systematic approach to uncertainty and sensitivity analysis. We access the uncertainty of landslide susceptibility maps produced with GIS-MCDA techniques. A new spatially-explicit approach and Dempster-Shafer Theory (DST) are employed to assess the uncertainties associated with two MCDA techniques, namely Analytical Hierarchical Process (AHP) and Ordered Weighted Averaging (OWA) implemented in GIS. The methodology is composed of three different phases. First, weights are computed to express the relative importance of factors (criteria) for landslide susceptibility. Next, the uncertainty and sensitivity of landslide susceptibility is analyzed as a function of weights using Monte Carlo Simulation and Global Sensitivity Analysis. Finally, the results are validated using a landslide inventory database and by applying DST. The comparisons of the obtained landslide susceptibility maps of both MCDA techniques with known landslides show that the AHP outperforms OWA. However, the OWA-generated landslide susceptibility map shows lower uncertainty than the AHP-generated map. The results demonstrate that further improvement in the accuracy of GIS-based MCDA can be achieved by employing an integrated uncertainty-sensitivity analysis approach, in which the uncertainty of landslide susceptibility model is decomposed and attributed to model's criteria weights.

  13. Implicit solution of Navier-Stokes equations on staggered curvilinear grids using a Newton-Krylov method with a novel analytical Jacobian.

    NASA Astrophysics Data System (ADS)

    Borazjani, Iman; Asgharzadeh, Hafez

    2015-11-01

    Flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates with explicit and semi-implicit schemes. Implicit schemes can be used to overcome these restrictions. However, implementing implicit solver for nonlinear equations including Navier-Stokes is not straightforward. Newton-Krylov subspace methods (NKMs) are one of the most advanced iterative methods to solve non-linear equations such as implicit descritization of the Navier-Stokes equation. The efficiency of NKMs massively depends on the Jacobian formation method, e.g., automatic differentiation is very expensive, and matrix-free methods slow down as the mesh is refined. Analytical Jacobian is inexpensive method, but derivation of analytical Jacobian for Navier-Stokes equation on staggered grid is challenging. The NKM with a novel analytical Jacobian was developed and validated against Taylor-Green vortex and pulsatile flow in a 90 degree bend. The developed method successfully handled the complex geometries such as an intracranial aneurysm with multiple overset grids, and immersed boundaries. It is shown that the NKM with an analytical Jacobian is 3 to 25 times faster than the fixed-point implicit Runge-Kutta method, and more than 100 times faster than automatic differentiation depending on the grid (size) and the flow problem. The developed methods are fully parallelized with parallel efficiency of 80-90% on the problems tested.

  14. Bending of an Infinite beam on a base with two parameters in the absence of a part of the base

    NASA Astrophysics Data System (ADS)

    Aleksandrovskiy, Maxim; Zaharova, Lidiya

    2018-03-01

    Currently, in connection with the rapid development of high-rise construction and the improvement of joint operation of high-rise structures and bases models, the questions connected with the use of various calculation methods become topical. The rigor of analytical methods is capable of more detailed and accurate characterization of the structures behavior, which will affect the reliability of objects and can lead to a reduction in their cost. In the article, a model with two parameters is used as a computational model of the base that can effectively take into account the distributive properties of the base by varying the coefficient reflecting the shift parameter. The paper constructs the effective analytical solution of the problem of a beam of infinite length interacting with a two-parameter voided base. Using the Fourier integral equations, the original differential equation is reduced to the Fredholm integral equation of the second kind with a degenerate kernel, and all the integrals are solved analytically and explicitly, which leads to an increase in the accuracy of the computations in comparison with the approximate methods. The paper consider the solution of the problem of a beam loaded with a concentrated force applied at the point of origin with a fixed value of the length of the dip section. The paper gives the analysis of the obtained results values for various parameters of coefficient taking into account cohesion of the ground.

  15. An Analytical Dynamics Approach to the Control of Mechanical Systems

    NASA Astrophysics Data System (ADS)

    Mylapilli, Harshavardhan

    A new and novel approach to the control of nonlinear mechanical systems is presented in this study. The approach is inspired by recent results in analytical dynamics that deal with the theory of constrained motion. The control requirements on the dynamical system are viewed from an analytical dynamics perspective and the theory of constrained motion is used to recast these control requirements as constraints on the dynamical system. Explicit closed form expressions for the generalized nonlinear control forces are obtained by using the fundamental equation of mechanics. The control so obtained is optimal at each instant of time and causes the constraints to be exactly satisfied. No linearizations and/or approximations of the nonlinear dynamical system are made, and no a priori structure is imposed on the nature of nonlinear controller. Three examples dealing with highly nonlinear complex dynamical systems that are chosen from diverse areas of discrete and continuum mechanics are presented to demonstrate the control approach. The first example deals with the energy control of underactuated inhomogeneous nonlinear lattices (or chains), the second example deals with the synchronization of the motion of multiple coupled slave gyros with that of a master gyro, and the final example deals with the control of incompressible hyperelastic rubber-like thin cantilever beams. Numerical simulations accompanying these examples show the ease, simplicity and the efficacy with which the control methodology can be applied and the accuracy with which the desired control objectives can be met.

  16. A fast method to compute Three-Dimensional Infrared Radiative Transfer in non scattering medium

    NASA Astrophysics Data System (ADS)

    Makke, Laurent; Musson-Genon, Luc; Carissimo, Bertrand

    2014-05-01

    The Atmospheric Radiation field has seen the development of more accurate and faster methods to take into account absoprtion in participating media. Radiative fog appears with clear sky condition due to a significant cooling during the night, so scattering is left out. Fog formation modelling requires accurate enough method to compute cooling rates. Thanks to High Performance Computing, multi-spectral approach of Radiative Transfer Equation resolution is most often used. Nevertheless, the coupling of three-dimensionnal radiative transfer with fluid dynamics is very detrimental to the computational cost. To reduce the time spent in radiation calculations, the following method uses analytical absorption functions fitted by Sasamori (1968) on Yamamoto's charts (Yamamoto,1956) to compute a local linear absorption coefficient. By averaging radiative properties, this method eliminates the spectral integration. For an isothermal atmosphere, analytical calculations lead to an explicit formula between emissivities functions and linear absorption coefficient. In the case of cooling to space approximation, this analytical expression gives very accurate results compared to correlated k-distribution. For non homogeneous paths, we propose a two steps algorithm. One-dimensional radiative quantities and linear absorption coefficient are computed by a two-flux method. Then, three-dimensional RTE under the grey medium assumption is solved with the DOM. Comparisons with measurements of radiative quantities during ParisFOG field (2006) shows the cability of this method to handle strong vertical variations of pressure/temperature and gases concentrations.

  17. CMEs' Speed, Travel Time, and Temperature: A Thermodynamic Approach

    NASA Astrophysics Data System (ADS)

    Durand-Manterola, Hector J.; Flandes, Alberto; Rivera, Ana Leonor; Lara, Alejandro; Niembro, Tatiana

    2017-12-01

    Due to their important role in space weather, coronal mass ejections or CMEs have been thoroughly studied in order to forecast their speed and transit time from the Sun to the Earth. We present a thermodynamic analytical model that describes the dynamics of CMEs. The thermodynamic approach has some advantages with respect to the hydrodynamic approach. First, it deals with the energy involved, which is a scalar quantity. Second, one may calculate the work done by the different forces separately and sum all contributions to determine the changes in speed, which simplifies the problem and allows us to obtain fully rigorous results. Our model considers the drag force, which dominates the dynamics of CMEs and the solar gravitational force, which has a much smaller effect, but it is, still, relevant enough to be considered. We derive an explicit analytical expression for the speed of CMEs in terms of its most relevant parameters and obtain an analytical expression for the CME temperature. The model is tested with a CME observed at three different heliocentric distances with three different spacecraft (SOHO, ACE, and Ulysses); also, with a set of 11 CMEs observed with the SOHO, Wind, and ACE spacecraft and, finally, with two events observed with the STEREO spacecraft. In all cases, we have a consistent agreement between the theoretical and the observed speeds and transit times. Additionally, for the set of 11 events, we estimate their temperatures at their departure position from their temperatures measured near the orbit of the Earth.

  18. Analytical results for the time-dependent current density distribution of expanding ultracold gases after a sudden change of the confining potential

    NASA Astrophysics Data System (ADS)

    Boumaza, R.; Bencheikh, K.

    2017-12-01

    Using the so-called operator product expansion to lowest order, we extend the work in Campbell et al (2015 Phys. Rev. Lett 114 125302) by deriving a simple analytical expression for the long-time asymptotic one-body reduced density matrix during free expansion for a one-dimensional system of bosons with large atom number interacting through a repulsive delta potential initially confined by a potential well. This density matrix allows direct access to the momentum distribution and also to the mass current density. For initially confining power-law potentials we give explicit expressions, in the limits of very weak and very strong interaction, for the current density distributions during the free expansion. In the second part of the work we consider the expansion of ultracold gas from a confining harmonic trap to another harmonic trap with a different frequency. For the case of a quantum impenetrable gas of bosons (a Tonks-Girardeau gas) with a given atom number, we present an exact analytical expression for the mass current distribution (mass transport) after release from one harmonic trap to another harmonic trap. It is shown that, for a harmonically quenched Tonks-Girardeau gas, the current distribution is a suitable collective observable and under the weak quench regime, it exhibits oscillations at the same frequencies as those recently predicted for the peak momentum distribution in the breathing mode. The analysis is extended to other possible quenched systems.

  19. From deep TLS validation to ensembles of atomic models built from elemental motions. II. Analysis of TLS refinement results by explicit interpretation

    DOE PAGES

    Afonine, Pavel V.; Adams, Paul D.; Urzhumtsev, Alexandre

    2018-06-08

    TLS modelling was developed by Schomaker and Trueblood to describe atomic displacement parameters through concerted (rigid-body) harmonic motions of an atomic group [Schomaker & Trueblood (1968), Acta Cryst. B 24 , 63–76]. The results of a TLS refinement are T , L and S matrices that provide individual anisotropic atomic displacement parameters (ADPs) for all atoms belonging to the group. These ADPs can be calculated analytically using a formula that relates the elements of the TLS matrices to atomic parameters. Alternatively, ADPs can be obtained numerically from the parameters of concerted atomic motions corresponding to the TLS matrices. Both proceduresmore » are expected to produce the same ADP values and therefore can be used to assess the results of TLS refinement. Here, the implementation of this approach in PHENIX is described and several illustrations, including the use of all models from the PDB that have been subjected to TLS refinement, are provided.« less

  20. Dynamical mean-field theory and weakly non-linear analysis for the phase separation of active Brownian particles

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

    Speck, Thomas; Menzel, Andreas M.; Bialké, Julian

    2015-06-14

    Recently, we have derived an effective Cahn-Hilliard equation for the phase separation dynamics of active Brownian particles by performing a weakly non-linear analysis of the effective hydrodynamic equations for density and polarization [Speck et al., Phys. Rev. Lett. 112, 218304 (2014)]. Here, we develop and explore this strategy in more detail and show explicitly how to get to such a large-scale, mean-field description starting from the microscopic dynamics. The effective free energy emerging from this approach has the form of a conventional Ginzburg-Landau function. On the coarsest scale, our results thus agree with the mapping of active phase separation ontomore » that of passive fluids with attractive interactions through a global effective free energy (motility-induced phase transition). Particular attention is paid to the square-gradient term necessary for the phase separation kinetics. We finally discuss results from numerical simulations corroborating the analytical results.« less

  1. Unsteady free convection flow of viscous fluids with analytical results by employing time-fractional Caputo-Fabrizio derivative (without singular kernel)

    NASA Astrophysics Data System (ADS)

    Ali Shah, Nehad; Mahsud, Yasir; Ali Zafar, Azhar

    2017-10-01

    This article introduces a theoretical study for unsteady free convection flow of an incompressible viscous fluid. The fluid flows near an isothermal vertical plate. The plate has a translational motion with time-dependent velocity. The equations governing the fluid flow are expressed in fractional differential equations by using a newly defined time-fractional Caputo-Fabrizio derivative without singular kernel. Explicit solutions for velocity, temperature and solute concentration are obtained by applying the Laplace transform technique. As the fractional parameter approaches to one, solutions for the ordinary fluid model are extracted from the general solutions of the fractional model. The results showed that, for the fractional model, the obtained solutions for velocity, temperature and concentration exhibit stationary jumps discontinuity across the plane at t=0 , while the solutions are continuous functions in the case of the ordinary model. Finally, numerical results for flow features at small-time are illustrated through graphs for various pertinent parameters.

  2. From deep TLS validation to ensembles of atomic models built from elemental motions. II. Analysis of TLS refinement results by explicit interpretation

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

    Afonine, Pavel V.; Adams, Paul D.; Urzhumtsev, Alexandre

    TLS modelling was developed by Schomaker and Trueblood to describe atomic displacement parameters through concerted (rigid-body) harmonic motions of an atomic group [Schomaker & Trueblood (1968), Acta Cryst. B 24 , 63–76]. The results of a TLS refinement are T , L and S matrices that provide individual anisotropic atomic displacement parameters (ADPs) for all atoms belonging to the group. These ADPs can be calculated analytically using a formula that relates the elements of the TLS matrices to atomic parameters. Alternatively, ADPs can be obtained numerically from the parameters of concerted atomic motions corresponding to the TLS matrices. Both proceduresmore » are expected to produce the same ADP values and therefore can be used to assess the results of TLS refinement. Here, the implementation of this approach in PHENIX is described and several illustrations, including the use of all models from the PDB that have been subjected to TLS refinement, are provided.« less

  3. Risk prioritisation using the analytic hierarchy process

    NASA Astrophysics Data System (ADS)

    Sum, Rabihah Md.

    2015-12-01

    This study demonstrated how to use the Analytic Hierarchy Process (AHP) to prioritise risks of an insurance company. AHP is a technique to structure complex problems by arranging elements of the problems in a hierarchy, assigning numerical values to subjective judgements on the relative importance of the elements and synthesizing the judgements to determine which elements have the highest priority. The study is motivated by wide application of AHP as a prioritisation technique in complex problems. It aims to show AHP is able to minimise some limitations of risk assessment technique using likelihood and impact. The study shows AHP is able to provide consistency check on subjective judgements, organise a large number of risks into a structured framework, assist risk managers to make explicit risk trade-offs, and provide an easy to understand and systematic risk assessment process.

  4. On the Coplanar Integrable Case of the Twice-Averaged Hill Problem with Central Body Oblateness

    NASA Astrophysics Data System (ADS)

    Vashkov'yak, M. A.

    2018-01-01

    The twice-averaged Hill problem with the oblateness of the central planet is considered in the case where its equatorial plane coincides with the plane of its orbital motion relative to the perturbing body. A qualitative study of this so-called coplanar integrable case was begun by Y. Kozai in 1963 and continued by M.L. Lidov and M.V. Yarskaya in 1974. However, no rigorous analytical solution of the problem can be obtained due to the complexity of the integrals. In this paper we obtain some quantitative evolution characteristics and propose an approximate constructive-analytical solution of the evolution system in the form of explicit time dependences of satellite orbit elements. The methodical accuracy has been estimated for several orbits of artificial lunar satellites by comparison with the numerical solution of the evolution system.

  5. Nonstationary Deformation of an Elastic Layer with Mixed Boundary Conditions

    NASA Astrophysics Data System (ADS)

    Kubenko, V. D.

    2016-11-01

    The analytic solution to the plane problem for an elastic layer under a nonstationary surface load is found for mixed boundary conditions: normal stress and tangential displacement are specified on one side of the layer (fourth boundary-value problem of elasticity) and tangential stress and normal displacement are specified on the other side of the layer (second boundary-value problem of elasticity). The Laplace and Fourier integral transforms are applied. The inverse Laplace and Fourier transforms are found exactly using tabulated formulas and convolution theorems for various nonstationary loads. Explicit analytical expressions for stresses and displacements are derived. Loads applied to a constant surface area and to a surface area varying in a prescribed manner are considered. Computations demonstrate the dependence of the normal stress on time and spatial coordinates. Features of wave processes are analyzed

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

    Krasnenko, V.; Boltrushko, V.; Hizhnyakov, V.

    Chemically bound states of benzene molecules with graphene are studied both analytically and numerically. The states are formed by switching off intrabonds of π-electrons in C{sub 6} rings to interbonds. A number of different undistorted and distorted structures are established both with aligned and with transversal mutual orientation of benzene and graphene. The vibronic interactions causing distortions of bound states are found, by using a combination of analytical and numerical considerations. This allows one to determine all electronic transitions of π-electrons without explicit numerical calculations of excited states, to find the conical intersections of potentials, and to show that themore » mechanism of distortions is the pseudo-Jahn-Teller effect. It is found that the aligned distorted benzene molecule placed between two graphene sheets makes a chemical bond with both of them, which may be used for fastening of graphene sheets together.« less

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

    Izacard, Olivier

    In magnetized plasma physics, almost all developed analytic theories assume a Maxwellian distribution function (MDF) and in some cases small deviations are described using the perturbation theory. The deviations with respect to the Maxwellian equilibrium, called kinetic effects, are required to be taken into account especially for fusion reactor plasmas. Generally, because the perturbation theory is not consistent with observed steady-state non-Maxwellians, these kinetic effects are numerically evaluated by very central processing unit (CPU)-expensive codes, avoiding the analytic complexity of velocity phase space integrals. We develop here a new method based on analytic non-Maxwellian distribution functions constructed from non-orthogonal basismore » sets in order to (i) use as few parameters as possible, (ii) increase the efficiency to model numerical and experimental non-Maxwellians, (iii) help to understand unsolved problems such as diagnostics discrepancies from the physical interpretation of the parameters, and (iv) obtain analytic corrections due to kinetic effects given by a small number of terms and removing the numerical error of the evaluation of velocity phase space integrals. This work does not attempt to derive new physical effects even if it could be possible to discover one from the better understandings of some unsolved problems, but here we focus on the analytic prediction of kinetic corrections from analytic non-Maxwellians. As applications, examples of analytic kinetic corrections are shown for the secondary electron emission, the Langmuir probe characteristic curve, and the entropy. This is done by using three analytic representations of the distribution function: the Kappa distribution function, the bi-modal or a new interpreted non-Maxwellian distribution function (INMDF). The existence of INMDFs is proved by new understandings of the experimental discrepancy of the measured electron temperature between two diagnostics in JET. As main results, it is shown that (i) the empirical formula for the secondary electron emission is not consistent with a MDF due to the presence of super-thermal particles, (ii) the super-thermal particles can replace a diffusion parameter in the Langmuir probe current formula, and (iii) the entropy can explicitly decrease in presence of sources only for the introduced INMDF without violating the second law of thermodynamics. Moreover, the first order entropy of an infinite number of super-thermal tails stays the same as the entropy of a MDF. In conclusion, the latter demystifies the Maxwell's demon by statistically describing non-isolated systems.« less

  8. A semi-analytical analysis of electro-thermo-hydrodynamic stability in dielectric nanofluids using Buongiorno's mathematical model together with more realistic boundary conditions

    NASA Astrophysics Data System (ADS)

    Wakif, Abderrahim; Boulahia, Zoubair; Sehaqui, Rachid

    2018-06-01

    The main aim of the present analysis is to examine the electroconvection phenomenon that takes place in a dielectric nanofluid under the influence of a perpendicularly applied alternating electric field. In this investigation, we assume that the nanofluid has a Newtonian rheological behavior and verifies the Buongiorno's mathematical model, in which the effects of thermophoretic and Brownian diffusions are incorporated explicitly in the governing equations. Moreover, the nanofluid layer is taken to be confined horizontally between two parallel plate electrodes, heated from below and cooled from above. In a fast pulse electric field, the onset of electroconvection is due principally to the buoyancy forces and the dielectrophoretic forces. Within the framework of the Oberbeck-Boussinesq approximation and the linear stability theory, the governing stability equations are solved semi-analytically by means of the power series method for isothermal, no-slip and non-penetrability conditions. In addition, the computational implementation with the impermeability condition implies that there exists no nanoparticles mass flux on the electrodes. On the other hand, the obtained analytical solutions are validated by comparing them to those available in the literature for the limiting case of dielectric fluids. In order to check the accuracy of our semi-analytical results obtained for the case of dielectric nanofluids, we perform further numerical and semi-analytical computations by means of the Runge-Kutta-Fehlberg method, the Chebyshev-Gauss-Lobatto spectral method, the Galerkin weighted residuals technique, the polynomial collocation method and the Wakif-Galerkin weighted residuals technique. In this analysis, the electro-thermo-hydrodynamic stability of the studied nanofluid is controlled through the critical AC electric Rayleigh number Rec , whose value depends on several physical parameters. Furthermore, the effects of various pertinent parameters on the electro-thermo-hydrodynamic stability of the nanofluidic system are discussed in more detail through graphical and tabular illustrations.

  9. Attitude importance as a moderator of the relationship between implicit and explicit attitude measures.

    PubMed

    Karpinski, Andrew; Steinman, Ross B; Hilton, James L

    2005-07-01

    The authors examined attitude importance as a moderator of the relationship between the Implicit Association Test (IAT) and explicit attitude measures. In Study 1 (N = 194), as ratings of attitude importance regarding the 2000 presidential election increased, the strength of the relationship between a Bush-Gore IAT and explicit attitude measures also increased. Study 2 provided a conceptual replication of these results using attitudes toward Coke and Pepsi (N = 112). In addition, across both studies, explicit attitude measures were better predictors of deliberative behaviors than IAT scores. In Study 3 (N = 77), the authors examined the role of elaboration as a mechanism by which attitude importance may moderate IAT-explicit attitude correlations. As predicted, increased elaboration resulted in stronger IAT-explicit attitude correlations. Other possible mechanisms by which attitude importance may moderate the IAT-explicit attitude relationship also are discussed.

  10. A framework for inference about carnivore density from unstructured spatial sampling of scat using detector dogs

    USGS Publications Warehouse

    Thompson, Craig M.; Royle, J. Andrew; Garner, James D.

    2012-01-01

    Wildlife management often hinges upon an accurate assessment of population density. Although undeniably useful, many of the traditional approaches to density estimation such as visual counts, livetrapping, or mark–recapture suffer from a suite of methodological and analytical weaknesses. Rare, secretive, or highly mobile species exacerbate these problems through the reality of small sample sizes and movement on and off study sites. In response to these difficulties, there is growing interest in the use of non-invasive survey techniques, which provide the opportunity to collect larger samples with minimal increases in effort, as well as the application of analytical frameworks that are not reliant on large sample size arguments. One promising survey technique, the use of scat detecting dogs, offers a greatly enhanced probability of detection while at the same time generating new difficulties with respect to non-standard survey routes, variable search intensity, and the lack of a fixed survey point for characterizing non-detection. In order to account for these issues, we modified an existing spatially explicit, capture–recapture model for camera trap data to account for variable search intensity and the lack of fixed, georeferenced trap locations. We applied this modified model to a fisher (Martes pennanti) dataset from the Sierra National Forest, California, and compared the results (12.3 fishers/100 km2) to more traditional density estimates. We then evaluated model performance using simulations at 3 levels of population density. Simulation results indicated that estimates based on the posterior mode were relatively unbiased. We believe that this approach provides a flexible analytical framework for reconciling the inconsistencies between detector dog survey data and density estimation procedures.

  11. Exponential asymptotics of homoclinic snaking

    NASA Astrophysics Data System (ADS)

    Dean, A. D.; Matthews, P. C.; Cox, S. M.; King, J. R.

    2011-12-01

    We study homoclinic snaking in the cubic-quintic Swift-Hohenberg equation (SHE) close to the onset of a subcritical pattern-forming instability. Application of the usual multiple-scales method produces a leading-order stationary front solution, connecting the trivial solution to the patterned state. A localized pattern may therefore be constructed by matching between two distant fronts placed back-to-back. However, the asymptotic expansion of the front is divergent, and hence should be truncated. By truncating optimally, such that the resultant remainder is exponentially small, an exponentially small parameter range is derived within which stationary fronts exist. This is shown to be a direct result of the 'locking' between the phase of the underlying pattern and its slowly varying envelope. The locking mechanism remains unobservable at any algebraic order, and can only be derived by explicitly considering beyond-all-orders effects in the tail of the asymptotic expansion, following the method of Kozyreff and Chapman as applied to the quadratic-cubic SHE (Chapman and Kozyreff 2009 Physica D 238 319-54, Kozyreff and Chapman 2006 Phys. Rev. Lett. 97 44502). Exponentially small, but exponentially growing, contributions appear in the tail of the expansion, which must be included when constructing localized patterns in order to reproduce the full snaking diagram. Implicit within the bifurcation equations is an analytical formula for the width of the snaking region. Due to the linear nature of the beyond-all-orders calculation, the bifurcation equations contain an analytically indeterminable constant, estimated in the previous work by Chapman and Kozyreff using a best fit approximation. A more accurate estimate of the equivalent constant in the cubic-quintic case is calculated from the iteration of a recurrence relation, and the subsequent analytical bifurcation diagram compared with numerical simulations, with good agreement.

  12. A hydrogeologic framework for characterizing summer streamflow sensitivity to climate warming in the Pacific Northwest, USA

    NASA Astrophysics Data System (ADS)

    Safeeq, M.; Grant, G. E.; Lewis, S. L.; Kramer, M. G.; Staab, B.

    2014-09-01

    Summer streamflows in the Pacific Northwest are largely derived from melting snow and groundwater discharge. As the climate warms, diminishing snowpack and earlier snowmelt will cause reductions in summer streamflow. Most regional-scale assessments of climate change impacts on streamflow use downscaled temperature and precipitation projections from general circulation models (GCMs) coupled with large-scale hydrologic models. Here we develop and apply an analytical hydrogeologic framework for characterizing summer streamflow sensitivity to a change in the timing and magnitude of recharge in a spatially explicit fashion. In particular, we incorporate the role of deep groundwater, which large-scale hydrologic models generally fail to capture, into streamflow sensitivity assessments. We validate our analytical streamflow sensitivities against two empirical measures of sensitivity derived using historical observations of temperature, precipitation, and streamflow from 217 watersheds. In general, empirically and analytically derived streamflow sensitivity values correspond. Although the selected watersheds cover a range of hydrologic regimes (e.g., rain-dominated, mixture of rain and snow, and snow-dominated), sensitivity validation was primarily driven by the snow-dominated watersheds, which are subjected to a wider range of change in recharge timing and magnitude as a result of increased temperature. Overall, two patterns emerge from this analysis: first, areas with high streamflow sensitivity also have higher summer streamflows as compared to low-sensitivity areas. Second, the level of sensitivity and spatial extent of highly sensitive areas diminishes over time as the summer progresses. Results of this analysis point to a robust, practical, and scalable approach that can help assess risk at the landscape scale, complement the downscaling approach, be applied to any climate scenario of interest, and provide a framework to assist land and water managers in adapting to an uncertain and potentially challenging future.

  13. Dynamic imaging model and parameter optimization for a star tracker.

    PubMed

    Yan, Jinyun; Jiang, Jie; Zhang, Guangjun

    2016-03-21

    Under dynamic conditions, star spots move across the image plane of a star tracker and form a smeared star image. This smearing effect increases errors in star position estimation and degrades attitude accuracy. First, an analytical energy distribution model of a smeared star spot is established based on a line segment spread function because the dynamic imaging process of a star tracker is equivalent to the static imaging process of linear light sources. The proposed model, which has a clear physical meaning, explicitly reflects the key parameters of the imaging process, including incident flux, exposure time, velocity of a star spot in an image plane, and Gaussian radius. Furthermore, an analytical expression of the centroiding error of the smeared star spot is derived using the proposed model. An accurate and comprehensive evaluation of centroiding accuracy is obtained based on the expression. Moreover, analytical solutions of the optimal parameters are derived to achieve the best performance in centroid estimation. Finally, we perform numerical simulations and a night sky experiment to validate the correctness of the dynamic imaging model, the centroiding error expression, and the optimal parameters.

  14. Analytic topologically nontrivial solutions of the (3 +1 )-dimensional U (1 ) gauged Skyrme model and extended duality

    NASA Astrophysics Data System (ADS)

    Avilés, L.; Canfora, F.; Dimakis, N.; Hidalgo, D.

    2017-12-01

    We construct the first analytic examples of topologically nontrivial solutions of the (3 +1 )-dimensional U (1 ) gauged Skyrme model within a finite box in (3 +1 )-dimensional flat space-time. There are two types of gauged solitons. The first type corresponds to gauged Skyrmions living within a finite volume. The second corresponds to gauged time crystals (smooth solutions of the U (1 ) gauged Skyrme model whose periodic time dependence is protected by a winding number). The notion of electromagnetic duality can be extended for these two types of configurations in the sense that the electric and one of the magnetic components can be interchanged. These analytic solutions show very explicitly the Callan-Witten mechanism (according to which magnetic monopoles may "swallow" part of the topological charge of the Skyrmion) since the electromagnetic field contributes directly to the conserved topological charge of the gauged Skyrmions. As it happens in superconductors, the magnetic field is suppressed in the core of the gauged Skyrmions. On the other hand, the electric field is strongly suppresed in the core of gauged time crystals.

  15. Will This Case Count? The Influence of Training on Treatment.

    PubMed

    Blakeman, Rachel; Goldberger, Marianne

    2016-12-01

    Mandated use of the couch-whether specifically stated or tacitly communicated by supervisors and colleagues-to fulfill requirements for graduation or certification is a significant disservice to candidates and their patients. In its training standards, it is argued, APsaA and its member institutes should state explicitly that a treatment can qualify as a psychoanalysis, regardless of whether the patient is using the couch, as long as the process is analytic and the candidate's thinking is demonstrably analytic. The mandate, however conveyed, that one must use the couch interferes with candidates' optimal analytic functioning, jeopardizing their patients' analyses. Data from infant observation, neuroscience, and facial expression studies-unavailable to earlier generations of analysts-support a more nuanced view of use of the couch. Each analysis is unique, and some analyses might well benefit from use of both the couch and the chair at different phases of treatment, but unless this is spelled out by ApsaA and its member institutes, candidates and junior analysts will be prevented from freely contemplating the clinical benefits or detriments of their use in specific cases.

  16. Normal stress differences from Oldroyd 8-constant framework: Exact analytical solution for large-amplitude oscillatory shear flow

    NASA Astrophysics Data System (ADS)

    Saengow, C.; Giacomin, A. J.

    2017-12-01

    The Oldroyd 8-constant framework for continuum constitutive theory contains a rich diversity of popular special cases for polymeric liquids. In this paper, we use part of our exact solution for shear stress to arrive at unique exact analytical solutions for the normal stress difference responses to large-amplitude oscillatory shear (LAOS) flow. The nonlinearity of the polymeric liquids, triggered by LAOS, causes these responses at even multiples of the test frequency. We call responses at a frequency higher than twice the test frequency higher harmonics. We find the new exact analytical solutions to be compact and intrinsically beautiful. These solutions reduce to those of our previous work on the special case of the corotational Maxwell fluid. Our solutions also agree with our new truncated Goddard integral expansion for the special case of the corotational Jeffreys fluid. The limiting behaviors of these exact solutions also yield new explicit expressions. Finally, we use our exact solutions to see how η∞ affects the normal stress differences in LAOS.

  17. First-and Second-Order Displacement Transfer Functions for Structural Shape Calculations Using Analytically Predicted Surface Strains

    NASA Technical Reports Server (NTRS)

    Ko, William L.; Fleischer, Van Tran

    2012-01-01

    New first- and second-order displacement transfer functions have been developed for deformed shape calculations of nonuniform cross-sectional beam structures such as aircraft wings. The displacement transfer functions are expressed explicitly in terms of beam geometrical parameters and surface strains (uniaxial bending strains) obtained at equally spaced strain stations along the surface of the beam structure. By inputting the measured or analytically calculated surface strains into the displacement transfer functions, one could calculate local slopes, deflections, and cross-sectional twist angles of the nonuniform beam structure for mapping the overall structural deformed shapes for visual display. The accuracy of deformed shape calculations by the first- and second-order displacement transfer functions are determined by comparing these values to the analytically predicted values obtained from finite element analyses. This comparison shows that the new displacement transfer functions could quite accurately calculate the deformed shapes of tapered cantilever tubular beams with different tapered angles. The accuracy of the present displacement transfer functions also are compared to those of the previously developed displacement transfer functions.

  18. Critical coupling and coherent perfect absorption for ranges of energies due to a complex gain and loss symmetric system

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

    Hasan, Mohammad, E-mail: mohammadhasan786@gmail.com; Ghatak, Ananya, E-mail: gananya04@gmail.com; Mandal, Bhabani Prasad, E-mail: bhabani.mandal@gmail.com

    2014-05-15

    We consider a non-Hermitian medium with a gain and loss symmetric, exponentially damped potential distribution to demonstrate different scattering features analytically. The condition for critical coupling (CC) for unidirectional wave and coherent perfect absorption (CPA) for bidirectional waves are obtained analytically for this system. The energy points at which total absorption occurs are shown to be the spectral singular points for the time reversed system. The possible energies at which CC occurs for left and right incidence are different. We further obtain periodic intervals with increasing periodicity of energy for CC and CPA to occur in this system. -- Highlights:more » •Energy ranges for CC and CPA are obtained explicitly for complex WS potential. •Analytical conditions for CC and CPA for PT symmetric WS potential are obtained. •Conditions for left and right CC are shown to be different. •Conditions for CC and CPA are shown to be that of SS for the time reversed system. •Our model shows the great flexibility of frequencies for CC and CPA.« less

  19. SU-G-206-06: Analytic Dose Function for CT Scans in Infinite Cylinders as a Function of Scan Length and Cylinder Radius

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

    Bakalyar, D; Feng, W; McKenney, S

    Purpose: The radiation dose absorbed at a particular radius ρ within the central plane of a long cylinder following a CT scan is a function of the length of the scan L and the cylinder radius R along with kVp and cylinder composition. An analytic function was created that that not only expresses these dependencies but is integrable in closed form over the area of the central plane. This feature facilitates explicit calculation of the planar average dose. The “approach to equilibrium” h(L) discussed in the TG111 report is seamlessly included in this function. Methods: For a cylindrically symmetric radiationmore » field, Monte Carlo calculations were performed to compute the dose distribution to long polyethylene cylinders for scans of varying L for cylinders ranging in radius from 5 to 20 cm. The function was developed from the resultant Monte Carlo data. In addition, the function was successfully fit to data taken from measurements on the 30 cm diameter ICRU/TG200 phantom using a real-time dosimeter. Results: Symmetry and continuity dictate a local extremum at the center which is a minimum for the larger sizes. There are competing effects as the beam penetrates the cylinder from the outside: attenuation, resulting in a decrease; scatter, abruptly increasing at the circumference. This competition may result in an absolute maximum between the center and outer edge leading to a “gull wing” shape for the radial dependence. For the smallest cylinders, scatter may dominate to the extent that there is an absolute maximum at the center. Conclusion: An integrable, analytic function has been developed that provides the radial dependency of dose for the central plane of a scan of length L for cylinders of varying diameter. Equivalently, we have developed h(L,R,ρ).« less

  20. A constitutive law for continuous fiber reinforced brittle matrix composites with fiber fragmentation and stress recovery

    NASA Astrophysics Data System (ADS)

    Neumeister, Jonas M.

    1993-08-01

    THE TENSILE BEHAVIOR of a brittle matrix composite is studied for post matrix crack saturation conditions. Scatter of fiber strength following the Weibull distribution as well as the influence of the major microstructural variables is considered. The stress in a fiber is assumed to recover linearly around a failure due to a fiber-matrix interface behavior mainly ruled by friction. The constitutive behavior for such a composite is analysed. Results are given for a simplified and a refined approximate description and compared with an analysis resulting from the exact analytical theory of fiber fragmentation. It is shown that the stress-strain relation for the refined model excellently follows the exact solution and gives the location of the maximum to within 1% in both stress and strain; for most materials the agreement is even better. Also it is shown that all relations can be normalized to depend on only two variables; a stress reference and the Weibull exponent. For systems with low scatter in fiber strength the simplified model is sufficient to determine the stress maximum but not the postcritical behavior. In addition, the simplified model gives explicit analytical expressions for the maximum stress and corresponding strain. None of the models contain any volume dependence or statistical scatter, but the maximum stress given by the stress-strain relation constitutes an upper bound for the ultimate tensile strength of the composite.

Some links on this page may take you to non-federal websites. Their policies may differ from this site.
Top