Quantum mechanical generalized phase-shift approach to atom-surface scattering: a Feshbach projection approach to dealing with closed channel effects.

PubMed

Maji, Kaushik; Kouri, Donald J

2011-03-28

We have developed a new method for solving quantum dynamical scattering problems, using the time-independent Schrödinger equation (TISE), based on a novel method to generalize a "one-way" quantum mechanical wave equation, impose correct boundary conditions, and eliminate exponentially growing closed channel solutions. The approach is readily parallelized to achieve approximate N(2) scaling, where N is the number of coupled equations. The full two-way nature of the TISE is included while propagating the wave function in the scattering variable and the full S-matrix is obtained. The new algorithm is based on a "Modified Cayley" operator splitting approach, generalizing earlier work where the method was applied to the time-dependent Schrödinger equation. All scattering variable propagation approaches to solving the TISE involve solving a Helmholtz-type equation, and for more than one degree of freedom, these are notoriously ill-behaved, due to the unavoidable presence of exponentially growing contributions to the numerical solution. Traditionally, the method used to eliminate exponential growth has posed a major obstacle to the full parallelization of such propagation algorithms. We stabilize by using the Feshbach projection operator technique to remove all the nonphysical exponentially growing closed channels, while retaining all of the propagating open channel components, as well as exponentially decaying closed channel components.

Exponential-fitted methods for integrating stiff systems of ordinary differential equations: Applications to homogeneous gas-phase chemical kinetics

NASA Technical Reports Server (NTRS)

Pratt, D. T.

1984-01-01

Conventional algorithms for the numerical integration of ordinary differential equations (ODEs) are based on the use of polynomial functions as interpolants. However, the exact solutions of stiff ODEs behave like decaying exponential functions, which are poorly approximated by polynomials. An obvious choice of interpolant are the exponential functions themselves, or their low-order diagonal Pade (rational function) approximants. A number of explicit, A-stable, integration algorithms were derived from the use of a three-parameter exponential function as interpolant, and their relationship to low-order, polynomial-based and rational-function-based implicit and explicit methods were shown by examining their low-order diagonal Pade approximants. A robust implicit formula was derived by exponential fitting the trapezoidal rule. Application of these algorithms to integration of the ODEs governing homogenous, gas-phase chemical kinetics was demonstrated in a developmental code CREK1D, which compares favorably with the Gear-Hindmarsh code LSODE in spite of the use of a primitive stepsize control strategy.

Stability of post-fertilization traveling waves

NASA Astrophysics Data System (ADS)

Flores, Gilberto; Plaza, Ramón G.

This paper studies the stability of a family of traveling wave solutions to the system proposed by Lane et al. [D.C. Lane, J.D. Murray, V.S. Manoranjan, Analysis of wave phenomena in a morphogenetic mechanochemical model and an application to post-fertilization waves on eggs, IMA J. Math. Appl. Med. Biol. 4 (4) (1987) 309-331], to model a pair of mechanochemical phenomena known as post-fertilization waves on eggs. The waves consist of an elastic deformation pulse on the egg's surface, and a free calcium concentration front. The family is indexed by a coupling parameter measuring contraction stress effects on the calcium concentration. This work establishes the spectral, linear and nonlinear orbital stability of these post-fertilization waves for small values of the coupling parameter. The usual methods for the spectral and evolution equations cannot be applied because of the presence of mixed partial derivatives in the elastic equation. Nonetheless, exponential decay of the directly constructed semigroup on the complement of the zero eigenspace is established. We show that small perturbations of the waves yield solutions to the nonlinear equations decaying exponentially to a phase-modulated traveling wave.

Siphons, Water Clocks, Cooling Coffee, and Leaking Capacitors: Classroom Activities and a Few Equations to Help Students Understand Radioactive Decay and Other Exponential Processes

ERIC Educational Resources Information Center

Brady, John B.

2009-01-01

Although an understanding of radiometric dating is central to the preparation of every geologist, many students struggle with the concepts and mathematics of radioactive decay. Physical demonstrations and hands-on experiments can be used to good effect in addressing this teaching conundrum. Water, heat, and electrons all move or flow in response…

Instability and sound emission from a flow over a curved surface

NASA Technical Reports Server (NTRS)

Maestrello, L.; Parikh, P.; Bayliss, A.

1988-01-01

The growth and decay of a wavepacket convecting in a boundary layer over a concave-convex surface is studied numerically using direct computations of the Navier-Stokes equations. The resulting sound radiation is computed using the linearized Euler equations with the pressure from the Navier-Stokes solution as a time-dependent boundary condition. It is shown that on the concave portion the amplitude of the wavepacket increases and its bandwidth broadens while on the convex portion some of the components in the packet are stabilized. The pressure field decays exponentially away from the surface and then algebraically exhibits a decay characteristic of acoustic waves in two dimensions. The far-field acoustic pressure exhibits a peak at a frequency corresponding to the inflow instability frequency.

The decay of 'mesotrons' (1939-1943), experimental particle physics in the age of innocence

NASA Astrophysics Data System (ADS)

Rossi, B.

An account is given of the experimental work carried out by the author and his associates during the years 1939 through 1943, which produced the first unambiguous evidence of the spontaneous decay of 'mesotrons', showed that this decay occurred according to an exponential law, as expected, and measured the mean life with a 3 percent accuracy. A byproduct of this work was a verification of the relativistic equation for the dilation of time intervals. Previously announced in STAR as N81-76151

Catalytic Bioscavengers Human Butyrylcholinesterase and Paraoxonase Sequestered to the Center for CNS

DTIC Science & Technology

2010-04-01

of radiolabeling fusion proteins without the denaturing effects coincident with oxidative radio-iodination associated with the chloramine T method...organ PS product = [(%ID/g)/AUC]*1000 Reportable Outcomes (1) The plasma concentration decay curve for AGT-185 is shown in Figure 1. The % of...injected dose (ID)/mL decreases rapidly in plasma following IV injection. This plasma decay curve was fit to the bi-exponential equation described above

Nonlinear modulation of an extraordinary wave under the conditions of parametric decay

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

Dorofeenko, V. G.; Krasovitskiy, V. B.; Turikov, V. A.

2012-06-15

A self-consistent set of Hamilton equations describing nonlinear saturation of the amplitude of oscillations excited under the conditions of parametric decay of an elliptically polarized extraordinary wave in cold plasma is solved analytically and numerically. It is shown that the exponential increase in the amplitude of the secondary wave excited at the half-frequency of the primary wave changes into a reverse process in which energy is returned to the primary wave and nonlinear oscillations propagating across the external magnetic field are generated. The system of 'slow' equations for the amplitudes, obtained by averaging the initial equations over the high-frequency period,more » is used to describe steady-state nonlinear oscillations in plasma.« less

The dynamics of charge transfer with and without a barrier: A very simplified model of cyclic voltammetry.

PubMed

Ouyang, Wenjun; Subotnik, Joseph E

2017-05-07

Using the Anderson-Holstein model, we investigate charge transfer dynamics between a molecule and a metal surface for two extreme cases. (i) With a large barrier, we show that the dynamics follow a single exponential decay as expected; (ii) without any barrier, we show that the dynamics are more complicated. On the one hand, if the metal-molecule coupling is small, single exponential dynamics persist. On the other hand, when the coupling between the metal and the molecule is large, the dynamics follow a biexponential decay. We analyze the dynamics using the Smoluchowski equation, develop a simple model, and explore the consequences of biexponential dynamics for a hypothetical cyclic voltammetry experiment.

Further Improvement in 3DGRAPE

NASA Technical Reports Server (NTRS)

Alter, Stephen

2004-01-01

3DGRAPE/AL:V2 denotes version 2 of the Three-Dimensional Grids About Anything by Poisson's Equation with Upgrades from Ames and Langley computer program. The preceding version, 3DGRAPE/AL, was described in Improved 3DGRAPE (ARC-14069) NASA Tech Briefs, Vol. 21, No. 5 (May 1997), page 66. These programs are so named because they generate volume grids by iteratively solving Poisson's Equation in three dimensions. The grids generated by the various versions of 3DGRAPE have been used in computational fluid dynamics (CFD). The main novel feature of 3DGRAPE/AL:V2 is the incorporation of an optional scheme in which anisotropic Lagrange-based trans-finite interpolation (ALBTFI) is coupled with exponential decay functions to compute and blend interior source terms. In the input to 3DGRAPE/AL:V2 the user can specify whether or not to invoke ALBTFI in combination with exponential-decay controls, angles, and cell size for controlling the character of grid lines. Of the known programs that solve elliptic partial differential equations for generating grids, 3DGRAPE/AL:V2 is the only code that offers a combination of speed and versatility with most options for controlling the densities and other characteristics of grids for CFD.

A garden of orchids: a generalized Harper equation at quadratic irrational frequencies

NASA Astrophysics Data System (ADS)

Mestel, B. D.; Osbaldestin, A. H.

2004-10-01

We consider a generalized Harper equation at quadratic irrational flux, showing, in the strong coupling limit, the fluctuations of the exponentially decaying eigenfunctions are governed by the dynamics of a renormalization operator on a renormalization strange set. This work generalizes previous analyses which have considered only the golden mean case. Projections of the renormalization strange sets are illustrated analogous to the 'orchid' present in the golden mean case.

On the Existence of Non-Oscillatory Phase Functions for Second Order Ordinary Differential Equations in the High-Frequency Regime

DTIC Science & Technology

2014-08-04

Chebyshev coefficients of both r and q decay exponentially, although those of r decay at a slightly slower rate. 10.2. Evaluation of Legendre polynomials ...In this experiment, we compare the cost of evaluating Legendre polynomials of large order using the standard recurrence relation with the cost of...doing so with a nonoscillatory phase function. For any integer n ě 0, the Legendre polynomial Pnpxq of order n is a solution of the second order

Quantum decoherence in electronic current flowing through carbon nanotubes induced by thermal atomic vibrations

NASA Astrophysics Data System (ADS)

Ishizeki, Keisuke; Sasaoka, Kenji; Konabe, Satoru; Souma, Satofumi; Yamamoto, Takahiro

2018-06-01

We theoretically investigate quantum decoherence in electronic currents flowing through metallic carbon nanotubes caused by thermal atomic vibrations using the time-dependent Schrödinger equation for an open system. We reveal that the quantum coherence of conduction electrons decays exponentially with tube length at a fixed temperature, and that the decay rate increases with temperature. We also find that the phase relaxation length due to the thermal atomic vibrations is inversely proportional to temperature.

Discrete diffraction managed solitons: Threshold phenomena and rapid decay for general nonlinearities

NASA Astrophysics Data System (ADS)

Choi, Mi-Ran; Hundertmark, Dirk; Lee, Young-Ran

2017-10-01

We prove a threshold phenomenon for the existence/non-existence of energy minimizing solitary solutions of the diffraction management equation for strictly positive and zero average diffraction. Our methods allow for a large class of nonlinearities; they are, for example, allowed to change sign, and the weakest possible condition, it only has to be locally integrable, on the local diffraction profile. The solutions are found as minimizers of a nonlinear and nonlocal variational problem which is translation invariant. There exists a critical threshold λcr such that minimizers for this variational problem exist if their power is bigger than λcr and no minimizers exist with power less than the critical threshold. We also give simple criteria for the finiteness and strict positivity of the critical threshold. Our proof of existence of minimizers is rather direct and avoids the use of Lions' concentration compactness argument. Furthermore, we give precise quantitative lower bounds on the exponential decay rate of the diffraction management solitons, which confirm the physical heuristic prediction for the asymptotic decay rate. Moreover, for ground state solutions, these bounds give a quantitative lower bound for the divergence of the exponential decay rate in the limit of vanishing average diffraction. For zero average diffraction, we prove quantitative bounds which show that the solitons decay much faster than exponentially. Our results considerably extend and strengthen the results of Hundertmark and Lee [J. Nonlinear Sci. 22, 1-38 (2012) and Commun. Math. Phys. 309(1), 1-21 (2012)].

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.

Focus Article: Oscillatory and long-range monotonic exponential decays of electrostatic interactions in ionic liquids and other electrolytes: The significance of dielectric permittivity and renormalized charges

NASA Astrophysics Data System (ADS)

Kjellander, Roland

2018-05-01

A unified treatment of oscillatory and monotonic exponential decays of interactions in electrolytes is displayed, which highlights the role of dielectric response of the fluid in terms of renormalized (effective) dielectric permittivity and charges. An exact, but physically transparent statistical mechanical formalism is thereby used, which is presented in a systematic, pedagogical manner. Both the oscillatory and monotonic behaviors are given by an equation for the decay length of screened electrostatic interactions that is very similar to the classical expression for the Debye length. The renormalized dielectric permittivities, which have similar roles for electrolytes as the dielectric constant has for pure polar fluids, consist in general of several entities with different physical meanings. They are connected to dielectric response of the fluid on the same length scale as the decay length of the screened interactions. Only in cases where the decay length is very long, these permittivities correspond approximately to a dielectric response in the long-wavelength limit, like the dielectric constant for polar fluids. Experimentally observed long-range exponentially decaying surface forces are analyzed as well as the oscillatory forces observed for short to intermediate surface separations. Both occur in some ionic liquids and in concentrated as well as very dilute electrolyte solutions. The coexisting modes of decay are in general determined by the bulk properties of the fluid and not by the solvation of the surfaces; in the present cases, they are given by the behavior of the screened Coulomb interaction of the bulk fluid. The surface-fluid interactions influence the amplitudes and signs or phases of the different modes of the decay, but not their decay lengths and wavelengths. The similarities between some ionic liquids and very dilute electrolyte solutions as regards both the long-range monotonic and the oscillatory decays are analyzed.

Physical and numerical sources of computational inefficiency in integration of chemical kinetic rate equations: Etiology, treatment and prognosis

NASA Technical Reports Server (NTRS)

Pratt, D. T.; Radhakrishnan, K.

1986-01-01

The design of a very fast, automatic black-box code for homogeneous, gas-phase chemical kinetics problems requires an understanding of the physical and numerical sources of computational inefficiency. Some major sources reviewed in this report are stiffness of the governing ordinary differential equations (ODE's) and its detection, choice of appropriate method (i.e., integration algorithm plus step-size control strategy), nonphysical initial conditions, and too frequent evaluation of thermochemical and kinetic properties. Specific techniques are recommended (and some advised against) for improving or overcoming the identified problem areas. It is argued that, because reactive species increase exponentially with time during induction, and all species exhibit asymptotic, exponential decay with time during equilibration, exponential-fitted integration algorithms are inherently more accurate for kinetics modeling than classical, polynomial-interpolant methods for the same computational work. But current codes using the exponential-fitted method lack the sophisticated stepsize-control logic of existing black-box ODE solver codes, such as EPISODE and LSODE. The ultimate chemical kinetics code does not exist yet, but the general characteristics of such a code are becoming apparent.

Transverse instability of periodic and generalized solitary waves for a fifth-order KP model

NASA Astrophysics Data System (ADS)

Haragus, Mariana; Wahlén, Erik

2017-02-01

We consider a fifth-order Kadomtsev-Petviashvili equation which arises as a two-dimensional model in the classical water-wave problem. This equation possesses a family of generalized line solitary waves which decay exponentially to periodic waves at infinity. We prove that these solitary waves are transversely spectrally unstable and that this instability is induced by the transverse instability of the periodic tails. We rely upon a detailed spectral analysis of some suitably chosen linear operators.

Compactness and robustness: Applications in the solution of integral equations for chemical kinetics and electromagnetic scattering

NASA Astrophysics Data System (ADS)

Zhou, Yajun

This thesis employs the topological concept of compactness to deduce robust solutions to two integral equations arising from chemistry and physics: the inverse Laplace problem in chemical kinetics and the vector wave scattering problem in dielectric optics. The inverse Laplace problem occurs in the quantitative understanding of biological processes that exhibit complex kinetic behavior: different subpopulations of transition events from the "reactant" state to the "product" state follow distinct reaction rate constants, which results in a weighted superposition of exponential decay modes. Reconstruction of the rate constant distribution from kinetic data is often critical for mechanistic understandings of chemical reactions related to biological macromolecules. We devise a "phase function approach" to recover the probability distribution of rate constants from decay data in the time domain. The robustness (numerical stability) of this reconstruction algorithm builds upon the continuity of the transformations connecting the relevant function spaces that are compact metric spaces. The robust "phase function approach" not only is useful for the analysis of heterogeneous subpopulations of exponential decays within a single transition step, but also is generalizable to the kinetic analysis of complex chemical reactions that involve multiple intermediate steps. A quantitative characterization of the light scattering is central to many meteoro-logical, optical, and medical applications. We give a rigorous treatment to electromagnetic scattering on arbitrarily shaped dielectric media via the Born equation: an integral equation with a strongly singular convolution kernel that corresponds to a non-compact Green operator. By constructing a quadratic polynomial of the Green operator that cancels out the kernel singularity and satisfies the compactness criterion, we reveal the universality of a real resonance mode in dielectric optics. Meanwhile, exploiting the properties of compact operators, we outline the geometric and physical conditions that guarantee a robust solution to the light scattering problem, and devise an asymptotic solution to the Born equation of electromagnetic scattering for arbitrarily shaped dielectric in a non-perturbative manner.

Propagation of Disturbances in AC Electricity Grids.

PubMed

Tamrakar, Samyak; Conrath, Michael; Kettemann, Stefan

2018-04-24

The energy transition towards high shares of renewable energy will affect the stability of electricity grids in many ways. Here, we aim to study its impact on propagation of disturbances by solving nonlinear swing equations describing coupled rotating masses of synchronous generators and motors on different grid topologies. We consider a tree, a square grid and as a real grid topology, the german transmission grid. We identify ranges of parameters with different transient dynamics: the disturbance decays exponentially in time, superimposed by oscillations with the fast decay rate of a single node, or with a smaller decay rate without oscillations. Most remarkably, as the grid inertia is lowered, nodes may become correlated, slowing down the propagation from ballistic to diffusive motion, decaying with a power law in time. Applying linear response theory we show that tree grids have a spectral gap leading to exponential relaxation as protected by topology and independent on grid size. Meshed grids are found to have a spectral gap which decreases with increasing grid size, leading to slow power law relaxation and collective diffusive propagation of disturbances. We conclude by discussing consequences if no measures are undertaken to preserve the grid inertia in the energy transition.

Propagation of solutions to the Fisher-KPP equation with slowly decaying initial data

NASA Astrophysics Data System (ADS)

Henderson, Christopher

2016-10-01

The Fisher-KPP equation is a model for population dynamics that has generated a huge amount of interest since its introduction in 1937. The speed with which a population spreads has been computed quite precisely when the initial data, u 0, decays exponentially. More recently, though, the case when the initial data decays more slowly has been studied. In Hamel F and Roques L (2010 J. Differ. Equ. 249 1726-45), the authors show that the level sets of height of m of u move super-linearly and may be bounded above and below by expressions of the form u0-1≤ft({{c}m}{{\\text{e}}-t}\\right) when u 0 decays algebraically of a small enough order. The constants c m for the upper and lower bounds that they obtain are not explicit and do not match. In this paper, we improve their precision for a broader class of initial data and for a broader class of equations. In particular, our approach yields the explicit highest order term in the location of the level sets, which in the most basic setting is given by u0-1≤ft(m{{\\text{e}}-t}/(1-m)\\right) as long as u 0 decays slower than {{\\text{e}}-\\sqrt{x}} . We generalize this to the previously unstudied setting when the nonlinearity is periodic in space. In addition, for large times, we characterize the profile of the solution in terms of a generalized logistic equation.

Properties of one-dimensional anharmonic lattice solitons

NASA Astrophysics Data System (ADS)

Szeftel, Jacob; Laurent-Gengoux, Pascal; Ilisca, Ernest; Hebbache, Mohamed

2000-12-01

The existence of bell- and kink-shaped solitons moving at constant velocity while keeping a permanent profile is studied in infinite periodic monoatomic chains of arbitrary anharmonicity by taking advantage of the equation of motion being integrable with respect to solitons. A second-order, non-linear differential equation involving advanced and retarded terms must be solved, which is done by implementing a scheme based on the finite element and Newton's methods. If the potential has a harmonic limit, the asymptotic time-decay behaves exponentially and there is a dispersion relation between propagation velocity and decay time. Inversely if the potential has no harmonic limit, the asymptotic regime shows up either as a power-law or faster than exponential. Excellent agreement is achieved with Toda's model. Illustrative examples are also given for the Fermi-Pasta-Ulam and sine-Gordon potentials. Owing to integrability an effective one-body potential is worked out in each case. Lattice and continuum solitons differ markedly from one another as regards the amplitude versus propagation velocity relationship and the asymptotic time behavior. The relevance of the linear stability analysis when applied to solitons propagating in an infinite crystal is questioned. The reasons preventing solitons from arising in a diatomic lattice are discussed.

Generalized hydrodynamic correlations and fractional memory functions

NASA Astrophysics Data System (ADS)

Rodríguez, Rosalio F.; Fujioka, Jorge

2015-12-01

A fractional generalized hydrodynamic (GH) model of the longitudinal velocity fluctuations correlation, and its associated memory function, for a complex fluid is analyzed. The adiabatic elimination of fast variables introduces memory effects in the transport equations, and the dynamic of the fluctuations is described by a generalized Langevin equation with long-range noise correlations. These features motivate the introduction of Caputo time fractional derivatives and allows us to calculate analytic expressions for the fractional longitudinal velocity correlation function and its associated memory function. Our analysis eliminates a spurious constant term in the non-fractional memory function found in the non-fractional description. It also produces a significantly slower power-law decay of the memory function in the GH regime that reduces to the well-known exponential decay in the non-fractional Navier-Stokes limit.

Fractional calculus and morphogen gradient formation

NASA Astrophysics Data System (ADS)

Yuste, Santos Bravo; Abad, Enrique; Lindenberg, Katja

2012-12-01

Some microscopic models for reactive systems where the reaction kinetics is limited by subdiffusion are described by means of reaction-subdiffusion equations where fractional derivatives play a key role. In particular, we consider subdiffusive particles described by means of a Continuous Time Random Walk (CTRW) model subject to a linear (first-order) death process. The resulting fractional equation is employed to study the developmental biology key problem of morphogen gradient formation for the case in which the morphogens are subdiffusive. If the morphogen degradation rate (reactivity) is constant, we find exponentially decreasing stationary concentration profiles, which are similar to the profiles found when the morphogens diffuse normally. However, for the case in which the degradation rate decays exponentially with the distance to the morphogen source, we find that the morphogen profiles are qualitatively different from the profiles obtained when the morphogens diffuse normally.

Lambert-Beer law in ocean waters: optical properties of water and of dissolved/suspended material, optical energy budgets.

PubMed

Stavn, R H

1988-01-15

The role of the Lambert-Beer law in ocean optics is critically examined. The Lambert-Beer law and the three-parameter model of the submarine light field are used to construct an optical energy budget for any hydrosol. It is further applied to the analytical exponential decay coefficient of the light field and used to estimate the optical properties and effects of the dissolved/suspended component in upper ocean layers. The concepts of the empirical exponential decay coefficient (diffuse attenuation coefficient) of the light field and a constant exponential decay coefficient for molecular water are analyzed quantitatively. A constant exponential decay coefficient for water is rejected. The analytical exponential decay coefficient is used to analyze optical gradients in ocean waters.

Elastic constants and dynamics in nematic liquid crystals

NASA Astrophysics Data System (ADS)

Humpert, Anja; Allen, Michael P.

2015-09-01

In this paper, we present molecular dynamics calculations of the Frank elastic constants, and associated time correlation functions, in nematic liquid crystals. We study two variants of the Gay-Berne potential, and use system sizes of half a million molecules, significantly larger than in previous studies of elastic behaviour. Equilibrium orientational fluctuations in reciprocal (k-) space were calculated, to determine the elastic constants by fitting at low |k|; our results indicate that small system size may be a source of inaccuracy in previous work. Furthermore, the dynamics of the Gay-Berne nematic were studied by calculating time correlation functions of components of the order tensor, together with associated components of the velocity field, for a set of wave vectors k. Confirming our earlier work, we found exponential decay for splay and twist correlations, and oscillatory exponential decay for the bend correlation. In this work, we confirm similar behaviour for the corresponding velocity components. In all cases, the decay rates, and oscillation frequencies, were found to be accurately proportional to k2 for small k, as predicted by the equations of nematodynamics. However, the observation of oscillatory bend fluctuations, and corresponding oscillatory shear flow decay, is in contradiction to the usual assumptions appearing in the literature, and in standard texts. We discuss the advantages and drawbacks of using large systems in these calculations.

A Lyapunov and Sacker–Sell spectral stability theory for one-step methods

DOE PAGES

Steyer, Andrew J.; Van Vleck, Erik S.

2018-04-13

Approximation theory for Lyapunov and Sacker–Sell spectra based upon QR techniques is used to analyze the stability of a one-step method solving a time-dependent (nonautonomous) linear ordinary differential equation (ODE) initial value problem in terms of the local error. Integral separation is used to characterize the conditioning of stability spectra calculations. The stability of the numerical solution by a one-step method of a nonautonomous linear ODE using real-valued, scalar, nonautonomous linear test equations is justified. This analysis is used to approximate exponential growth/decay rates on finite and infinite time intervals and establish global error bounds for one-step methods approximating uniformly,more » exponentially stable trajectories of nonautonomous and nonlinear ODEs. A time-dependent stiffness indicator and a one-step method that switches between explicit and implicit Runge–Kutta methods based upon time-dependent stiffness are developed based upon the theoretical results.« less

A Lyapunov and Sacker–Sell spectral stability theory for one-step methods

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

Steyer, Andrew J.; Van Vleck, Erik S.

Approximation theory for Lyapunov and Sacker–Sell spectra based upon QR techniques is used to analyze the stability of a one-step method solving a time-dependent (nonautonomous) linear ordinary differential equation (ODE) initial value problem in terms of the local error. Integral separation is used to characterize the conditioning of stability spectra calculations. The stability of the numerical solution by a one-step method of a nonautonomous linear ODE using real-valued, scalar, nonautonomous linear test equations is justified. This analysis is used to approximate exponential growth/decay rates on finite and infinite time intervals and establish global error bounds for one-step methods approximating uniformly,more » exponentially stable trajectories of nonautonomous and nonlinear ODEs. A time-dependent stiffness indicator and a one-step method that switches between explicit and implicit Runge–Kutta methods based upon time-dependent stiffness are developed based upon the theoretical results.« less

Proportional Feedback Control of Energy Intake During Obesity Pharmacotherapy.

PubMed

Hall, Kevin D; Sanghvi, Arjun; Göbel, Britta

2017-12-01

Obesity pharmacotherapies result in an exponential time course for energy intake whereby large early decreases dissipate over time. This pattern of declining drug efficacy to decrease energy intake results in a weight loss plateau within approximately 1 year. This study aimed to elucidate the physiology underlying the exponential decay of drug effects on energy intake. Placebo-subtracted energy intake time courses were examined during long-term obesity pharmacotherapy trials for 14 different drugs or drug combinations within the theoretical framework of a proportional feedback control system regulating human body weight. Assuming each obesity drug had a relatively constant effect on average energy intake and did not affect other model parameters, our model correctly predicted that long-term placebo-subtracted energy intake was linearly related to early reductions in energy intake according to a prespecified equation with no free parameters. The simple model explained about 70% of the variance between drug studies with respect to the long-term effects on energy intake, although a significant proportional bias was evident. The exponential decay over time of obesity pharmacotherapies to suppress energy intake can be interpreted as a relatively constant effect of each drug superimposed on a physiological feedback control system regulating body weight. © 2017 The Obesity Society.

Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations

NASA Astrophysics Data System (ADS)

Indekeu, Joseph O.; Smets, Ruben

2017-08-01

Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically.

Harmonic statistics

NASA Astrophysics Data System (ADS)

Eliazar, Iddo

2017-05-01

The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their 'public relations' for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process: a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of this object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford's law, and 1/f noise.

Detection of weak signals in memory thermal baths.

PubMed

Jiménez-Aquino, J I; Velasco, R M; Romero-Bastida, M

2014-11-01

The nonlinear relaxation time and the statistics of the first passage time distribution in connection with the quasideterministic approach are used to detect weak signals in the decay process of the unstable state of a Brownian particle embedded in memory thermal baths. The study is performed in the overdamped approximation of a generalized Langevin equation characterized by an exponential decay in the friction memory kernel. A detection criterion for each time scale is studied: The first one is referred to as the receiver output, which is given as a function of the nonlinear relaxation time, and the second one is related to the statistics of the first passage time distribution.

Rigorous Numerics for ill-posed PDEs: Periodic Orbits in the Boussinesq Equation

NASA Astrophysics Data System (ADS)

Castelli, Roberto; Gameiro, Marcio; Lessard, Jean-Philippe

2018-04-01

In this paper, we develop computer-assisted techniques for the analysis of periodic orbits of ill-posed partial differential equations. As a case study, our proposed method is applied to the Boussinesq equation, which has been investigated extensively because of its role in the theory of shallow water waves. The idea is to use the symmetry of the solutions and a Newton-Kantorovich type argument (the radii polynomial approach) to obtain rigorous proofs of existence of the periodic orbits in a weighted ℓ1 Banach space of space-time Fourier coefficients with exponential decay. We present several computer-assisted proofs of the existence of periodic orbits at different parameter values.

Scaling analysis and instantons for thermally assisted tunneling and quantum Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Jiang, Zhang; Smelyanskiy, Vadim N.; Isakov, Sergei V.; Boixo, Sergio; Mazzola, Guglielmo; Troyer, Matthias; Neven, Hartmut

2017-01-01

We develop an instantonic calculus to derive an analytical expression for the thermally assisted tunneling decay rate of a metastable state in a fully connected quantum spin model. The tunneling decay problem can be mapped onto the Kramers escape problem of a classical random dynamical field. This dynamical field is simulated efficiently by path-integral quantum Monte Carlo (QMC). We show analytically that the exponential scaling with the number of spins of the thermally assisted quantum tunneling rate and the escape rate of the QMC process are identical. We relate this effect to the existence of a dominant instantonic tunneling path. The instanton trajectory is described by nonlinear dynamical mean-field theory equations for a single-site magnetization vector, which we solve exactly. Finally, we derive scaling relations for the "spiky" barrier shape when the spin tunneling and QMC rates scale polynomially with the number of spins N while a purely classical over-the-barrier activation rate scales exponentially with N .

Rayleigh-Bloch waves trapped by a periodic perturbation: exact solutions

NASA Astrophysics Data System (ADS)

Merzon, A.; Zhevandrov, P.; Romero Rodríguez, M. I.; De la Paz Méndez, J. E.

2018-06-01

Exact solutions describing the Rayleigh-Bloch waves for the two-dimensional Helmholtz equation are constructed in the case when the refractive index is a sum of a constant and a small amplitude function which is periodic in one direction and of finite support in the other. These solutions are quasiperiodic along the structure and exponentially decay in the orthogonal direction. A simple formula for the dispersion relation of these waves is obtained.

A Study of the Thermal Environment Developed by a Traveling Slipper at High Velocity

DTIC Science & Technology

2013-03-01

Power Partition Function The next partition function takes the same formulation as the powered function but now the exponent is squared. The...function and note the squared term in the exponent . 66 Equation 4.27 (4.36) Thus far the three partition functions each give a predicted...hypothesized that the function would fall somewhere between the first exponential decay function and the power function. However, by squaring the exponent

Propagation of mechanical waves through a stochastic medium with spherical symmetry

NASA Astrophysics Data System (ADS)

Avendaño, Carlos G.; Reyes, J. Adrián

2018-01-01

We theoretically analyze the propagation of outgoing mechanical waves through an infinite isotropic elastic medium possessing spherical symmetry whose Lamé coefficients and density are spatial random functions characterized by well-defined statistical parameters. We derive the differential equation that governs the average displacement for a system whose properties depend on the radial coordinate. We show that such an equation is an extended version of the well-known Bessel differential equation whose perturbative additional terms contain coefficients that depend directly on the squared noise intensities and the autocorrelation lengths in an exponential decay fashion. We numerically solve the second order differential equation for several values of noise intensities and autocorrelation lengths and compare the corresponding displacement profiles with that of the exact analytic solution for the case of absent inhomogeneities.

Octanol reduces end-plate channel lifetime

PubMed Central

Gage, Peter W.; McBurney, Robert N.; Van Helden, Dirk

1978-01-01

1. Post-synaptic effects of n-octanol at concentrations of 0·1-1 mM were examined in toad sartorius muscles by use of extracellular and voltage-clamp techniques. 2. Octanol depressed the amplitude and duration of miniature end-plate currents and hence depressed neuromuscular transmission. 3. The decay of miniature end-plate currents remained exponential in octanol solutions even when the time constant of decay (τD) was decreased by 80-90%. 4. The lifetime of end-plate channels, obtained by analysis of acetylcholine noise, was also decreased by octanol. The average lifetime measured from noise spectra agreed reasonably well with the time constant of decay of miniature end-plate currents, both in control solution and in octanol solutions. 5. Octanol caused a reduction in the conductance of end-plate channels. Single channel conductance was on average about 25 pS in control solution and 20 pS in octanol. 6. In most cells the normal voltage sensitivity of the decay of miniature end-plate currents was retained in octanol solutions. The lifetime of end-plate channels measured from acetylcholine noise also remained voltage-sensitive in octanol solutions. In some experiments in which channel lifetime was exceptionally reduced the voltage sensitivity was less than normal. 7. In octanol solutions, τD was still very sensitive to temperature changes in most cells although in some the temperature sensitivity of τD was clearly reduced. Changes in τD with temperature could generally be fitted by the Arrhenius equation suggesting that a single step reaction controlled the decay of currents both in control and in octanol solutions. In some cells in which τD became less than 0·3 ms, the relationship between τD and temperature became inconsistent with the Arrhenius equation. 8. As the decay of end-plate currents in octanol solutions remains exponential, and the voltage and temperature sensitivity can be unchanged even when τD is significantly reduced, it seems likely that octanol decreases τD by increasing the rate of the reaction which normally controls the lifetime of end-plate channels. PMID:203674

Modeling the pressure inactivation of Escherichia coli and Salmonella typhimurium in sapote mamey ( Pouteria sapota (Jacq.) H.E. Moore & Stearn) pulp.

PubMed

Saucedo-Reyes, Daniela; Carrillo-Salazar, José A; Román-Padilla, Lizbeth; Saucedo-Veloz, Crescenciano; Reyes-Santamaría, María I; Ramírez-Gilly, Mariana; Tecante, Alberto

2018-03-01

High hydrostatic pressure inactivation kinetics of Escherichia coli ATCC 25922 and Salmonella enterica subsp. enterica serovar Typhimurium ATCC 14028 ( S. typhimurium) in a low acid mamey pulp at four pressure levels (300, 350, 400, and 450 MPa), different exposure times (0-8 min), and temperature of 25 ± 2℃ were obtained. Survival curves showed deviations from linearity in the form of a tail (upward concavity). The primary models tested were the Weibull model, the modified Gompertz equation, and the biphasic model. The Weibull model gave the best goodness of fit ( R 2 adj  > 0.956, root mean square error < 0.290) in the modeling and the lowest Akaike information criterion value. Exponential-logistic and exponential decay models, and Bigelow-type and an empirical models for b'( P) and n( P) parameters, respectively, were tested as alternative secondary models. The process validation considered the two- and one-step nonlinear regressions for making predictions of the survival fraction; both regression types provided an adequate goodness of fit and the one-step nonlinear regression clearly reduced fitting errors. The best candidate model according to the Akaike theory information, with better accuracy and more reliable predictions was the Weibull model integrated by the exponential-logistic and exponential decay secondary models as a function of time and pressure (two-step procedure) or incorporated as one equation (one-step procedure). Both mathematical expressions were used to determine the t d parameter, where the desired reductions ( 5D) (considering d = 5 ( t 5 ) as the criterion of 5 Log 10 reduction (5 D)) in both microorganisms are attainable at 400 MPa for 5.487 ± 0.488 or 5.950 ± 0.329 min, respectively, for the one- or two-step nonlinear procedure.

Measuring the viscosity of whole bovine lens using a fiber optic oxygen sensing system

PubMed Central

Thao, Mai T.; Perez, Daniel; Dillon, James

2014-01-01

Purpose To obtain a better understanding of oxygen and nutrient transport within the lens, the viscosity of whole lenses was investigated using a fiber optic oxygen sensor (optode). The diffusion coefficient of oxygen was calculated using the Stokes-Einstein equation at the slip boundary condition. Methods The optode was used to measure the oxygen decay signal in samples consisting of different glycerol/water solutions with known viscosities. The oxygen decay signal was fitted to a double exponential decay rate equation, and the lifetimes (tau) were calculated. It was determined that the tau-viscosity relationship is linear, which served as the standard curve. The same procedure was applied to fresh bovine lenses, and the unknown viscosity of the bovine lens was calculated from the tau-viscosity relationship. Results The average viscosity in a whole bovine lens was determined to be 5.74±0.88 cP by our method. Using the Stokes-Einstein equation at the slip boundary condition, the diffusion coefficient for oxygen was calculated to be 8.2 × 10−6 cm2/s. Conclusions These data indicate a higher resistance to flow for oxygen and nutrients in the lens than what is currently assumed in the literature. Overall, this study allows a better understanding of oxygen transport within the lens. PMID:24505211

Evidence of the Exponential Decay Emission in the Swift Gamma-ray Bursts

NASA Technical Reports Server (NTRS)

Sakamoto, T.; Sato, G.; Hill, J.E.; Krimm, H.A.; Yamazaki, R.; Takami, K.; Swindell, S.; Osborne, J.P.

2007-01-01

We present a systematic study of the steep decay emission of gamma-ray bursts (GRBs) observed by the Swift X-Ray Telescope (XRT). In contrast to the analysis in recent literature, instead of extrapolating the data of Burst Alert Telescope (BAT) down into the XRT energy range, we extrapolated the XRT data up to the BAT energy range, 15-25 keV, to produce the BAT and XRT composite light curve. Based on our composite light curve fitting, we have confirmed the existence of an exponential decay component which smoothly connects the BAT prompt data to the XRT steep decay for several GRBs. We also find that the XRT steep decay for some of the bursts can be well fitted by a combination of a power-law with an exponential decay model. We discuss that this exponential component may be the emission from an external shock and a sign of the deceleration of the outflow during the prompt phase.

Estimation of the light field inside photosynthetic microorganism cultures through Mittag-Leffler functions at depleted light conditions

NASA Astrophysics Data System (ADS)

Fuente, David; Lizama, Carlos; Urchueguía, Javier F.; Conejero, J. Alberto

2018-01-01

Light attenuation within suspensions of photosynthetic microorganisms has been widely described by the Lambert-Beer equation. However, at depths where most of the light has been absorbed by the cells, light decay deviates from the exponential behaviour and shows a lower attenuation than the corresponding from the purely exponential fall. This discrepancy can be modelled through the Mittag-Leffler function, extending Lambert-Beer law via a tuning parameter α that takes into account the attenuation process. In this work, we describe a fractional Lambert-Beer law to estimate light attenuation within cultures of model organism Synechocystis sp. PCC 6803. Indeed, we benchmark the measured light field inside cultures of two different Synechocystis strains, namely the wild-type and the antenna mutant strain called Olive at five different cell densities, with our in silico results. The Mittag-Leffler hyper-parameter α that best fits the data is 0.995, close to the exponential case. One of the most striking results to emerge from this work is that unlike prior literature on the subject, this one provides experimental evidence on the validity of fractional calculus for determining the light field. We show that by applying the fractional Lambert-Beer law for describing light attenuation, we are able to properly model light decay in photosynthetic microorganisms suspensions.

The Quantum-to-Classical Transition in Strongly Interacting Nanoscale Systems

NASA Astrophysics Data System (ADS)

Benatov, Latchezar Latchezarov

This thesis comprises two separate but related studies, dealing with two strongly interacting nanoscale systems on the border between the quantum and classical domains. In Part 1, we use a Born-Markov approximated master equation approach to study the symmetrized-in-frequency current noise spectrum and the oscillator steady state of a nanoelectromechanical system where a nanoscale resonator is coupled linearly via its momentum to a quantum point contact (QPC). Our current noise spectra exhibit clear signatures of the quantum correlations between the QPC current and the back-action force on the oscillator at a value of the relative tunneling phase where such correlations are expected to be maximized. We also show that the steady state of the oscillator obeys a classical Fokker-Planck equation, but can experience thermomechanical noise squeezing in the presence of a momentum-coupled detector bath and a position-coupled environmental bath. Besides, the full master equation clearly shows that half of the detector back-action is correlated with electron tunneling, indicating a departure from the model of the detector as an effective bath and suggesting that a future calculation valid at lower bias voltage, stronger tunneling and/or stronger coupling might reveal interesting quantum effects in the oscillator dynamics. In the second part of the thesis, we study the subsystem dynamics and thermalization of an oscillator-spin star model, where a nanomechanical resonator is coupled to a few two-level systems (TLS's). We use a fourth-order Runge-Kutta numerical algorithm to integrate the Schrodinger equation for the system and obtain our results. We find that the oscillator reaches a Boltzmann steady state when the TLS bath is initially in a thermal state at a temperature higher than the oscillator phonon energy. This occurs in both chaotic and integrable systems, and despite the small number of spins (only six) and the lack of couplings between them. At the same time, pure initial states do not thermalize well in our system, indicating that mixed state thermalization stems from the thermal nature of the initial bath state. Under the influence of a thermal TLS bath, oscillator Fock states decay in an approximately exponential manner, but there is also a concave-down trend at very early times, possibly indicative of Gaussian decay. In the case of initial Fock state superpositions, the diagonal density matrix element behaves very similarly to single initial Fock states, while the off-diagonal matrix element decays sinusoidally with an exponentially decreasing amplitude. The off-diagonal decay time is much smaller then the diagonal one, indicating that superposition states decohere much faster than they decay. Both decay times decrease with increasing Fock state number, but more slowly than the 1/n dependence seen in the presence of an external ohmic bath.

Decay of homogeneous turbulence from a specified state

NASA Technical Reports Server (NTRS)

Deissler, R. G.

1972-01-01

The homogeneous turbulence problem is formulated by first specifying the multipoint velocity correlations or their spectral equivalents at an initial time. Those quantities, together with the correlation or spectral equations, are then used to calculate initial time derivatives of correlations or spectra. The derivatives in turn are used in time series to calculate the evolution of turbulence quantities with time. When the problem is treated in this way, the correlation equations are closed by the initial specification of the turbulence and no closure assumption is necessary. An exponential series which is an iterative solution of the Navier stokes equations gave much better results than a Taylor power series when used with the limited available initial data. In general, the agreement between theory and experiment was good.

Plasma fluctuations as Markovian noise.

PubMed

Li, B; Hazeltine, R D; Gentle, K W

2007-12-01

Noise theory is used to study the correlations of stationary Markovian fluctuations that are homogeneous and isotropic in space. The relaxation of the fluctuations is modeled by the diffusion equation. The spatial correlations of random fluctuations are modeled by the exponential decay. Based on these models, the temporal correlations of random fluctuations, such as the correlation function and the power spectrum, are calculated. We find that the diffusion process can give rise to the decay of the correlation function and a broad frequency spectrum of random fluctuations. We also find that the transport coefficients may be estimated by the correlation length and the correlation time. The theoretical results are compared with the observed plasma density fluctuations from the tokamak and helimak experiments.

Similarity Solutions on Mixed Convection Heat Transfer from a Horizontal Surface Saturated in a Porous Medium with Internal Heat Generation

NASA Astrophysics Data System (ADS)

Ferdows, M.; Liu, D.

2017-02-01

The aim of this work is to study the mixed convection boundary layer flow from a horizontal surface embedded in a porous medium with exponential decaying internal heat generation (IHG). Boundary layer equations are reduced to two ordinary differential equations for the dimensionless stream function and temperature with two parameters: ɛ, the mixed convection parameter, and λ, the exponent of x. This problem is numerically solved with a system of parameters using built-in codes in Maple. The influences of these parameters on velocity and temperature profiles, and the Nusselt number, are thoroughly compared and discussed.

Effects of proliferation on the decay of thermotolerance in Chinese hamster cells.

PubMed

Armour, E P; Li, G C; Hahn, G M

1985-09-01

Development and decay of thermotolerance were observed in Chinese hamster HA-1 cells. The thermotolerance kinetics of exponentially growing and fed plateau-phase cells were compared. Following a 10-min heat exposure at 45 degrees C, cells in both growth states had similar rates of development of tolerance to a subsequent 45-min exposure at 45 degrees C. This thermotolerant state started to decay between 12 and 24 hr after the initial heat exposure. The decay appeared to initiate slightly sooner in the exponentially growing cells when compared to the fed plateau-phase cells. During the decay phase, the rate of thermotolerance decay was similar in the two growth conditions. In other experiments, cells were induced to divide at a slower rate by chronic growth (3 months) in a low concentration of fetal calf serum. Under these low serum conditions cells became more sensitive to heat and the rate of decay of thermotolerance remained the same for exponentially growing cells. Plateau-phase cells were also more sensitive, but thermotolerance decayed more rapidly in these cells. Although dramatic cell cycle perturbations were seen in the exponentially growing cells, these changes appeared not to be related to thermotolerance kinetics.

Initial-boundary value problem to 2D Boussinesq equations for MHD convection with stratification effects

NASA Astrophysics Data System (ADS)

Bian, Dongfen; Liu, Jitao

2017-12-01

This paper is concerned with the initial-boundary value problem to 2D magnetohydrodynamics-Boussinesq system with the temperature-dependent viscosity, thermal diffusivity and electrical conductivity. First, we establish the global weak solutions under the minimal initial assumption. Then by imposing higher regularity assumption on the initial data, we obtain the global strong solution with uniqueness. Moreover, the exponential decay rates of weak solutions and strong solution are obtained respectively.

How exponential are FREDs?

NASA Astrophysics Data System (ADS)

Schaefer, Bradley E.; Dyson, Samuel E.

1996-08-01

A common Gamma-Ray Burst-light curve shape is the ``FRED'' or ``fast-rise exponential-decay.'' But how exponential is the tail? Are they merely decaying with some smoothly decreasing decline rate, or is the functional form an exponential to within the uncertainties? If the shape really is an exponential, then it would be reasonable to assign some physically significant time scale to the burst. That is, there would have to be some specific mechanism that produces the characteristic decay profile. So if an exponential is found, then we will know that the decay light curve profile is governed by one mechanism (at least for simple FREDs) instead of by complex/multiple mechanisms. As such, a specific number amenable to theory can be derived for each FRED. We report on the fitting of exponentials (and two other shapes) to the tails of ten bright BATSE bursts. The BATSE trigger numbers are 105, 257, 451, 907, 1406, 1578, 1883, 1885, 1989, and 2193. Our technique was to perform a least square fit to the tail from some time after peak until the light curve approaches background. We find that most FREDs are not exponentials, although a few come close. But since the other candidate shapes come close just as often, we conclude that the FREDs are misnamed.

Geomorphic effectiveness of long profile shape and role of inherent geological controls, Ganga River Basin, India

NASA Astrophysics Data System (ADS)

Sonam, Sonam; Jain, Vikrant

2017-04-01

River long profile is one of the fundamental geomorphic parameters which provides a platform to study interaction of geological and geomorphic processes at different time scales. Long profile shape is governed by geological processes at 10 ^ 5 - 10 ^ 6 years' time scale and it controls the modern day (10 ^ 0 - 10 ^ 1 years' time scale) fluvial processes by controlling the spatial variability of channel slope. Identification of an appropriate model for river long profile may provide a tool to analyse the quantitative relationship between basin geology, profile shape and its geomorphic effectiveness. A systematic analysis of long profiles has been carried for the Himalayan tributaries of the Ganga River basin. Long profile shape and stream power distribution pattern is derived using SRTM DEM data (90 m spatial resolution). Peak discharge data from 34 stations is used for hydrological analysis. Lithological variability and major thrusts are marked along the river long profile. The best fit of long profile is analysed for power, logarithmic and exponential function. Second order exponential function provides the best representation of long profiles. The second order exponential equation is Z = K1*exp(-β1*L) + K2*exp(-β2*L), where Z is elevation of channel long profile, L is the length, K and β are coefficients of the exponential function. K1 and K2 are the proportion of elevation change of the long profile represented by β1 (fast) and β2 (slow) decay coefficients of the river long profile. Different values of coefficients express the variability in long profile shapes and is related with the litho-tectonic variability of the study area. Channel slope of long profile is estimated taking the derivative of exponential function. Stream power distribution pattern along long profile is estimated by superimposing the discharge and long profile slope. Sensitivity analysis of stream power distribution with decay coefficients of the second order exponential equation is evaluated for a range of coefficient values. Our analysis suggests that the amplitude of stream power peak value is dependent on K1, the proportion of elevation change coming under the fast decay exponent and the location of stream power peak is dependent of the long profile decay coefficient (β1). Different long profile shapes owing to litho-tectonic variability across the Himalayas are responsible for spatial variability of stream power distribution pattern. Most of the stream power peaks lie in the Higher Himalaya. In general, eastern rivers have higher stream power in hinterland area and low stream power in the alluvial plains. This is responsible for, 1) higher erosion rate and sediment supply in hinterland of eastern rivers, 2) the incised and stable nature of channels in the western alluvial plains and 3) aggrading channels with dynamic nature in the eastern alluvial plains. Our study shows that the spatial variability of litho-units defines the coefficients of long profile function which in turn controls the position and magnitude of stream power maxima and hence the geomorphic variability in a fluvial system.

Vibrations of an Euler-Bernoulli beam with hysteretic damping arising from dispersed frictional microcracks

NASA Astrophysics Data System (ADS)

Maiti, Soumyabrata; Bandyopadhyay, Ritwik; Chatterjee, Anindya

2018-01-01

We study free and harmonically forced vibrations of an Euler-Bernoulli beam with rate-independent hysteretic dissipation. The dissipation follows a model proposed elsewhere for materials with randomly dispersed frictional microcracks. The virtual work of distributed dissipative moments is approximated using Gaussian quadrature, yielding a few discrete internal hysteretic states. Lagrange's equations are obtained for the modal coordinates. Differential equations for the modal coordinates and internal states are integrated together. Free vibrations decay exponentially when a single mode dominates. With multiple modes active, higher modes initially decay rapidly while lower modes decay relatively slowly. Subsequently, lower modes show their own characteristic modal damping, while small amplitude higher modes show more erratic decay. Large dissipation, for the adopted model, leads mathematically to fast and damped oscillations in the limit, unlike viscously overdamped systems. Next, harmonically forced, lightly damped responses of the beam are studied using both a slow frequency sweep and a shooting-method based search for periodic solutions along with numerical continuation. Shooting method and frequency sweep results match for large ranges of frequency. The shooting method struggles near resonances, where internal states collapse into lower dimensional behavior and Newton-Raphson iterations fail. Near the primary resonances, simple numerically-aided harmonic balance gives excellent results. Insights are also obtained into the harmonic content of secondary resonances.

The shock waves in decaying supersonic turbulence

NASA Astrophysics Data System (ADS)

Smith, M. D.; Mac Low, M.-M.; Zuev, J. M.

2000-04-01

We here analyse numerical simulations of supersonic, hypersonic and magnetohydrodynamic turbulence that is free to decay. Our goals are to understand the dynamics of the decay and the characteristic properties of the shock waves produced. This will be useful for interpretation of observations of both motions in molecular clouds and sources of non-thermal radiation. We find that decaying hypersonic turbulence possesses an exponential tail of fast shocks and an exponential decay in time, i.e. the number of shocks is proportional to t exp (-ktv) for shock velocity jump v and mean initial wavenumber k. In contrast to the velocity gradients, the velocity Probability Distribution Function remains Gaussian with a more complex decay law. The energy is dissipated not by fast shocks but by a large number of low Mach number shocks. The power loss peaks near a low-speed turn-over in an exponential distribution. An analytical extension of the mapping closure technique is able to predict the basic decay features. Our analytic description of the distribution of shock strengths should prove useful for direct modeling of observable emission. We note that an exponential distribution of shocks such as we find will, in general, generate very low excitation shock signatures.

Statistical properties and correlation functions for drift waves

NASA Technical Reports Server (NTRS)

Horton, W.

1986-01-01

The dissipative one-field drift wave equation is solved using the pseudospectral method to generate steady-state fluctuations. The fluctuations are analyzed in terms of space-time correlation functions and modal probability distributions. Nearly Gaussian statistics and exponential decay of the two-time correlation functions occur in the presence of electron dissipation, while in the absence of electron dissipation long-lived vortical structures occur. Formulas from renormalized, Markovianized statistical turbulence theory are given in a local approximation to interpret the dissipative turbulence.

Exponential Decay of Reconstruction Error from Binary Measurements of Sparse Signals

DTIC Science & Technology

2014-08-01

that the required condition of Corollary 9, namely q ≥ Cδ−4s̃ log(n/s̃), is still satisfied. The result follows from massaging the equations, as...study of the relationship of heart attacks to various factors may test whether certain subjects have heart attacks in a short window of time and other...subjects have heart attacks in a long window of time. The main message of this paper is that by carefully choosing this threshold the accuracy of

Deformation dependence of proton decay rates and angular distributions in a time-dependent approach

NASA Astrophysics Data System (ADS)

Carjan, N.; Talou, P.; Strottman, D.

1998-12-01

A new, time-dependent, approach to proton decay from axially symmetric deformed nuclei is presented. The two-dimensional time-dependent Schrödinger equation for the interaction between the emitted proton and the rest of the nucleus is solved numerically for well defined initial quasi-stationary proton states. Applied to the hypothetical proton emission from excited states in deformed nuclei of 208Pb, this approach shows that the problem cannot be reduced to one dimension. There are in general more than one directions of emission with wide distributions around them, determined mainly by the quantum numbers of the initial wave function rather than by the potential landscape. The distribution of the "residual" angular momentum and its variation in time play a major role in the determination of the decay rate. In a couple of cases, no exponential decay was found during the calculated time evolution (2×10-21 sec) although more than half of the wave function escaped during that time.

Collective coherence in nearest neighbor coupled metamaterials: A metasurface ruler equation

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

Xu, Ningning; Zhang, Weili, E-mail: weili.zhang@okstate.edu; Singh, Ranjan, E-mail: ranjans@ntu.edu.sg

The collective coherent interactions in a meta-atom lattice are the key to myriad applications and functionalities offered by metasurfaces. We demonstrate a collective coherent response of the nearest neighbor coupled split-ring resonators whose resonance shift decays exponentially in the strong near-field coupled regime. This occurs due to the dominant magnetic coupling between the nearest neighbors which leads to the decay of the electromagnetic near fields. Based on the size scaling behavior of the different periodicity metasurfaces, we identified a collective coherent metasurface ruler equation. From the coherent behavior, we also show that the near-field coupling in a metasurface lattice existsmore » even when the periodicity exceeds the resonator size. The identification of a universal coherence in metasurfaces and their scaling behavior would enable the design of novel metadevices whose spectral tuning response based on near-field effects could be calibrated across microwave, terahertz, infrared, and the optical parts of the electromagnetic spectrum.« less

Motion of a Rigid Body in a Special Lorentz Gas: Loss of Memory Effect

NASA Astrophysics Data System (ADS)

Koike, Kai

2018-06-01

Linear motion of a rigid body in a special kind of Lorentz gas is mathematically analyzed. The rigid body moves against gas drag according to Newton's equation. The gas model is a special Lorentz gas consisting of gas molecules and background obstacles, which was introduced in Tsuji and Aoki (J Stat Phys 146:620-645, 2012). The specular boundary condition is imposed on the resulting kinetic equation. This study complements the numerical study by Tsuji and Aoki cited above—although the setting in this paper is slightly different from theirs, qualitatively the same asymptotic behavior is proved: The velocity V(t) of the rigid body decays exponentially if the obstacles undergo thermal motion; if the obstacles are motionless, then the velocity V(t) decays algebraically with a rate t^{- 5} independent of the spatial dimension. This demonstrates the idea that interaction of the molecules with the background obstacles destroys the memory effect due to recollision.

Diffusive processes in a stochastic magnetic field

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

Wang, H.; Vlad, M.; Vanden Eijnden, E.

1995-05-01

The statistical representation of a fluctuating (stochastic) magnetic field configuration is studied in detail. The Eulerian correlation functions of the magnetic field are determined, taking into account all geometrical constraints: these objects form a nondiagonal matrix. The Lagrangian correlations, within the reasonable Corrsin approximation, are reduced to a single scalar function, determined by an integral equation. The mean square perpendicular deviation of a geometrical point moving along a perturbed field line is determined by a nonlinear second-order differential equation. The separation of neighboring field lines in a stochastic magnetic field is studied. We find exponentiation lengths of both signs describing,more » in particular, a decay (on the average) of any initial anisotropy. The vanishing sum of these exponentiation lengths ensures the existence of an invariant which was overlooked in previous works. Next, the separation of a particle`s trajectory from the magnetic field line to which it was initially attached is studied by a similar method. Here too an initial phase of exponential separation appears. Assuming the existence of a final diffusive phase, anomalous diffusion coefficients are found for both weakly and strongly collisional limits. The latter is identical to the well known Rechester-Rosenbluth coefficient, which is obtained here by a more quantitative (though not entirely deductive) treatment than in earlier works.« less

The Analysis of Fluorescence Decay by a Method of Moments

PubMed Central

Isenberg, Irvin; Dyson, Robert D.

1969-01-01

The fluorescence decay of the excited state of most biopolymers, and biopolymer conjugates and complexes, is not, in general, a simple exponential. The method of moments is used to establish a means of analyzing such multi-exponential decays. The method is tested by the use of computer simulated data, assuming that the limiting error is determined by noise generated by a pseudorandom number generator. Multi-exponential systems with relatively closely spaced decay constants may be successfully analyzed. The analyses show the requirements, in terms of precision, that data must meet. The results may be used both as an aid in the design of equipment and in the analysis of data subsequently obtained. PMID:5353139

A reformulation of the coupled perturbed self-consistent field equations entirely within a local atomic orbital density matrix-based scheme

NASA Astrophysics Data System (ADS)

Ochsenfeld, Christian; Head-Gordon, Martin

1997-05-01

To exploit the exponential decay found in numerical studies for the density matrix and its derivative with respect to nuclear displacements, we reformulate the coupled perturbed self-consistent field (CPSCF) equations and a quadratically convergent SCF (QCSCF) method for Hartree-Fock and density functional theory within a local density matrix-based scheme. Our D-CPSCF (density matrix-based CPSCF) and D-QCSCF schemes open the way for exploiting sparsity and to achieve asymptotically linear scaling of computational complexity with molecular size ( M), in case of D-CPSCF for all O( M) derivative densities. Furthermore, these methods are even for small molecules strongly competitive to conventional algorithms.

Metal-induced gap states in ferroelectric capacitors and its relationship with complex band structures

NASA Astrophysics Data System (ADS)

Junquera, Javier; Aguado-Puente, Pablo

2013-03-01

At metal-isulator interfaces, the metallic wave functions with an energy eigenvalue within the band gap decay exponentially inside the dielectric (metal-induced gap states, MIGS). These MIGS can be actually regarded as Bloch functions with an associated complex wave vector. Usually only real values of the wave vectors are discussed in text books, since infinite periodicity is assumed and, in that situation, wave functions growing exponentially in any direction would not be physically valid. However, localized wave functions with an exponential decay are indeed perfectly valid solution of the Schrodinger equation in the presence of defects, surfaces or interfaces. For this reason, properties of MIGS have been typically discussed in terms of the complex band structure of bulk materials. The probable dependence on the interface particulars has been rarely taken into account explicitly due to the difficulties to include them into the model or simulations. We aim to characterize from first-principles simulations the MIGS in realistic ferroelectric capacitors and their connection with the complex band structure of the ferroelectric material. We emphasize the influence of the real interface beyond the complex band structure of bulk materials. Financial support provided by MICINN Grant FIS2009-12721-C04-02, and by the European Union Grant No. CP-FP 228989-2 ``OxIDes''. Computer resources provided by the RES.

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

Eliazar, Iddo, E-mail: eliazar@post.tau.ac.il

The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their ‘public relations’ for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process: a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of thismore » object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford’s law, and 1/f noise. - Highlights: • Harmonic statistics are described and reviewed in detail. • Connections to various statistical laws are established. • Connections to perturbation, renormalization and dynamics are established.« less

Magnesium flux during continuous venovenous haemodiafiltration with heparin and citrate anticoagulation.

PubMed

Brain, Matthew; Anderson, Mike; Parkes, Scott; Fowler, Peter

2012-12-01

To describe magnesium flux and serum concentrations in ICU patients receiving continuous venovenous haemodiafiltration (CVVHDF). Samples were collected from 22 CVVHDF circuits using citrate anticoagulation solutions (Prismocitrate 10/2 and Prism0cal) and from 26 circuits using Hemosol B0 and heparin anticoagulation. CVVHDF prescription, magnesium supplementation and anticoagulation choice was by the treating intensivist. We analysed 334 sample sets consisting of arterial, prefilter and postfilter blood and effluent. Magnesium loss was calculated from an equation for conservation of mass, and arterial magnesium concentration was described by an equation for exponential decay. Using flow rates typical of adults receiving CVVHDF, we determined a median half-life for arterial magnesium concentration to decay to a new steady state of 4.73 hours (interquartile range [IQR], 3.73-7.32 hours). Median arterial magnesium concentration was 0.88mmol/L (IQR, 0.83-0.97mmol/L) in the heparin group and 0.79mmol/L (IQR, 0.69-0.91mmol/L) in the citrate group. Arterial magnesium concentrations fell below the reference range regularly in the citrate group and, when low, there was magnesium flux from dialysate to patient. Magnesium loss was greater in patients receiving citrate. Exponential decline in magnesium concentrations was sufficiently rapid that subtherapeutic serum magnesium concentrations may occur well before detection when once-daily sampling was used. Measurements should be interpreted with regard to timing of magnesium infusions. We suggest that continuous renal replacement therapy fluids with higher magnesium concentrations be introduced in the critical care setting.

On the origin of non-exponential fluorescence decays in enzyme-ligand complex

NASA Astrophysics Data System (ADS)

Wlodarczyk, Jakub; Kierdaszuk, Borys

2004-05-01

Complex fluorescence decays have usually been analyzed with the aid of a multi-exponential model, but interpretation of the individual exponential terms has not been adequately characterized. In such cases the intensity decays were also analyzed in terms of the continuous lifetime distribution as a consequence of an interaction of fluorophore with environment, conformational heterogeneity or their dynamical nature. We show that non-exponential fluorescence decay of the enzyme-ligand complexes may results from time dependent energy transport. The latter, to our opinion, may be accounted for by electron transport from the protein tyrosines to their neighbor residues. We introduce the time-dependent hopping rate in the form v(t)~(a+bt)-1. This in turn leads to the luminescence decay function in the form I(t)=Ioexp(-t/τ1)(1+lt/γτ2)-γ. Such a decay function provides good fits to highly complex fluorescence decays. The power-like tail implies the time hierarchy in migration energy process due to the hierarchical energy-level structure. Moreover, such a power-like term is a manifestation of so called Tsallis nonextensive statistic and is suitable for description of the systems with long-range interactions, memory effect as well as with fluctuations of characteristic lifetime of fluorescence. The proposed decay function was applied in analysis of fluorescence decays of tyrosine protein, i.e. the enzyme purine nucleoside phosphorylase from E. coli in a complex with formycin A (an inhibitor) and orthophosphate (a co-substrate).

Statistical assessment of bi-exponential diffusion weighted imaging signal characteristics induced by intravoxel incoherent motion in malignant breast tumors

PubMed Central

Wong, Oi Lei; Lo, Gladys G.; Chan, Helen H. L.; Wong, Ting Ting; Cheung, Polly S. Y.

2016-01-01

Background The purpose of this study is to statistically assess whether bi-exponential intravoxel incoherent motion (IVIM) model better characterizes diffusion weighted imaging (DWI) signal of malignant breast tumor than mono-exponential Gaussian diffusion model. Methods 3 T DWI data of 29 malignant breast tumors were retrospectively included. Linear least-square mono-exponential fitting and segmented least-square bi-exponential fitting were used for apparent diffusion coefficient (ADC) and IVIM parameter quantification, respectively. F-test and Akaike Information Criterion (AIC) were used to statistically assess the preference of mono-exponential and bi-exponential model using region-of-interests (ROI)-averaged and voxel-wise analysis. Results For ROI-averaged analysis, 15 tumors were significantly better fitted by bi-exponential function and 14 tumors exhibited mono-exponential behavior. The calculated ADC, D (true diffusion coefficient) and f (pseudo-diffusion fraction) showed no significant differences between mono-exponential and bi-exponential preferable tumors. Voxel-wise analysis revealed that 27 tumors contained more voxels exhibiting mono-exponential DWI decay while only 2 tumors presented more bi-exponential decay voxels. ADC was consistently and significantly larger than D for both ROI-averaged and voxel-wise analysis. Conclusions Although the presence of IVIM effect in malignant breast tumors could be suggested, statistical assessment shows that bi-exponential fitting does not necessarily better represent the DWI signal decay in breast cancer under clinically typical acquisition protocol and signal-to-noise ratio (SNR). Our study indicates the importance to statistically examine the breast cancer DWI signal characteristics in practice. PMID:27709078

Teaching Exponential Growth and Decay: Examples from Medicine

ERIC Educational Resources Information Center

Hobbie, Russell K.

1973-01-01

A treatment of exponential growth and decay is sketched which does not require knowledge of calculus, and hence, it can be applied to many cases in the biological and medical sciences. Some examples are bacterial growth, sterilization, clearance, and drug absorption. (DF)

Robust Bayesian Fluorescence Lifetime Estimation, Decay Model Selection and Instrument Response Determination for Low-Intensity FLIM Imaging

PubMed Central

Rowley, Mark I.; Coolen, Anthonius C. C.; Vojnovic, Borivoj; Barber, Paul R.

2016-01-01

We present novel Bayesian methods for the analysis of exponential decay data that exploit the evidence carried by every detected decay event and enables robust extension to advanced processing. Our algorithms are presented in the context of fluorescence lifetime imaging microscopy (FLIM) and particular attention has been paid to model the time-domain system (based on time-correlated single photon counting) with unprecedented accuracy. We present estimates of decay parameters for mono- and bi-exponential systems, offering up to a factor of two improvement in accuracy compared to previous popular techniques. Results of the analysis of synthetic and experimental data are presented, and areas where the superior precision of our techniques can be exploited in Förster Resonance Energy Transfer (FRET) experiments are described. Furthermore, we demonstrate two advanced processing methods: decay model selection to choose between differing models such as mono- and bi-exponential, and the simultaneous estimation of instrument and decay parameters. PMID:27355322

Cooperative bi-exponential decay of dye emission coupled via plasmons.

PubMed

Lyvers, David P; Moazzezi, Mojtaba; de Silva, Vashista C; Brown, Dean P; Urbas, Augustine M; Rostovtsev, Yuri V; Drachev, Vladimir P

2018-06-22

Bi-exponential decay of dye fluorescence near the surface of plasmonic metamaterials and core-shell nanoparticles is shown to be an intrinsic property of the coupled system. Indeed, the Dicke, cooperative states involve two groups of transitions: super-radiant, from the most excited to the ground states and sub-radiant, which cannot reach the ground state. The relaxation in the sub-radiant system occurs mainly due to the interaction with the plasmon modes. Our theory shows that the relaxation leads to the population of the sub-radiant states by dephasing the super-radiant Dicke states giving rise to the bi-exponential decay in agreement with the experiments. We use a set of metamaterial samples consisting of gratings of paired silver nanostrips coated with Rh800 dye molecules, having resonances in the same spectral range. The bi-exponential decay is demonstrated for Au\\SiO 2 \\ATTO655 core-shell nanoparticles as well, which persists even when averaging over a broad range of the coupling parameter.

A Time Domain Analysis of Gust-Cascade Interaction Noise

NASA Technical Reports Server (NTRS)

Nallasamy, M.; Hixon, R.; Sawyer, S. D.; Dyson, R. W.

2003-01-01

The gust response of a 2 D cascade is studied by solving the full nonlinear Euler equations employing higher order accurate spatial differencing and time stepping techniques. The solutions exhibit the exponential decay of the two circumferential mode orders of the cutoff blade passing frequency (BPF) tone and propagation of one circumferential mode order at 2BPF, as would be expected for the flow configuration considered. Two frequency excitations indicate that the interaction between the frequencies and the self interaction contribute to the amplitude of the propagating mode.

On the origin of stretched exponential (Kohlrausch) relaxation kinetics in the room temperature luminescence decay of colloidal quantum dots.

PubMed

Bodunov, E N; Antonov, Yu A; Simões Gamboa, A L

2017-03-21

The non-exponential room temperature luminescence decay of colloidal quantum dots is often well described by a stretched exponential function. However, the physical meaning of the parameters of the function is not clear in the majority of cases reported in the literature. In this work, the room temperature stretched exponential luminescence decay of colloidal quantum dots is investigated theoretically in an attempt to identify the underlying physical mechanisms associated with the parameters of the function. Three classes of non-radiative transition processes between the excited and ground states of colloidal quantum dots are discussed: long-range resonance energy transfer, multiphonon relaxation, and contact quenching without diffusion. It is shown that multiphonon relaxation cannot explain a stretched exponential functional form of the luminescence decay while such dynamics of relaxation can be understood in terms of long-range resonance energy transfer to acceptors (molecules, quantum dots, or anharmonic molecular vibrations) in the environment of the quantum dots acting as energy-donors or by contact quenching by acceptors (surface traps or molecules) distributed statistically on the surface of the quantum dots. These non-radiative transition processes are assigned to different ranges of the stretching parameter β.

Finite-temperature effects in helical quantum turbulence

NASA Astrophysics Data System (ADS)

Clark Di Leoni, Patricio; Mininni, Pablo D.; Brachet, Marc E.

2018-04-01

We perform a study of the evolution of helical quantum turbulence at different temperatures by solving numerically the Gross-Pitaevskii and the stochastic Ginzburg-Landau equations, using up to 40963 grid points with a pseudospectral method. We show that for temperatures close to the critical one, the fluid described by these equations can act as a classical viscous flow, with the decay of the incompressible kinetic energy and the helicity becoming exponential. The transition from this behavior to the one observed at zero temperature is smooth as a function of temperature. Moreover, the presence of strong thermal effects can inhibit the development of a proper turbulent cascade. We provide Ansätze for the effective viscosity and friction as a function of the temperature.

Fourier/Chebyshev methods for the incompressible Navier-Stokes equations in finite domains

NASA Technical Reports Server (NTRS)

Corral, Roque; Jimenez, Javier

1992-01-01

A fully spectral numerical scheme for the incompressible Navier-Stokes equations in domains which are infinite or semi-infinite in one dimension. The domain is not mapped, and standard Fourier or Chebyshev expansions can be used. The handling of the infinite domain does not introduce any significant overhead. The scheme assumes that the vorticity in the flow is essentially concentrated in a finite region, which is represented numerically by standard spectral collocation methods. To accomodate the slow exponential decay of the velocities at infinity, extra expansion functions are introduced, which are handled analytically. A detailed error analysis is presented, and two applications to Direct Numerical Simulation of turbulent flows are discussed in relation with the numerical performance of the scheme.

On the Time-Dependent Analysis of Gamow Decay

ERIC Educational Resources Information Center

Durr, Detlef; Grummt, Robert; Kolb, Martin

2011-01-01

Gamow's explanation of the exponential decay law uses complex "eigenvalues" and exponentially growing "eigenfunctions". This raises the question, how Gamow's description fits into the quantum mechanical description of nature, which is based on real eigenvalues and square integrable wavefunctions. Observing that the time evolution of any…

Compressed exponential relaxation in liquid silicon: Universal feature of the crossover from ballistic to diffusive behavior in single-particle dynamics

NASA Astrophysics Data System (ADS)

Morishita, Tetsuya

2012-07-01

We report a first-principles molecular-dynamics study of the relaxation dynamics in liquid silicon (l-Si) over a wide temperature range (1000-2200 K). We find that the intermediate scattering function for l-Si exhibits a compressed exponential decay above 1200 K including the supercooled regime, which is in stark contrast to that for normal "dense" liquids which typically show stretched exponential decay in the supercooled regime. The coexistence of particles having ballistic-like motion and those having diffusive-like motion is demonstrated, which accounts for the compressed exponential decay in l-Si. An attempt to elucidate the crossover from the ballistic to the diffusive regime in the "time-dependent" diffusion coefficient is made and the temperature-independent universal feature of the crossover is disclosed.

Simplifying the Mathematical Treatment of Radioactive Decay

ERIC Educational Resources Information Center

Auty, Geoff

2011-01-01

Derivation of the law of radioactive decay is considered without prior knowledge of calculus or the exponential series. Calculus notation and exponential functions are used because ultimately they cannot be avoided, but they are introduced in a simple way and explained as needed. (Contains 10 figures, 1 box, and 1 table.)

Exploring Exponential Decay Using Limited Resources

ERIC Educational Resources Information Center

DePierro, Ed; Garafalo, Fred; Gordon, Patrick

2018-01-01

Science students need exposure to activities that will help them to become familiar with phenomena exhibiting exponential decay. This paper describes an experiment that allows students to determine the rate of thermal energy loss by a hot object to its surroundings. It requires limited equipment, is safe, and gives reasonable results. Students…

Application of sound and temperature to control boundary-layer transition

NASA Technical Reports Server (NTRS)

Maestrello, Lucio; Parikh, Paresh; Bayliss, A.; Huang, L. S.; Bryant, T. D.

1987-01-01

The growth and decay of a wave packet convecting in a boundary layer over a concave-convex surface and its active control by localized surface heating are studied numerically using direct computations of the Navier-Stokes equations. The resulting sound radiations are computed using linearized Euler equations with the pressure from the Navier-Stokes solution as a time-dependent boundary condition. It is shown that on the concave portion the amplitude of the wave packet increases and its bandwidth broadens while on the convex portion some of the components in the packet are stabilized. The pressure field decays exponentially away from the surface and then algebraically, exhibiting a decay characteristic of acoustic waves in two dimensions. The far-field acoustic behavior exhibits a super-directivity type of behavior with a beaming downstream. Active control by surface heating is shown to reduce the growth of the wave packet but have little effect on acoustic far field behavior for the cases considered. Active control by sound emanating from the surface of an airfoil in the vicinity of the leading edge is experimentally investigated. The purpose is to control the separated region at high angles of attack. The results show that injection of sound at shedding frequency of the flow is effective in an increase of lift and reduction of drag.

W-transform for exponential stability of second order delay differential equations without damping terms.

PubMed

Domoshnitsky, Alexander; Maghakyan, Abraham; Berezansky, Leonid

2017-01-01

In this paper a method for studying stability of the equation [Formula: see text] not including explicitly the first derivative is proposed. We demonstrate that although the corresponding ordinary differential equation [Formula: see text] is not exponentially stable, the delay equation can be exponentially stable.

Analysis and modeling of localized invariant solutions in pipe flow

NASA Astrophysics Data System (ADS)

Ritter, Paul; Zammert, Stefan; Song, Baofang; Eckhardt, Bruno; Avila, Marc

2018-01-01

Turbulent spots surrounded by laminar flow are a landmark of transitional shear flows, but the dependence of their kinematic properties on spatial structure is poorly understood. We here investigate this dependence in pipe flow for Reynolds numbers between 1500 and 5000. We compute spatially localized relative periodic orbits in long pipes and show that their upstream and downstream fronts decay exponentially towards the laminar profile. This allows us to model the fronts by employing the linearized Navier-Stokes equations, and the resulting model yields the spatial decay rate and the front velocity profiles of the periodic orbits as a function of Reynolds number, azimuthal wave number, and propagation speed. In addition, when applied to a localized turbulent puff, the model is shown to accurately approximate the spatial decay rate of its upstream and downstream tails. Our study provides insight into the relationship between the kinematics and spatial structure of localized turbulence and more generally into the physics of localization.

Vortex equations: Singularities, numerical solution, and axisymmetric vortex breakdown

NASA Technical Reports Server (NTRS)

Bossel, H. H.

1972-01-01

A method of weighted residuals for the computation of rotationally symmetric quasi-cylindrical viscous incompressible vortex flow is presented and used to compute a wide variety of vortex flows. The method approximates the axial velocity and circulation profiles by series of exponentials having (N + 1) and N free parameters, respectively. Formal integration results in a set of (2N + 1) ordinary differential equations for the free parameters. The governing equations are shown to have an infinite number of discrete singularities corresponding to critical values of the swirl parameters. The computations point to the controlling influence of the inner core flow on vortex behavior. They also confirm the existence of two particular critical swirl parameter values: one separates vortex flow which decays smoothly from vortex flow which eventually breaks down, and the second is the first singularity of the quasi-cylindrical system, at which point physical vortex breakdown is thought to occur.

Local perturbations perturb—exponentially-locally

NASA Astrophysics Data System (ADS)

De Roeck, W.; Schütz, M.

2015-06-01

We elaborate on the principle that for gapped quantum spin systems with local interaction, "local perturbations [in the Hamiltonian] perturb locally [the groundstate]." This principle was established by Bachmann et al. [Commun. Math. Phys. 309, 835-871 (2012)], relying on the "spectral flow technique" or "quasi-adiabatic continuation" [M. B. Hastings, Phys. Rev. B 69, 104431 (2004)] to obtain locality estimates with sub-exponential decay in the distance to the spatial support of the perturbation. We use ideas of Hamza et al. [J. Math. Phys. 50, 095213 (2009)] to obtain similarly a transformation between gapped eigenvectors and their perturbations that is local with exponential decay. This allows to improve locality bounds on the effect of perturbations on the low lying states in certain gapped models with a unique "bulk ground state" or "topological quantum order." We also give some estimate on the exponential decay of correlations in models with impurities where some relevant correlations decay faster than one would naively infer from the global gap of the system, as one also expects in disordered systems with a localized groundstate.

Time Asymmetric Quantum Mechanics

NASA Astrophysics Data System (ADS)

Bohm, Arno R.; Gadella, Manuel; Kielanowski, Piotr

2011-09-01

The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone-von Neumann theorem, the solutions of the dynamical equations, the Schrödinger equation (1) for states or the Heisenberg equation (6a) for observables are given by a unitary group. Dirac kets require the concept of a RHS (rigged Hilbert space) of Schwartz functions; for this kind of RHS a mathematical theorem also leads to time symmetric group evolution. Scattering theory suggests to distinguish mathematically between states (defined by a preparation apparatus) and observables (defined by a registration apparatus (detector)). If one requires that scattering resonances of width Γ and exponentially decaying states of lifetime τ=h/Γ should be the same physical entities (for which there is sufficient evidence) one is led to a pair of RHS's of Hardy functions and connected with it, to a semigroup time evolution t0≤t<∞, with the puzzling result that there is a quantum mechanical beginning of time, just like the big bang time for the universe, when it was a quantum system. The decay of quasi-stable particles is used to illustrate this quantum mechanical time asymmetry. From the analysis of these processes, we show that the properties of rigged Hilbert spaces of Hardy functions are suitable for a formulation of time asymmetry in quantum mechanics.

Analysis of volumetric response of pituitary adenomas receiving adjuvant CyberKnife stereotactic radiosurgery with the application of an exponential fitting model.

PubMed

Yu, Yi-Lin; Yang, Yun-Ju; Lin, Chin; Hsieh, Chih-Chuan; Li, Chiao-Zhu; Feng, Shao-Wei; Tang, Chi-Tun; Chung, Tzu-Tsao; Ma, Hsin-I; Chen, Yuan-Hao; Ju, Da-Tong; Hueng, Dueng-Yuan

2017-01-01

Tumor control rates of pituitary adenomas (PAs) receiving adjuvant CyberKnife stereotactic radiosurgery (CK SRS) are high. However, there is currently no uniform way to estimate the time course of the disease. The aim of this study was to analyze the volumetric responses of PAs after CK SRS and investigate the application of an exponential decay model in calculating an accurate time course and estimation of the eventual outcome.A retrospective review of 34 patients with PAs who received adjuvant CK SRS between 2006 and 2013 was performed. Tumor volume was calculated using the planimetric method. The percent change in tumor volume and tumor volume rate of change were compared at median 4-, 10-, 20-, and 36-month intervals. Tumor responses were classified as: progression for >15% volume increase, regression for ≤15% decrease, and stabilization for ±15% of the baseline volume at the time of last follow-up. For each patient, the volumetric change versus time was fitted with an exponential model.The overall tumor control rate was 94.1% in the 36-month (range 18-87 months) follow-up period (mean volume change of -43.3%). Volume regression (mean decrease of -50.5%) was demonstrated in 27 (79%) patients, tumor stabilization (mean change of -3.7%) in 5 (15%) patients, and tumor progression (mean increase of 28.1%) in 2 (6%) patients (P = 0.001). Tumors that eventually regressed or stabilized had a temporary volume increase of 1.07% and 41.5% at 4 months after CK SRS, respectively (P = 0.017). The tumor volume estimated using the exponential fitting equation demonstrated high positive correlation with the actual volume calculated by magnetic resonance imaging (MRI) as tested by Pearson correlation coefficient (0.9).Transient progression of PAs post-CK SRS was seen in 62.5% of the patients receiving CK SRS, and it was not predictive of eventual volume regression or progression. A three-point exponential model is of potential predictive value according to relative distribution. An exponential decay model can be used to calculate the time course of tumors that are ultimately controlled.

Unfolding of Ubiquitin Studied by Picosecond Time-Resolved Fluorescence of the Tyrosine Residue

PubMed Central

Noronha, Melinda; Lima, João C.; Bastos, Margarida; Santos, Helena; Maçanita, António L.

2004-01-01

The photophysics of the single tyrosine in bovine ubiquitin (UBQ) was studied by picosecond time-resolved fluorescence spectroscopy, as a function of pH and along thermal and chemical unfolding, with the following results: First, at room temperature (25°C) and below pH 1.5, native UBQ shows single-exponential decays. From pH 2 to 7, triple-exponential decays were observed and the three decay times were attributed to the presence of tyrosine, a tyrosine-carboxylate hydrogen-bonded complex, and excited-state tyrosinate. Second, at pH 1.5, the water-exposed tyrosine of either thermally or chemically unfolded UBQ decays as a sum of two exponentials. The double-exponential decays were interpreted and analyzed in terms of excited-state intramolecular electron transfer from the phenol to the amide moiety, occurring in one of the three rotamers of tyrosine in UBQ. The values of the rate constants indicate the presence of different unfolded states and an increase in the mobility of the tyrosine residue during unfolding. Finally, from the pre-exponential coefficients of the fluorescence decays, the unfolding equilibrium constants (KU) were calculated, as a function of temperature or denaturant concentration. Despite the presence of different unfolded states, both thermal and chemical unfolding data of UBQ could be fitted to a two-state model. The thermodynamic parameters Tm = 54.6°C, ΔHTm = 56.5 kcal/mol, and ΔCp = 890 cal/mol//K, were determined from the unfolding equilibrium constants calculated accordingly, and compared to values obtained by differential scanning calorimetry also under the assumption of a two-state transition, Tm = 57.0°C, ΔHm= 51.4 kcal/mol, and ΔCp = 730 cal/mol//K. PMID:15454455

Crossover from anomalous to normal diffusion in porous media

NASA Astrophysics Data System (ADS)

Aarão Reis, F. D. A.; di Caprio, Dung

2014-06-01

Random walks (RW) of particles adsorbed in the internal walls of porous deposits produced by ballistic-type growth models are studied. The particles start at the external surface of the deposits and enter their pores in order to simulate an external flux of a species towards a porous solid. For short times, the walker concentration decays as a stretched exponential of the depth z, but a crossover to long-time normal diffusion is observed in most samples. The anomalous concentration profile remains at long times in very porous solids if the walker steps are restricted to nearest neighbors and is accompanied with subdiffusion features. These findings are correlated with a decay of the explored area with z. The study of RW of tracer particles left at the internal part of the solid rules out an interpretation by diffusion equations with position-dependent coefficients. A model of RW in a tube of decreasing cross section explains those results by showing long crossovers from an effective subdiffusion regime to an asymptotic normal diffusion. The crossover position and density are analytically calculated for a tube with area decreasing exponentially with z and show good agreement with numerical data. The anomalous decay of the concentration profile is interpreted as a templating effect of the tube shape on the total number of diffusing particles at each depth, while the volumetric concentration in the actually explored porous region may not have significant decay. These results may explain the anomalous diffusion of metal atoms in porous deposits observed in recent works. They also confirm the difficulty in interpreting experimental or computational data on anomalous transport reported in recent works, particularly if only the concentration profiles are measured.

Isaac Newton and the astronomical refraction.

PubMed

Lehn, Waldemar H

2008-12-01

In a short interval toward the end of 1694, Isaac Newton developed two mathematical models for the theory of the astronomical refraction and calculated two refraction tables, but did not publish his theory. Much effort has been expended, starting with Biot in 1836, in the attempt to identify the methods and equations that Newton used. In contrast to previous work, a closed form solution is identified for the refraction integral that reproduces the table for his first model (in which density decays linearly with elevation). The parameters of his second model, which includes the exponential variation of pressure in an isothermal atmosphere, have also been identified by reproducing his results. The implication is clear that in each case Newton had derived exactly the correct equations for the astronomical refraction; furthermore, he was the first to do so.

Nonequilibrium Phase Transition in a Periodically Driven XY Spin Chain

NASA Astrophysics Data System (ADS)

Prosen, Tomaž; Ilievski, Enej

2011-08-01

We present a general formulation of Floquet states of periodically time-dependent open Markovian quasifree fermionic many-body systems in terms of a discrete Lyapunov equation. Illustrating the technique, we analyze periodically kicked XY spin-(1)/(2) chain which is coupled to a pair of Lindblad reservoirs at its ends. A complex phase diagram is reported with reentrant phases of long range and exponentially decaying spin-spin correlations as some of the system’s parameters are varied. The structure of phase diagram is reproduced in terms of counting nontrivial stationary points of Floquet quasiparticle dispersion relation.

Exponentially decaying interaction potential of cavity solitons

NASA Astrophysics Data System (ADS)

Anbardan, Shayesteh Rahmani; Rimoldi, Cristina; Kheradmand, Reza; Tissoni, Giovanna; Prati, Franco

2018-03-01

We analyze the interaction of two cavity solitons in an optically injected vertical cavity surface emitting laser above threshold. We show that they experience an attractive force even when their distance is much larger than their diameter, and eventually they merge. Since the merging time depends exponentially on the initial distance, we suggest that the attraction could be associated with an exponentially decaying interaction potential, similarly to what is found for hydrophobic materials. We also show that the merging time is simply related to the characteristic times of the laser, photon lifetime, and carrier lifetime.

Dissipative particle dynamics study of velocity autocorrelation function and self-diffusion coefficient in terms of interaction potential strength

NASA Astrophysics Data System (ADS)

Zohravi, Elnaz; Shirani, Ebrahim; Pishevar, Ahmadreza; Karimpour, Hossein

2018-07-01

This research focuses on numerically investigating the self-diffusion coefficient and velocity autocorrelation function (VACF) of a dissipative particle dynamics (DPD) fluid as a function of the conservative interaction strength. Analytic solutions to VACF and self-diffusion coefficients in DPD were obtained by many researchers in some restricted cases including ideal gases, without the account of conservative force. As departure from the ideal gas conditions are accentuated with increasing the relative proportion of conservative force, it is anticipated that the VACF should gradually deviate from its normally expected exponentially decay. This trend is confirmed through numerical simulations and an expression in terms of the conservative force parameter, density and temperature is proposed for the self-diffusion coefficient. As it concerned the VACF, the equivalent Langevin equation describing Brownian motion of particles with a harmonic potential is adapted to the problem and reveals an exponentially decaying oscillatory pattern influenced by the conservative force parameter, dissipative parameter and temperature. Although the proposed model for obtaining the self-diffusion coefficient with consideration of the conservative force could not be verified due to computational complexities, nonetheless the Arrhenius dependency of the self-diffusion coefficient to temperature and pressure permits to certify our model over a definite range of DPD parameters.

Autoregressive processes with exponentially decaying probability distribution functions: applications to daily variations of a stock market index.

PubMed

Porto, Markus; Roman, H Eduardo

2002-04-01

We consider autoregressive conditional heteroskedasticity (ARCH) processes in which the variance sigma(2)(y) depends linearly on the absolute value of the random variable y as sigma(2)(y) = a+b absolute value of y. While for the standard model, where sigma(2)(y) = a + b y(2), the corresponding probability distribution function (PDF) P(y) decays as a power law for absolute value of y-->infinity, in the linear case it decays exponentially as P(y) approximately exp(-alpha absolute value of y), with alpha = 2/b. We extend these results to the more general case sigma(2)(y) = a+b absolute value of y(q), with 0 < q < 2. We find stretched exponential decay for 1 < q < 2 and stretched Gaussian behavior for 0 < q < 1. As an application, we consider the case q=1 as our starting scheme for modeling the PDF of daily (logarithmic) variations in the Dow Jones stock market index. When the history of the ARCH process is taken into account, the resulting PDF becomes a stretched exponential even for q = 1, with a stretched exponent beta = 2/3, in a much better agreement with the empirical data.

Escape time, relaxation, and sticky states of a softened Henon-Heiles model: Low-frequency vibrational mode effects and glass relaxation

NASA Astrophysics Data System (ADS)

Toledo-Marín, J. Quetzalcóatl; Naumis, Gerardo G.

2018-04-01

Here we study the relaxation of a chain consisting of three masses joined by nonlinear springs and periodic conditions when the stiffness is weakened. This system, when expressed in their normal coordinates, yields a softened Henon-Heiles system. By reducing the stiffness of one low-frequency vibrational mode, a faster relaxation is enabled. This is due to a reduction of the energy barrier heights along the softened normal mode as well as for a widening of the opening channels of the energy landscape in configurational space. The relaxation is for the most part exponential, and can be explained by a simple flux equation. Yet, for some initial conditions the relaxation follows as a power law, and in many cases there is a regime change from exponential to power-law decay. We pinpoint the initial conditions for the power-law decay, finding two regions of sticky states. For such states, quasiperiodic orbits are found since almost for all components of the initial momentum orientation, the system is trapped inside two pockets of configurational space. The softened Henon-Heiles model presented here is intended as the simplest model in order to understand the interplay of rigidity, nonlinear interactions and relaxation for nonequilibrium systems such as glass-forming melts or soft matter. Our softened system can be applied to model β relaxation in glasses and suggest that local reorientational jumps can have an exponential and a nonexponential contribution for relaxation, the latter due to asymmetric molecules sticking in cages for certain orientations.

Memory behaviors of entropy production rates in heat conduction

NASA Astrophysics Data System (ADS)

Li, Shu-Nan; Cao, Bing-Yang

2018-02-01

Based on the relaxation time approximation and first-order expansion, memory behaviors in heat conduction are found between the macroscopic and Boltzmann-Gibbs-Shannon (BGS) entropy production rates with exponentially decaying memory kernels. In the frameworks of classical irreversible thermodynamics (CIT) and BGS statistical mechanics, the memory dependency on the integrated history is unidirectional, while for the extended irreversible thermodynamics (EIT) and BGS entropy production rates, the memory dependences are bidirectional and coexist with the linear terms. When macroscopic and microscopic relaxation times satisfy a specific relationship, the entropic memory dependences will be eliminated. There also exist initial effects in entropic memory behaviors, which decay exponentially. The second-order term are also discussed, which can be understood as the global non-equilibrium degree. The effects of the second-order term are consisted of three parts: memory dependency, initial value and linear term. The corresponding memory kernels are still exponential and the initial effects of the global non-equilibrium degree also decay exponentially.

A Nonequilibrium Rate Formula for Collective Motions of Complex Molecular Systems

NASA Astrophysics Data System (ADS)

Yanao, Tomohiro; Koon, Wang Sang; Marsden, Jerrold E.

2010-09-01

We propose a compact reaction rate formula that accounts for a non-equilibrium distribution of residence times of complex molecules, based on a detailed study of the coarse-grained phase space of a reaction coordinate. We take the structural transition dynamics of a six-atom Morse cluster between two isomers as a prototype of multi-dimensional molecular reactions. Residence time distribution of one of the isomers shows an exponential decay, while that of the other isomer deviates largely from the exponential form and has multiple peaks. Our rate formula explains such equilibrium and non-equilibrium distributions of residence times in terms of the rates of diffusions of energy and the phase of the oscillations of the reaction coordinate. Rapid diffusions of energy and the phase generally give rise to the exponential decay of residence time distribution, while slow diffusions give rise to a non-exponential decay with multiple peaks. We finally make a conjecture about a general relationship between the rates of the diffusions and the symmetry of molecular mass distributions.

Dual exponential polynomials and linear differential equations

NASA Astrophysics Data System (ADS)

Wen, Zhi-Tao; Gundersen, Gary G.; Heittokangas, Janne

2018-01-01

We study linear differential equations with exponential polynomial coefficients, where exactly one coefficient is of order greater than all the others. The main result shows that a nontrivial exponential polynomial solution of such an equation has a certain dual relationship with the maximum order coefficient. Several examples illustrate our results and exhibit possibilities that can occur.

Development and Retrospective Clinical Assessment of a Patient-Specific Closed-Form Integro-Differential Equation Model of Plasma Dilution.

PubMed

Atlas, Glen; Li, John K-J; Amin, Shawn; Hahn, Robert G

2017-01-01

A closed-form integro-differential equation (IDE) model of plasma dilution (PD) has been derived which represents both the intravenous (IV) infusion of crystalloid and the postinfusion period. Specifically, PD is mathematically represented using a combination of constant ratio, differential, and integral components. Furthermore, this model has successfully been applied to preexisting data, from a prior human study, in which crystalloid was infused for a period of 30 minutes at the beginning of thyroid surgery. Using Euler's formula and a Laplace transform solution to the IDE, patients could be divided into two distinct groups based on their response to PD during the infusion period. Explicitly, Group 1 patients had an infusion-based PD response which was modeled using an exponentially decaying hyperbolic sine function, whereas Group 2 patients had an infusion-based PD response which was modeled using an exponentially decaying trigonometric sine function. Both Group 1 and Group 2 patients had postinfusion PD responses which were modeled using the same combination of hyperbolic sine and hyperbolic cosine functions. Statistically significant differences, between Groups 1 and 2, were noted with respect to the area under their PD curves during both the infusion and postinfusion periods. Specifically, Group 2 patients exhibited a response to PD which was most likely consistent with a preoperative hypovolemia. Overall, this IDE model of PD appears to be highly "adaptable" and successfully fits clinically-obtained human data on a patient-specific basis, during both the infusion and postinfusion periods. In addition, patient-specific IDE modeling of PD may be a useful adjunct in perioperative fluid management and in assessing clinical volume kinetics, of crystalloid solutions, in real time.

Development and Retrospective Clinical Assessment of a Patient-Specific Closed-Form Integro-Differential Equation Model of Plasma Dilution

PubMed Central

Atlas, Glen; Li, John K-J; Amin, Shawn; Hahn, Robert G

2017-01-01

A closed-form integro-differential equation (IDE) model of plasma dilution (PD) has been derived which represents both the intravenous (IV) infusion of crystalloid and the postinfusion period. Specifically, PD is mathematically represented using a combination of constant ratio, differential, and integral components. Furthermore, this model has successfully been applied to preexisting data, from a prior human study, in which crystalloid was infused for a period of 30 minutes at the beginning of thyroid surgery. Using Euler’s formula and a Laplace transform solution to the IDE, patients could be divided into two distinct groups based on their response to PD during the infusion period. Explicitly, Group 1 patients had an infusion-based PD response which was modeled using an exponentially decaying hyperbolic sine function, whereas Group 2 patients had an infusion-based PD response which was modeled using an exponentially decaying trigonometric sine function. Both Group 1 and Group 2 patients had postinfusion PD responses which were modeled using the same combination of hyperbolic sine and hyperbolic cosine functions. Statistically significant differences, between Groups 1 and 2, were noted with respect to the area under their PD curves during both the infusion and postinfusion periods. Specifically, Group 2 patients exhibited a response to PD which was most likely consistent with a preoperative hypovolemia. Overall, this IDE model of PD appears to be highly “adaptable” and successfully fits clinically-obtained human data on a patient-specific basis, during both the infusion and postinfusion periods. In addition, patient-specific IDE modeling of PD may be a useful adjunct in perioperative fluid management and in assessing clinical volume kinetics, of crystalloid solutions, in real time. PMID:29123436

Analytically-derived sensitivities in one-dimensional models of solute transport in porous media

USGS Publications Warehouse

Knopman, D.S.

1987-01-01

Analytically-derived sensitivities are presented for parameters in one-dimensional models of solute transport in porous media. Sensitivities were derived by direct differentiation of closed form solutions for each of the odel, and by a time integral method for two of the models. Models are based on the advection-dispersion equation and include adsorption and first-order chemical decay. Boundary conditions considered are: a constant step input of solute, constant flux input of solute, and exponentially decaying input of solute at the upstream boundary. A zero flux is assumed at the downstream boundary. Initial conditions include a constant and spatially varying distribution of solute. One model simulates the mixing of solute in an observation well from individual layers in a multilayer aquifer system. Computer programs produce output files compatible with graphics software in which sensitivities are plotted as a function of either time or space. (USGS)

Forces on nuclei moving on autoionizing molecular potential energy surfaces.

PubMed

Moiseyev, Nimrod

2017-01-14

Autoionization of molecular systems occurs in diatomic molecules and in small biochemical systems. Quantum chemistry packages enable calculation of complex potential energy surfaces (CPESs). The imaginary part of the CPES is associated with the autoionization decay rate, which is a function of the molecular structure. Molecular dynamics simulations, within the framework of the Born-Oppenheimer approximation, require the definition of a force field. The ability to calculate the forces on the nuclei in bio-systems when autoionization takes place seems to rely on an understanding of radiative damages in RNA and DNA arising from the release of slow moving electrons which have long de Broglie wavelengths. This work addresses calculation of the real forces on the nuclei moving on the CPES. By using the transformation of the time-dependent Schrödinger equation, previously used by Madelung, we proved that the classical forces on nuclei moving on the CPES correlated with the gradient of the real part of the CPES. It was proved that the force on the nuclei of the metastable molecules is time independent although the probability to detect metastable molecules exponentially decays. The classical force is obtained from the transformed Schrödinger equation when ℏ=0 and the Schrödinger equation is reduced to the classical (Newtonian) equations of motion. The forces on the nuclei regardless on what potential energy surface they move (parent CPES or product real PESs) vary in time due to the autoionization process.

Asymptotic analysis of quasilinear parabolic-hyperbolic equations describing the large longitudinal motion of a light viscoelastic bar with a heavy attachment

NASA Astrophysics Data System (ADS)

Yip, Shui Cheung

We study the longitudinal motion of a nonlinearly viscoelastic bar with one end fixed and the other end attached to a heavy tip mass. This problem is a precise continuum mechanical analog of the basic discrete mechanical problem of the motion of a mass point on a (massless) spring. This motion is governed by an initial-boundary-value problem for a class of third-order quasilinear parabolic-hyperbolic partial differential equations subject to a nonstandard boundary condition, which is the equation of motion of the tip mass. The ratio of the mass of the bar to that of the tip mass is taken to be a small parameter varepsilon. We prove that this problem has a unique regular solution that admits a valid asymptotic expansion, including an initial-layer expansion, in powers of varepsilon for varepsilon near 0. The fundamental constitutive hypothesis that the tension be a uniformly monotone function of the strain rate plays a critical role in a delicate proof that each term of the initial layer expansion decays exponentially in time. These results depend on new decay estimates for the solution of quasilinear parabolic equations. The constitutive hypothesis that the viscosity become large where the bar nears total compression leads to important uniform bounds for the strain and the strain rate. Higher-order energy estimates support the proof by the Schauder Fixed-Point Theorem of the existence of solutions having a level of regularity appropriate for the asymptotics.

Pointwise convergence of derivatives of Lagrange interpolation polynomials for exponential weights

NASA Astrophysics Data System (ADS)

Damelin, S. B.; Jung, H. S.

2005-01-01

For a general class of exponential weights on the line and on (-1,1), we study pointwise convergence of the derivatives of Lagrange interpolation. Our weights include even weights of smooth polynomial decay near +/-[infinity] (Freud weights), even weights of faster than smooth polynomial decay near +/-[infinity] (Erdos weights) and even weights which vanish strongly near +/-1, for example Pollaczek type weights.

On the heterogeneity of fluorescence lifetime of room temperature ionic liquids: onset of a journey for exploring red emitting dyes.

PubMed

Ghosh, Anup; Chatterjee, Tanmay; Mandal, Prasun K

2012-06-25

An excitation and emission wavelength dependent non-exponential fluorescence decay behaviour of room temperature ionic liquids (RTILs) has been noted. Average fluorescence lifetimes have been found to vary by a factor of three or more. Red emitting dyes dissolved in RTILs are found to follow hitherto unobserved single exponential fluorescence decay behaviour.

A note on trans-Planckian tail effects

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

Graef, L.L.; Brandenberger, R., E-mail: leilagraef@usp.br, E-mail: rhb@physics.mcgill.ca

2015-09-01

We study the proposal by Mersini et al. [1] that the observed dark energy might be explained by the back-reaction of the set of tail modes in a theory with a dispersion relation in which the mode frequency decays exponentially in the trans-Planckian regime. The matter tail modes are frozen out, however they induce metric fluctuations. The energy-momentum tensor with which the tail modes effect the background geometry obtains contributions from both metric and matter fluctuations. We calculate the equation of state induced by the tail modes taking into account the gravitational contribution. We find that, in contrast to themore » case of frozen super-Hubble cosmological fluctuations, in this case the matter perturbations dominate, and they yield an equation of state which to leading order takes the form of a positive cosmological constant.« less

Technique for Very High Order Nonlinear Simulation and Validation

NASA Technical Reports Server (NTRS)

Dyson, Rodger W.

2001-01-01

Finding the sources of sound in large nonlinear fields via direct simulation currently requires excessive computational cost. This paper describes a simple technique for efficiently solving the multidimensional nonlinear Euler equations that significantly reduces this cost and demonstrates a useful approach for validating high order nonlinear methods. Up to 15th order accuracy in space and time methods were compared and it is shown that an algorithm with a fixed design accuracy approaches its maximal utility and then its usefulness exponentially decays unless higher accuracy is used. It is concluded that at least a 7th order method is required to efficiently propagate a harmonic wave using the nonlinear Euler equations to a distance of 5 wavelengths while maintaining an overall error tolerance that is low enough to capture both the mean flow and the acoustics.

Decrease of Fisher information and the information geometry of evolution equations for quantum mechanical probability amplitudes.

PubMed

Cafaro, Carlo; Alsing, Paul M

2018-04-01

The relevance of the concept of Fisher information is increasing in both statistical physics and quantum computing. From a statistical mechanical standpoint, the application of Fisher information in the kinetic theory of gases is characterized by its decrease along the solutions of the Boltzmann equation for Maxwellian molecules in the two-dimensional case. From a quantum mechanical standpoint, the output state in Grover's quantum search algorithm follows a geodesic path obtained from the Fubini-Study metric on the manifold of Hilbert-space rays. Additionally, Grover's algorithm is specified by constant Fisher information. In this paper, we present an information geometric characterization of the oscillatory or monotonic behavior of statistically parametrized squared probability amplitudes originating from special functional forms of the Fisher information function: constant, exponential decay, and power-law decay. Furthermore, for each case, we compute both the computational speed and the availability loss of the corresponding physical processes by exploiting a convenient Riemannian geometrization of useful thermodynamical concepts. Finally, we briefly comment on the possibility of using the proposed methods of information geometry to help identify a suitable trade-off between speed and thermodynamic efficiency in quantum search algorithms.

Decrease of Fisher information and the information geometry of evolution equations for quantum mechanical probability amplitudes

NASA Astrophysics Data System (ADS)

Cafaro, Carlo; Alsing, Paul M.

2018-04-01

The relevance of the concept of Fisher information is increasing in both statistical physics and quantum computing. From a statistical mechanical standpoint, the application of Fisher information in the kinetic theory of gases is characterized by its decrease along the solutions of the Boltzmann equation for Maxwellian molecules in the two-dimensional case. From a quantum mechanical standpoint, the output state in Grover's quantum search algorithm follows a geodesic path obtained from the Fubini-Study metric on the manifold of Hilbert-space rays. Additionally, Grover's algorithm is specified by constant Fisher information. In this paper, we present an information geometric characterization of the oscillatory or monotonic behavior of statistically parametrized squared probability amplitudes originating from special functional forms of the Fisher information function: constant, exponential decay, and power-law decay. Furthermore, for each case, we compute both the computational speed and the availability loss of the corresponding physical processes by exploiting a convenient Riemannian geometrization of useful thermodynamical concepts. Finally, we briefly comment on the possibility of using the proposed methods of information geometry to help identify a suitable trade-off between speed and thermodynamic efficiency in quantum search algorithms.

The exponential behavior and stabilizability of the stochastic magnetohydrodynamic equations

NASA Astrophysics Data System (ADS)

Wang, Huaqiao

2018-06-01

This paper studies the two-dimensional stochastic magnetohydrodynamic equations which are used to describe the turbulent flows in magnetohydrodynamics. The exponential behavior and the exponential mean square stability of the weak solutions are proved by the application of energy method. Furthermore, we establish the pathwise exponential stability by using the exponential mean square stability. When the stochastic perturbations satisfy certain additional hypotheses, we can also obtain pathwise exponential stability results without using the mean square stability.

Electrostatic screening in classical Coulomb fluids: exponential or power-law decay or both? An investigation into the effect of dispersion interactions

NASA Astrophysics Data System (ADS)

Kjellander, Roland

2006-04-01

It is shown that the nature of the non-electrostatic part of the pair interaction potential in classical Coulomb fluids can have a profound influence on the screening behaviour. Two cases are compared: (i) when the non-electrostatic part equals an arbitrary finite-ranged interaction and (ii) when a dispersion r-6 interaction potential is included. A formal analysis is done in exact statistical mechanics, including an investigation of the bridge function. It is found that the Coulombic r-1 and the dispersion r-6 potentials are coupled in a very intricate manner as regards the screening behaviour. The classical one-component plasma (OCP) is a particularly clear example due to its simplicity and is investigated in detail. When the dispersion r-6 potential is turned on, the screened electrostatic potential from a particle goes from a monotonic exponential decay, exp(-κr)/r, to a power-law decay, r-8, for large r. The pair distribution function acquire, at the same time, an r-10 decay for large r instead of the exponential one. There still remains exponentially decaying contributions to both functions, but these contributions turn oscillatory when the r-6 interaction is switched on. When the Coulomb interaction is turned off but the dispersion r-6 pair potential is kept, the decay of the pair distribution function for large r goes over from the r-10 to an r-6 behaviour, which is the normal one for fluids of electroneutral particles with dispersion interactions. Differences and similarities compared to binary electrolytes are pointed out.

Exploiting fast detectors to enter a new dimension in room-temperature crystallography

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

Owen, Robin L., E-mail: robin.owen@diamond.ac.uk; Paterson, Neil; Axford, Danny

2014-05-01

A departure from a linear or an exponential decay in the diffracting power of macromolecular crystals is observed and accounted for through consideration of a multi-state sequential model. A departure from a linear or an exponential intensity decay in the diffracting power of protein crystals as a function of absorbed dose is reported. The observation of a lag phase raises the possibility of collecting significantly more data from crystals held at room temperature before an intolerable intensity decay is reached. A simple model accounting for the form of the intensity decay is reintroduced and is applied for the first timemore » to high frame-rate room-temperature data collection.« less

Solvent dynamics and electron transfer reactions

NASA Astrophysics Data System (ADS)

Rasaiah, Jayendran C.; Zhu, Jianjun

1994-02-01

Recent experimental and theoretical studies of the influence of solvent dynamics on electron transfer (ET) reactions are discussed. It is seen that the survival probabilities of the reactants and products can be obtained as the solution to an integral equation using experimental or simulation data on the solvation dynamics. The theory developed for ET between thermally equilibrated reactants in solution, in which the ligand vibrations were treated classically, is extended to include quantum effects on the inner-shell ligand vibration and electron transfer from a nonequilibrium initial state prepared, for example, by laser excitation. This leads to a slight modification of the integral equation which is easily solved on a personal computer to provide results that can be directly compared with experiment. Analytic approximations to the solutions of the integral equation, ranging from a single exponential to multiexponential time dependence of the survival probabilities are discussed. The rate constant for the single exponential decay of the reactants interpolates between the thermal equilibrium rate constant kie (that is independent of solvent dynamics) and a diffusion controlled rate constant kid (determined by solvent dynamics) and also between the wide (A=0) and narrow (A=1) window limits dominated by inner-sphere ligand vibration and outer-sphere solvent reorganization respectively. The explicit dependence of the integral equation solutions on solvation dynamics S(t), the free energy of reaction ΔG0, the total reorganization energy λ and its partitioning between ligand vibration λq and solvent polarization fluctuations λ0, and the nature of the initial state should be useful in the analysis and design of ET experiments in different solvents.

Classification of the line-soliton solutions of KPII

NASA Astrophysics Data System (ADS)

Chakravarty, Sarbarish; Kodama, Yuji

2008-07-01

In the previous papers (notably, Kodama Y 2004 J. Phys. A: Math. Gen. 37 11169-90, Biondini G and Chakravarty S 2006 J. Math. Phys. 47 033514), a large variety of line-soliton solutions of the Kadomtsev-Petviashvili II (KPII) equation was found. The line-soliton solutions are solitary waves which decay exponentially in the (x, y)-plane except along certain rays. In this paper, it is shown that those solutions are classified by asymptotic information of the solution as |y| → ∞. The present work then unravels some interesting relations between the line-soliton classification scheme and classical results in the theory of permutations.

Novel mechanism of dissipation in synthetic rotary motors

NASA Astrophysics Data System (ADS)

Barbu, Corina; Crespi, Vincent

2007-03-01

We study novel mechanisms of dissipation in nanoscale and molecular-scale motors. In traditional treatments of such systems, the background degrees of freedom are integrated out into a thermal bath, and the rotator is coupled directly to this bath via phenomenological terms such as viscous damping or Langevin forces. We have investigated a situation in which one degree of freedom is pulled out from the thermal bath and into the explicit equations of motion, interposed between the bath and the motor. We describe a regime in which the deceleration of an unpowered rotor follows a universal power law, rather than a standard exponential decay.

Decay rates of Gaussian-type I-balls and Bose-enhancement effects in 3+1 dimensions

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

Kawasaki, Masahiro; Yamada, Masaki; ICRR, University of Tokyo, Kashiwa, 277-8582

2014-02-03

I-balls/oscillons are long-lived spatially localized lumps of a scalar field which may be formed after inflation. In the scalar field theory with monomial potential nearly and shallower than quadratic, which is motivated by chaotic inflationary models and supersymmetric theories, the scalar field configuration of I-balls is approximately Gaussian. If the I-ball interacts with another scalar field, the I-ball eventually decays into radiation. Recently, it was pointed out that the decay rate of I-balls increases exponentially by the effects of Bose enhancement under some conditions and a non-perturbative method to compute the exponential growth rate has been derived. In this paper,more » we apply the method to the Gaussian-type I-ball in 3+1 dimensions assuming spherical symmetry, and calculate the partial decay rates into partial waves, labelled by the angular momentum of daughter particles. We reveal the conditions that the I-ball decays exponentially, which are found to depend on the mass and angular momentum of daughter particles and also be affected by the quantum uncertainty in the momentum of daughter particles.« less

Decay rates of Gaussian-type I-balls and Bose-enhancement effects in 3+1 dimensions

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

Kawasaki, Masahiro; Yamada, Masaki, E-mail: kawasaki@icrr.u-tokyo.ac.jp, E-mail: yamadam@icrr.u-tokyo.ac.jp

2014-02-01

I-balls/oscillons are long-lived spatially localized lumps of a scalar field which may be formed after inflation. In the scalar field theory with monomial potential nearly and shallower than quadratic, which is motivated by chaotic inflationary models and supersymmetric theories, the scalar field configuration of I-balls is approximately Gaussian. If the I-ball interacts with another scalar field, the I-ball eventually decays into radiation. Recently, it was pointed out that the decay rate of I-balls increases exponentially by the effects of Bose enhancement under some conditions and a non-perturbative method to compute the exponential growth rate has been derived. In this paper,more » we apply the method to the Gaussian-type I-ball in 3+1 dimensions assuming spherical symmetry, and calculate the partial decay rates into partial waves, labelled by the angular momentum of daughter particles. We reveal the conditions that the I-ball decays exponentially, which are found to depend on the mass and angular momentum of daughter particles and also be affected by the quantum uncertainty in the momentum of daughter particles.« less

Analysis of volumetric response of pituitary adenomas receiving adjuvant CyberKnife stereotactic radiosurgery with the application of an exponential fitting model

PubMed Central

Yu, Yi-Lin; Yang, Yun-Ju; Lin, Chin; Hsieh, Chih-Chuan; Li, Chiao-Zhu; Feng, Shao-Wei; Tang, Chi-Tun; Chung, Tzu-Tsao; Ma, Hsin-I; Chen, Yuan-Hao; Ju, Da-Tong; Hueng, Dueng-Yuan

2017-01-01

Abstract Tumor control rates of pituitary adenomas (PAs) receiving adjuvant CyberKnife stereotactic radiosurgery (CK SRS) are high. However, there is currently no uniform way to estimate the time course of the disease. The aim of this study was to analyze the volumetric responses of PAs after CK SRS and investigate the application of an exponential decay model in calculating an accurate time course and estimation of the eventual outcome. A retrospective review of 34 patients with PAs who received adjuvant CK SRS between 2006 and 2013 was performed. Tumor volume was calculated using the planimetric method. The percent change in tumor volume and tumor volume rate of change were compared at median 4-, 10-, 20-, and 36-month intervals. Tumor responses were classified as: progression for >15% volume increase, regression for ≤15% decrease, and stabilization for ±15% of the baseline volume at the time of last follow-up. For each patient, the volumetric change versus time was fitted with an exponential model. The overall tumor control rate was 94.1% in the 36-month (range 18–87 months) follow-up period (mean volume change of −43.3%). Volume regression (mean decrease of −50.5%) was demonstrated in 27 (79%) patients, tumor stabilization (mean change of −3.7%) in 5 (15%) patients, and tumor progression (mean increase of 28.1%) in 2 (6%) patients (P = 0.001). Tumors that eventually regressed or stabilized had a temporary volume increase of 1.07% and 41.5% at 4 months after CK SRS, respectively (P = 0.017). The tumor volume estimated using the exponential fitting equation demonstrated high positive correlation with the actual volume calculated by magnetic resonance imaging (MRI) as tested by Pearson correlation coefficient (0.9). Transient progression of PAs post-CK SRS was seen in 62.5% of the patients receiving CK SRS, and it was not predictive of eventual volume regression or progression. A three-point exponential model is of potential predictive value according to relative distribution. An exponential decay model can be used to calculate the time course of tumors that are ultimately controlled. PMID:28121913

A modified exponential behavioral economic demand model to better describe consumption data.

PubMed

Koffarnus, Mikhail N; Franck, Christopher T; Stein, Jeffrey S; Bickel, Warren K

2015-12-01

Behavioral economic demand analyses that quantify the relationship between the consumption of a commodity and its price have proven useful in studying the reinforcing efficacy of many commodities, including drugs of abuse. An exponential equation proposed by Hursh and Silberberg (2008) has proven useful in quantifying the dissociable components of demand intensity and demand elasticity, but is limited as an analysis technique by the inability to correctly analyze consumption values of zero. We examined an exponentiated version of this equation that retains all the beneficial features of the original Hursh and Silberberg equation, but can accommodate consumption values of zero and improves its fit to the data. In Experiment 1, we compared the modified equation with the unmodified equation under different treatments of zero values in cigarette consumption data collected online from 272 participants. We found that the unmodified equation produces different results depending on how zeros are treated, while the exponentiated version incorporates zeros into the analysis, accounts for more variance, and is better able to estimate actual unconstrained consumption as reported by participants. In Experiment 2, we simulated 1,000 datasets with demand parameters known a priori and compared the equation fits. Results indicated that the exponentiated equation was better able to replicate the true values from which the test data were simulated. We conclude that an exponentiated version of the Hursh and Silberberg equation provides better fits to the data, is able to fit all consumption values including zero, and more accurately produces true parameter values. (PsycINFO Database Record (c) 2015 APA, all rights reserved).

A note on trans-Planckian tail effects

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

Graef, L.L.; Instituto de Física, Universidade de São Paulo, Rua do Matão travessa R, São Paulo, SP, 05508-090; Brandenberger, R.

2015-09-09

We study the proposal by Mersini et al. http://dx.doi.org/10.1103/PhysRevD.64.043508 that the observed dark energy might be explained by the back-reaction of the set of tail modes in a theory with a dispersion relation in which the mode frequency decays exponentially in the trans-Planckian regime. The matter tail modes are frozen out, however they induce metric fluctuations. The energy-momentum tensor with which the tail modes effect the background geometry obtains contributions from both metric and matter fluctuations. We calculate the equation of state induced by the tail modes taking into account the gravitational contribution. We find that, in contrast to themore » case of frozen super-Hubble cosmological fluctuations, in this case the matter perturbations dominate, and they yield an equation of state which to leading order takes the form of a positive cosmological constant.« less

Nonexponential Decoherence and Subdiffusion in Atom-Optics Kicked Rotor.

PubMed

Sarkar, Sumit; Paul, Sanku; Vishwakarma, Chetan; Kumar, Sunil; Verma, Gunjan; Sainath, M; Rapol, Umakant D; Santhanam, M S

2017-04-28

Quantum systems lose coherence upon interaction with the environment and tend towards classical states. Quantum coherence is known to exponentially decay in time so that macroscopic quantum superpositions are generally unsustainable. In this work, slower than exponential decay of coherences is experimentally realized in an atom-optics kicked rotor system subjected to nonstationary Lévy noise in the applied kick sequence. The slower coherence decay manifests in the form of quantum subdiffusion that can be controlled through the Lévy exponent. The experimental results are in good agreement with the analytical estimates and numerical simulations for the mean energy growth and momentum profiles of an atom-optics kicked rotor.

Nonadiabatic dynamics of electron scattering from adsorbates in surface bands

NASA Astrophysics Data System (ADS)

Gumhalter, Branko; Šiber, Antonio; Buljan, Hrvoje; Fauster, Thomas

2008-10-01

We present a comparative study of nonadiabatic dynamics of electron scattering in quasi-two-dimensional surface band which is induced by the long-range component of the interactions with a random array of adsorbates. Using three complementary model descriptions of intraband spatiotemporal propagation of quasiparticles that go beyond the single-adsorbate scattering approach we are able to identify distinct subsequent regimes of evolution of an electron following its promotion into an unoccupied band state: (i) early quadratic or ballistic decay of the initial-state survival probability within the Heisenberg uncertainty window, (ii) preasymptotic exponential decay governed by the self-consistent Fermi golden rule scattering rate, and (iii) asymptotic decay described by a combined inverse power-law and logarithmic behavior. The developed models are applied to discuss the dynamics of intraband adsorbate-induced scattering of hot electrons excited into the n=1 image-potential band on Cu(100) surface during the first stage of a two-photon photoemission process. Estimates of crossovers between the distinct evolution regimes enable assessments of the lifespan of a standard quasiparticle behavior and thereby of the range of applicability of the widely used Fermi golden rule and optical Bloch equations approach for description of adsorbate-induced quasiparticle decay and dephasing in ultrafast experiments.

Anomalous NMR Relaxation in Cartilage Matrix Components and Native Cartilage: Fractional-Order Models

PubMed Central

Magin, Richard L.; Li, Weiguo; Velasco, M. Pilar; Trujillo, Juan; Reiter, David A.; Morgenstern, Ashley; Spencer, Richard G.

2011-01-01

We present a fractional-order extension of the Bloch equations to describe anomalous NMR relaxation phenomena (T1 and T2). The model has solutions in the form of Mittag-Leffler and stretched exponential functions that generalize conventional exponential relaxation. Such functions have been shown by others to be useful for describing dielectric and viscoelastic relaxation in complex, heterogeneous materials. Here, we apply these fractional-order T1 and T2 relaxation models to experiments performed at 9.4 and 11.7 Tesla on type I collagen gels, chondroitin sulfate mixtures, and to bovine nasal cartilage (BNC), a largely isotropic and homogeneous form of cartilage. The results show that the fractional-order analysis captures important features of NMR relaxation that are typically described by multi-exponential decay models. We find that the T2 relaxation of BNC can be described in a unique way by a single fractional-order parameter (α), in contrast to the lack of uniqueness of multi-exponential fits in the realistic setting of a finite signal-to-noise ratio. No anomalous behavior of T1 was observed in BNC. In the single-component gels, for T2 measurements, increasing the concentration of the largest components of cartilage matrix, collagen and chondroitin sulfate, results in a decrease in α, reflecting a more restricted aqueous environment. The quality of the curve fits obtained using Mittag-Leffler and stretched exponential functions are in some cases superior to those obtained using mono- and bi-exponential models. In both gels and BNC, α appears to account for microstructural complexity in the setting of an altered distribution of relaxation times. This work suggests the utility of fractional-order models to describe T2 NMR relaxation processes in biological tissues. PMID:21498095

Anomalous NMR relaxation in cartilage matrix components and native cartilage: Fractional-order models

NASA Astrophysics Data System (ADS)

Magin, Richard L.; Li, Weiguo; Pilar Velasco, M.; Trujillo, Juan; Reiter, David A.; Morgenstern, Ashley; Spencer, Richard G.

2011-06-01

We present a fractional-order extension of the Bloch equations to describe anomalous NMR relaxation phenomena ( T1 and T2). The model has solutions in the form of Mittag-Leffler and stretched exponential functions that generalize conventional exponential relaxation. Such functions have been shown by others to be useful for describing dielectric and viscoelastic relaxation in complex, heterogeneous materials. Here, we apply these fractional-order T1 and T2 relaxation models to experiments performed at 9.4 and 11.7 Tesla on type I collagen gels, chondroitin sulfate mixtures, and to bovine nasal cartilage (BNC), a largely isotropic and homogeneous form of cartilage. The results show that the fractional-order analysis captures important features of NMR relaxation that are typically described by multi-exponential decay models. We find that the T2 relaxation of BNC can be described in a unique way by a single fractional-order parameter ( α), in contrast to the lack of uniqueness of multi-exponential fits in the realistic setting of a finite signal-to-noise ratio. No anomalous behavior of T1 was observed in BNC. In the single-component gels, for T2 measurements, increasing the concentration of the largest components of cartilage matrix, collagen and chondroitin sulfate, results in a decrease in α, reflecting a more restricted aqueous environment. The quality of the curve fits obtained using Mittag-Leffler and stretched exponential functions are in some cases superior to those obtained using mono- and bi-exponential models. In both gels and BNC, α appears to account for micro-structural complexity in the setting of an altered distribution of relaxation times. This work suggests the utility of fractional-order models to describe T2 NMR relaxation processes in biological tissues.

Large-amplitude jumps and non-Gaussian dynamics in highly concentrated hard sphere fluids.

PubMed

Saltzman, Erica J; Schweizer, Kenneth S

2008-05-01

Our microscopic stochastic nonlinear Langevin equation theory of activated dynamics has been employed to study the real-space van Hove function of dense hard sphere fluids and suspensions. At very short times, the van Hove function is a narrow Gaussian. At sufficiently high volume fractions, such that the entropic barrier to relaxation is greater than the thermal energy, its functional form evolves with time to include a rapidly decaying component at small displacements and a long-range exponential tail. The "jump" or decay length scale associated with the tail increases with time (or particle root-mean-square displacement) at fixed volume fraction, and with volume fraction at the mean alpha relaxation time. The jump length at the alpha relaxation time is predicted to be proportional to a measure of the decoupling of self-diffusion and structural relaxation. At long times corresponding to mean displacements of order a particle diameter, the volume fraction dependence of the decay length disappears. A good superposition of the exponential tail feature based on the jump length as a scaling variable is predicted at high volume fractions. Overall, the theoretical results are in good accord with recent simulations and experiments. The basic aspects of the theory are also compared with a classic jump model and a dynamically facilitated continuous time random-walk model. Decoupling of the time scales of different parts of the relaxation process predicted by the theory is qualitatively similar to facilitated dynamics models based on the concept of persistence and exchange times if the elementary event is assumed to be associated with transport on a length scale significantly smaller than the particle size.

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

Rout, Dipak; Vijaya, R.; Centre for Lasers and Photonics, Indian Institute of Technology Kanpur, Kanpur 208016

Well-ordered opaline photonic crystals are grown by inward growing self-assembly method from Rhodamine B dye-doped polystyrene colloids. Subsequent to self-assembly, the crystals are infiltrated with gold nanoparticles of 40 nm diameter. Measurements of the stopband features and photoluminescence intensity from these crystals are supplemented by fluorescence decay time analysis. The fluorescence decay times from the dye-doped photonic crystals before and after the infiltration are dramatically different from each other. A lowered fluorescence decay time was observed for the case of gold infiltrated crystal along with an enhanced emission intensity. Double-exponential decay nature of the fluorescence from the dye-doped crystal gets convertedmore » into single-exponential decay upon the infiltration of gold nanoparticles due to the resonant radiative process resulting from the overlap of the surface plasmon resonance with the emission spectrum. The influence of localized surface plasmon due to gold nanoparticles on the increase in emission intensity and decrease in decay time of the emitters is established.« less

Exponential Mixing of the 3D Stochastic Navier-Stokes Equations Driven by Mildly Degenerate Noises

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

Albeverio, Sergio; Debussche, Arnaud, E-mail: arnaud.debussche@bretagne.ens-cachan.fr; Xu Lihu, E-mail: Lihu.Xu@brunel.ac.uk

2012-10-15

We prove the strong Feller property and exponential mixing for 3D stochastic Navier-Stokes equation driven by mildly degenerate noises (i.e. all but finitely many Fourier modes being forced) via a Kolmogorov equation approach.

Teaching Radioactive Decay and Radiometric Dating: An Analog Activity Based on Fluid Dynamics

ERIC Educational Resources Information Center

Claiborne, Lily L.; Miller, Calvin F.

2012-01-01

We present a new laboratory activity for teaching radioactive decay by using hydrodynamic processes as an analog and an evaluation of its efficacy in the classroom. A fluid flowing from an upper beaker into a lower beaker (shampoo in this case) behaves mathematically identically to radioactive decay, mimicking the exponential decay process,…

Statistical Properties of Lorenz-like Flows, Recent Developments and Perspectives

NASA Astrophysics Data System (ADS)

Araujo, Vitor; Galatolo, Stefano; Pacifico, Maria José

We comment on the mathematical results about the statistical behavior of Lorenz equations and its attractor, and more generally on the class of singular hyperbolic systems. The mathematical theory of such kind of systems turned out to be surprisingly difficult. It is remarkable that a rigorous proof of the existence of the Lorenz attractor was presented only around the year 2000 with a computer-assisted proof together with an extension of the hyperbolic theory developed to encompass attractors robustly containing equilibria. We present some of the main results on the statistical behavior of such systems. We show that for attractors of three-dimensional flows, robust chaotic behavior is equivalent to the existence of certain hyperbolic structures, known as singular-hyperbolicity. These structures, in turn, are associated with the existence of physical measures: in low dimensions, robust chaotic behavior for flows ensures the existence of a physical measure. We then give more details on recent results on the dynamics of singular-hyperbolic (Lorenz-like) attractors: (1) there exists an invariant foliation whose leaves are forward contracted by the flow (and further properties which are useful to understand the statistical properties of the dynamics); (2) there exists a positive Lyapunov exponent at every orbit; (3) there is a unique physical measure whose support is the whole attractor and which is the equilibrium state with respect to the center-unstable Jacobian; (4) this measure is exact dimensional; (5) the induced measure on a suitable family of cross-sections has exponential decay of correlations for Lipschitz observables with respect to a suitable Poincaré return time map; (6) the hitting time associated to Lorenz-like attractors satisfy a logarithm law; (7) the geometric Lorenz flow satisfies the Almost Sure Invariance Principle (ASIP) and the Central Limit Theorem (CLT); (8) the rate of decay of large deviations for the volume measure on the ergodic basin of a geometric Lorenz attractor is exponential; (9) a class of geometric Lorenz flows exhibits robust exponential decay of correlations; (10) all geometric Lorenz flows are rapidly mixing and their time-1 map satisfies both ASIP and CLT.

Well hydraulics in pumping tests with exponentially decayed rates of abstraction in confined aquifers

NASA Astrophysics Data System (ADS)

Wen, Zhang; Zhan, Hongbin; Wang, Quanrong; Liang, Xing; Ma, Teng; Chen, Chen

2017-05-01

Actual field pumping tests often involve variable pumping rates which cannot be handled by the classical constant-rate or constant-head test models, and often require a convolution process to interpret the test data. In this study, we proposed a semi-analytical model considering an exponentially decreasing pumping rate started at a certain (higher) rate and eventually stabilized at a certain (lower) rate for cases with or without wellbore storage. A striking new feature of the pumping test with an exponentially decayed rate is that the drawdowns will decrease over a certain period of time during intermediate pumping stage, which has never been seen before in constant-rate or constant-head pumping tests. It was found that the drawdown-time curve associated with an exponentially decayed pumping rate function was bounded by two asymptotic curves of the constant-rate tests with rates equaling to the starting and stabilizing rates, respectively. The wellbore storage must be considered for a pumping test without an observation well (single-well test). Based on such characteristics of the time-drawdown curve, we developed a new method to estimate the aquifer parameters by using the genetic algorithm.

Spins Dynamics in a Dissipative Environment: Hierarchal Equations of Motion Approach Using a Graphics Processing Unit (GPU).

PubMed

Tsuchimoto, Masashi; Tanimura, Yoshitaka

2015-08-11

A system with many energy states coupled to a harmonic oscillator bath is considered. To study quantum non-Markovian system-bath dynamics numerically rigorously and nonperturbatively, we developed a computer code for the reduced hierarchy equations of motion (HEOM) for a graphics processor unit (GPU) that can treat the system as large as 4096 energy states. The code employs a Padé spectrum decomposition (PSD) for a construction of HEOM and the exponential integrators. Dynamics of a quantum spin glass system are studied by calculating the free induction decay signal for the cases of 3 × 2 to 3 × 4 triangular lattices with antiferromagnetic interactions. We found that spins relax faster at lower temperature due to transitions through a quantum coherent state, as represented by the off-diagonal elements of the reduced density matrix, while it has been known that the spins relax slower due to suppression of thermal activation in a classical case. The decay of the spins are qualitatively similar regardless of the lattice sizes. The pathway of spin relaxation is analyzed under a sudden temperature drop condition. The Compute Unified Device Architecture (CUDA) based source code used in the present calculations is provided as Supporting Information .

Bacterial genomes lacking long-range correlations may not be modeled by low-order Markov chains: the role of mixing statistics and frame shift of neighboring genes.

PubMed

Cocho, Germinal; Miramontes, Pedro; Mansilla, Ricardo; Li, Wentian

2014-12-01

We examine the relationship between exponential correlation functions and Markov models in a bacterial genome in detail. Despite the well known fact that Markov models generate sequences with correlation function that decays exponentially, simply constructed Markov models based on nearest-neighbor dimer (first-order), trimer (second-order), up to hexamer (fifth-order), and treating the DNA sequence as being homogeneous all fail to predict the value of exponential decay rate. Even reading-frame-specific Markov models (both first- and fifth-order) could not explain the fact that the exponential decay is very slow. Starting with the in-phase coding-DNA-sequence (CDS), we investigated correlation within a fixed-codon-position subsequence, and in artificially constructed sequences by packing CDSs with out-of-phase spacers, as well as altering CDS length distribution by imposing an upper limit. From these targeted analyses, we conclude that the correlation in the bacterial genomic sequence is mainly due to a mixing of heterogeneous statistics at different codon positions, and the decay of correlation is due to the possible out-of-phase between neighboring CDSs. There are also small contributions to the correlation from bases at the same codon position, as well as by non-coding sequences. These show that the seemingly simple exponential correlation functions in bacterial genome hide a complexity in correlation structure which is not suitable for a modeling by Markov chain in a homogeneous sequence. Other results include: use of the (absolute value) second largest eigenvalue to represent the 16 correlation functions and the prediction of a 10-11 base periodicity from the hexamer frequencies. Copyright © 2014 Elsevier Ltd. All rights reserved.

Tailpulse signal generator

DOEpatents

Baker, John [Walnut Creek, CA; Archer, Daniel E [Knoxville, TN; Luke, Stanley John [Pleasanton, CA; Decman, Daniel J [Livermore, CA; White, Gregory K [Livermore, CA

2009-06-23

A tailpulse signal generating/simulating apparatus, system, and method designed to produce electronic pulses which simulate tailpulses produced by a gamma radiation detector, including the pileup effect caused by the characteristic exponential decay of the detector pulses, and the random Poisson distribution pulse timing for radioactive materials. A digital signal process (DSP) is programmed and configured to produce digital values corresponding to pseudo-randomly selected pulse amplitudes and pseudo-randomly selected Poisson timing intervals of the tailpulses. Pulse amplitude values are exponentially decayed while outputting the digital value to a digital to analog converter (DAC). And pulse amplitudes of new pulses are added to decaying pulses to simulate the pileup effect for enhanced realism in the simulation.

A Parametric Study of Fine-scale Turbulence Mixing Noise

NASA Technical Reports Server (NTRS)

Khavaran, Abbas; Bridges, James; Freund, Jonathan B.

2002-01-01

The present paper is a study of aerodynamic noise spectra from model functions that describe the source. The study is motivated by the need to improve the spectral shape of the MGBK jet noise prediction methodology at high frequency. The predicted spectral shape usually appears less broadband than measurements and faster decaying at high frequency. Theoretical representation of the source is based on Lilley's equation. Numerical simulations of high-speed subsonic jets as well as some recent turbulence measurements reveal a number of interesting statistical properties of turbulence correlation functions that may have a bearing on radiated noise. These studies indicate that an exponential spatial function may be a more appropriate representation of a two-point correlation compared to its Gaussian counterpart. The effect of source non-compactness on spectral shape is discussed. It is shown that source non-compactness could well be the differentiating factor between the Gaussian and exponential model functions. In particular, the fall-off of the noise spectra at high frequency is studied and it is shown that a non-compact source with an exponential model function results in a broader spectrum and better agreement with data. An alternate source model that represents the source as a covariance of the convective derivative of fine-scale turbulence kinetic energy is also examined.

Magnetic pattern at supergranulation scale: the void size distribution

NASA Astrophysics Data System (ADS)

Berrilli, F.; Scardigli, S.; Del Moro, D.

2014-08-01

The large-scale magnetic pattern observed in the photosphere of the quiet Sun is dominated by the magnetic network. This network, created by photospheric magnetic fields swept into convective downflows, delineates the boundaries of large-scale cells of overturning plasma and exhibits "voids" in magnetic organization. These voids include internetwork fields, which are mixed-polarity sparse magnetic fields that populate the inner part of network cells. To single out voids and to quantify their intrinsic pattern we applied a fast circle-packing-based algorithm to 511 SOHO/MDI high-resolution magnetograms acquired during the unusually long solar activity minimum between cycles 23 and 24. The computed void distribution function shows a quasi-exponential decay behavior in the range 10-60 Mm. The lack of distinct flow scales in this range corroborates the hypothesis of multi-scale motion flows at the solar surface. In addition to the quasi-exponential decay, we have found that the voids depart from a simple exponential decay at about 35 Mm.

Velocity and stress autocorrelation decay in isothermal dissipative particle dynamics

NASA Astrophysics Data System (ADS)

Chaudhri, Anuj; Lukes, Jennifer R.

2010-02-01

The velocity and stress autocorrelation decay in a dissipative particle dynamics ideal fluid model is analyzed in this paper. The autocorrelation functions are calculated at three different friction parameters and three different time steps using the well-known Groot/Warren algorithm and newer algorithms including self-consistent leap-frog, self-consistent velocity Verlet and Shardlow first and second order integrators. At low friction values, the velocity autocorrelation function decays exponentially at short times, shows slower-than exponential decay at intermediate times, and approaches zero at long times for all five integrators. As friction value increases, the deviation from exponential behavior occurs earlier and is more pronounced. At small time steps, all the integrators give identical decay profiles. As time step increases, there are qualitative and quantitative differences between the integrators. The stress correlation behavior is markedly different for the algorithms. The self-consistent velocity Verlet and the Shardlow algorithms show very similar stress autocorrelation decay with change in friction parameter, whereas the Groot/Warren and leap-frog schemes show variations at higher friction factors. Diffusion coefficients and shear viscosities are calculated using Green-Kubo integration of the velocity and stress autocorrelation functions. The diffusion coefficients match well-known theoretical results at low friction limits. Although the stress autocorrelation function is different for each integrator, fluctuates rapidly, and gives poor statistics for most of the cases, the calculated shear viscosities still fall within range of theoretical predictions and nonequilibrium studies.

The true quantum face of the "exponential" decay: Unstable systems in rest and in motion

NASA Astrophysics Data System (ADS)

Urbanowski, K.

2017-12-01

Results of theoretical studies and numerical calculations presented in the literature suggest that the survival probability P0(t) has the exponential form starting from times much smaller than the lifetime τ up to times t ⪢τ and that P0(t) exhibits inverse power-law behavior at the late time region for times longer than the so-called crossover time T ⪢ τ (The crossover time T is the time when the late time deviations of P0(t) from the exponential form begin to dominate). More detailed analysis of the problem shows that in fact the survival probability P0(t) can not take the pure exponential form at any time interval including times smaller than the lifetime τ or of the order of τ and it has has an oscillating form. We also study the survival probability of moving relativistic unstable particles with definite momentum . These studies show that late time deviations of the survival probability of these particles from the exponential-like form of the decay law, that is the transition times region between exponential-like and non-exponential form of the survival probability, should occur much earlier than it follows from the classical standard considerations.

Temporal and spatial binning of TCSPC data to improve signal-to-noise ratio and imaging speed

NASA Astrophysics Data System (ADS)

Walsh, Alex J.; Beier, Hope T.

2016-03-01

Time-correlated single photon counting (TCSPC) is the most robust method for fluorescence lifetime imaging using laser scanning microscopes. However, TCSPC is inherently slow making it ineffective to capture rapid events due to the single photon product per laser pulse causing extensive acquisition time limitations and the requirement of low fluorescence emission efficiency to avoid bias of measurement towards short lifetimes. Furthermore, thousands of photons per pixel are required for traditional instrument response deconvolution and fluorescence lifetime exponential decay estimation. Instrument response deconvolution and fluorescence exponential decay estimation can be performed in several ways including iterative least squares minimization and Laguerre deconvolution. This paper compares the limitations and accuracy of these fluorescence decay analysis techniques to accurately estimate double exponential decays across many data characteristics including various lifetime values, lifetime component weights, signal-to-noise ratios, and number of photons detected. Furthermore, techniques to improve data fitting, including binning data temporally and spatially, are evaluated as methods to improve decay fits and reduce image acquisition time. Simulation results demonstrate that binning temporally to 36 or 42 time bins, improves accuracy of fits for low photon count data. Such a technique reduces the required number of photons for accurate component estimation if lifetime values are known, such as for commercial fluorescent dyes and FRET experiments, and improve imaging speed 10-fold.

Laser range profile of cones

NASA Astrophysics Data System (ADS)

Zhou, Wenzhen; Gong, Yanjun; Wang, Mingjun; Gong, Lei

2016-10-01

technology. Laser one-dimensional range profile can reflect the characteristics of the target shape and surface material. These techniques were motivated by applications of laser radar to target discrimination in ballistic missile defense. The radar equation of pulse laser about cone is given in this paper. This paper demonstrates the analytical model of laser one-dimensional range profile of cone based on the radar equation of the pulse laser. Simulations results of laser one-dimensional range profiles of some cones are given. Laser one-dimensional range profiles of cone, whose surface material with diffuse lambertian reflectance, is given in this paper. Laser one-dimensional range profiles of cone, whose surface mater with diffuse materials whose retroreflectance can be modeled closely with an exponential term that decays with increasing incidence angles, is given in this paper. Laser one-dimensional range profiles of different pulse width of cone is given in this paper. The influences of surface material, pulse width, attitude on the one-dimensional range are analyzed. The laser two-dimensional range profile is two-dimensional scattering imaging of pulse laser of target. The two-dimensional range profile of roughness target can provide range resolved information. An analytical model of two-dimensional laser range profile of cone is proposed. The simulations of two-dimensional laser range profiles of some cones are given. Laser two-dimensional range profiles of cone, whose surface mater with diffuse lambertian reflectance, is given in this paper. Laser two-dimensional range profiles of cone, whose surface mater with diffuse materials whose retroreflectance can be modeled closely with an exponential term that decays with increasing incidence angles, is given in this paper. The influence of pulse width, surface material on laser two-dimensional range profile is analyzed. Laser one-dimensional range profile and laser two-dimensional range profile are called as laser range profile (LRP).

Effects of calcium (Ca(2+)) extrusion mechanisms on electrophysiological properties in a hypoglossal motoneuron: insight from a mathematical model.

PubMed

Horn, Kyle G; Solomon, Irene C

2014-01-01

Spike-frequency dynamics and spike shape can provide insight into the types of ion channels present in any given neuron and give a sense for the precise response any neuron may have to a given input stimulus. Motoneuron firing frequency over time is especially important due to its direct effect on motor output. Of particular interest is intracellular Ca(2+), which exerts a powerful influence on both firing properties over time and spike shape. In order to better understand the cellular mechanisms for the regulation of intracellular Ca(2+) and their effect on spiking behavior, we have modified a computational model of an HM to include a variety of Ca(2+) handling processes. For the current study, a series of HM models that include Ca(2+) pumps, Na(+)/Ca(2+) exchangers, and a generic exponential decay of excess Ca(2+) were generated. Simulations from these models indicate that although each extrusion mechanism exerts a similar effect on voltage, the firing properties change distinctly with the inclusion of additional Ca(2+)-related mechanisms: BK channels, Ca(2+) buffering, and diffusion of [Ca(2+)]i modeled via a linear diffusion partial differential equation. While an exponential decay of Ca(2+) seems to adequately capture short-term changes in firing frequency seen in biological data, internal diffusion of Ca(2+) appears to be necessary for capturing longer term frequency changes. © 2014 Elsevier B.V. All rights reserved.

Chaotic dynamics and diffusion in a piecewise linear equation

NASA Astrophysics Data System (ADS)

Shahrear, Pabel; Glass, Leon; Edwards, Rod

2015-03-01

Genetic interactions are often modeled by logical networks in which time is discrete and all gene activity states update simultaneously. However, there is no synchronizing clock in organisms. An alternative model assumes that the logical network is preserved and plays a key role in driving the dynamics in piecewise nonlinear differential equations. We examine dynamics in a particular 4-dimensional equation of this class. In the equation, two of the variables form a negative feedback loop that drives a second negative feedback loop. By modifying the original equations by eliminating exponential decay, we generate a modified system that is amenable to detailed analysis. In the modified system, we can determine in detail the Poincaré (return) map on a cross section to the flow. By analyzing the eigenvalues of the map for the different trajectories, we are able to show that except for a set of measure 0, the flow must necessarily have an eigenvalue greater than 1 and hence there is sensitive dependence on initial conditions. Further, there is an irregular oscillation whose amplitude is described by a diffusive process that is well-modeled by the Irwin-Hall distribution. There is a large class of other piecewise-linear networks that might be analyzed using similar methods. The analysis gives insight into possible origins of chaotic dynamics in periodically forced dynamical systems.

Picosecond absorption anisotropy of polymethine and squarylium dyes in liquid and polymeric media

NASA Astrophysics Data System (ADS)

Przhonska, Olga V.; Hagan, David J.; Novikov, Evgueni; Lepkowicz, Richard; Van Stryland, Eric W.; Bondar, Mikhail V.; Slominsky, Yuriy L.; Kachkovski, Alexei D.

2001-11-01

Time-resolved excitation-probe polarization measurements are performed for polymethine and squarylium dyes in ethanol and an elastopolymer of polyurethane acrylate (PUA). These molecules exhibit strong excited-state absorption in the visible, which results in reverse saturable absorption (RSA). In pump-probe experiments, we observe a strong angular dependence of the RSA decay kinetics upon variation of the angle between pump and probe polarizations. The difference in absorption anisotropy kinetics in ethanol and PUA is detected and analyzed. Anisotropy decay curves in ethanol follow a single exponential decay leading to complete depolarization of the excited state. We also observe complete depolarization in PUA, in which case the anisotropy decay follows a double exponential behavior. Possible rotations in the PUA polymeric matrix are connected with the existence of local microcavities of free volume. We believe that the fast decay component is connected with the rotation of molecular fragments and the slower decay component is connected with the rotation of entire molecules in local microcavities, which is possible because of the elasticity of the polymeric material.

Analog detection for cavity lifetime spectroscopy

DOEpatents

Zare, Richard N.; Harb, Charles C.; Paldus, Barbara A.; Spence, Thomas G.

2001-05-15

An analog detection system for determining a ring-down rate or decay rate 1/.tau. of an exponentially decaying ring-down beam issuing from a lifetime or ring-down cavity during a ring-down phase. Alternatively, the analog detection system determines a build-up rate of an exponentially growing beam issuing from the cavity during a ring-up phase. The analog system can be employed in continuous wave cavity ring-down spectroscopy (CW CRDS) and pulsed CRDS (P CRDS) arrangements utilizing any type of ring-down cavity including ring-cavities and linear cavities.

Analog detection for cavity lifetime spectroscopy

DOEpatents

Zare, Richard N.; Harb, Charles C.; Paldus, Barbara A.; Spence, Thomas G.

2003-01-01

An analog detection system for determining a ring-down rate or decay rate 1/.tau. of an exponentially decaying ring-down beam issuing from a lifetime or ring-down cavity during a ring-down phase. Alternatively, the analog detection system determines a build-up rate of an exponentially growing beam issuing from the cavity during a ring-up phase. The analog system can be employed in continuous wave cavity ring-down spectroscopy (CW CRDS) and pulsed CRDS (P CRDS) arrangements utilizing any type of ring-down cavity including ring-cavities and linear cavities.

An Exponential Finite Difference Technique for Solving Partial Differential Equations. M.S. Thesis - Toledo Univ., Ohio

NASA Technical Reports Server (NTRS)

Handschuh, Robert F.

1987-01-01

An exponential finite difference algorithm, as first presented by Bhattacharya for one-dimensianal steady-state, heat conduction in Cartesian coordinates, has been extended. The finite difference algorithm developed was used to solve the diffusion equation in one-dimensional cylindrical coordinates and applied to two- and three-dimensional problems in Cartesian coordinates. The method was also used to solve nonlinear partial differential equations in one (Burger's equation) and two (Boundary Layer equations) dimensional Cartesian coordinates. Predicted results were compared to exact solutions where available, or to results obtained by other numerical methods. It was found that the exponential finite difference method produced results that were more accurate than those obtained by other numerical methods, especially during the initial transient portion of the solution. Other applications made using the exponential finite difference technique included unsteady one-dimensional heat transfer with temperature varying thermal conductivity and the development of the temperature field in a laminar Couette flow.

exponential finite difference technique for solving partial differential equations

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

Handschuh, R.F.

1987-01-01

An exponential finite difference algorithm, as first presented by Bhattacharya for one-dimensianal steady-state, heat conduction in Cartesian coordinates, has been extended. The finite difference algorithm developed was used to solve the diffusion equation in one-dimensional cylindrical coordinates and applied to two- and three-dimensional problems in Cartesian coordinates. The method was also used to solve nonlinear partial differential equations in one (Burger's equation) and two (Boundary Layer equations) dimensional Cartesian coordinates. Predicted results were compared to exact solutions where available, or to results obtained by other numerical methods. It was found that the exponential finite difference method produced results that weremore » more accurate than those obtained by other numerical methods, especially during the initial transient portion of the solution. Other applications made using the exponential finite difference technique included unsteady one-dimensional heat transfer with temperature varying thermal conductivity and the development of the temperature field in a laminar Couette flow.« less

Decaying two-dimensional turbulence in a circular container.

PubMed

Schneider, Kai; Farge, Marie

2005-12-09

We present direct numerical simulations of two-dimensional decaying turbulence at initial Reynolds number 5 x 10(4) in a circular container with no-slip boundary conditions. Starting with random initial conditions the flow rapidly exhibits self-organization into coherent vortices. We study their formation and the role of the viscous boundary layer on the production and decay of integral quantities. The no-slip wall produces vortices which are injected into the bulk flow and tend to compensate the enstrophy dissipation. The self-organization of the flow is reflected by the transition of the initially Gaussian vorticity probability density function (PDF) towards a distribution with exponential tails. Because of the presence of coherent vortices the pressure PDF become strongly skewed with exponential tails for negative values.

On exponential stability of linear Levin-Nohel integro-differential equations

NASA Astrophysics Data System (ADS)

Tien Dung, Nguyen

2015-02-01

The aim of this paper is to investigate the exponential stability for linear Levin-Nohel integro-differential equations with time-varying delays. To the best of our knowledge, the exponential stability for such equations has not yet been discussed. In addition, since we do not require that the kernel and delay are continuous, our results improve those obtained in Becker and Burton [Proc. R. Soc. Edinburgh, Sect. A: Math. 136, 245-275 (2006)]; Dung [J. Math. Phys. 54, 082705 (2013)]; and Jin and Luo [Comput. Math. Appl. 57(7), 1080-1088 (2009)].

Central Limit Theorem for Exponentially Quasi-local Statistics of Spin Models on Cayley Graphs

NASA Astrophysics Data System (ADS)

Reddy, Tulasi Ram; Vadlamani, Sreekar; Yogeshwaran, D.

2018-04-01

Central limit theorems for linear statistics of lattice random fields (including spin models) are usually proven under suitable mixing conditions or quasi-associativity. Many interesting examples of spin models do not satisfy mixing conditions, and on the other hand, it does not seem easy to show central limit theorem for local statistics via quasi-associativity. In this work, we prove general central limit theorems for local statistics and exponentially quasi-local statistics of spin models on discrete Cayley graphs with polynomial growth. Further, we supplement these results by proving similar central limit theorems for random fields on discrete Cayley graphs taking values in a countable space, but under the stronger assumptions of α -mixing (for local statistics) and exponential α -mixing (for exponentially quasi-local statistics). All our central limit theorems assume a suitable variance lower bound like many others in the literature. We illustrate our general central limit theorem with specific examples of lattice spin models and statistics arising in computational topology, statistical physics and random networks. Examples of clustering spin models include quasi-associated spin models with fast decaying covariances like the off-critical Ising model, level sets of Gaussian random fields with fast decaying covariances like the massive Gaussian free field and determinantal point processes with fast decaying kernels. Examples of local statistics include intrinsic volumes, face counts, component counts of random cubical complexes while exponentially quasi-local statistics include nearest neighbour distances in spin models and Betti numbers of sub-critical random cubical complexes.

Simultaneous Gaussian and exponential inversion for improved analysis of shales by NMR relaxometry

USGS Publications Warehouse

Washburn, Kathryn E.; Anderssen, Endre; Vogt, Sarah J.; Seymour, Joseph D.; Birdwell, Justin E.; Kirkland, Catherine M.; Codd, Sarah L.

2014-01-01

Nuclear magnetic resonance (NMR) relaxometry is commonly used to provide lithology-independent porosity and pore-size estimates for petroleum resource evaluation based on fluid-phase signals. However in shales, substantial hydrogen content is associated with solid and fluid signals and both may be detected. Depending on the motional regime, the signal from the solids may be best described using either exponential or Gaussian decay functions. When the inverse Laplace transform, the standard method for analysis of NMR relaxometry results, is applied to data containing Gaussian decays, this can lead to physically unrealistic responses such as signal or porosity overcall and relaxation times that are too short to be determined using the applied instrument settings. We apply a new simultaneous Gaussian-Exponential (SGE) inversion method to simulated data and measured results obtained on a variety of oil shale samples. The SGE inversion produces more physically realistic results than the inverse Laplace transform and displays more consistent relaxation behavior at high magnetic field strengths. Residuals for the SGE inversion are consistently lower than for the inverse Laplace method and signal overcall at short T2 times is mitigated. Beyond geological samples, the method can also be applied in other fields where the sample relaxation consists of both Gaussian and exponential decays, for example in material, medical and food sciences.

Numerical simulations in stochastic mechanics

NASA Astrophysics Data System (ADS)

McClendon, Marvin; Rabitz, Herschel

1988-05-01

The stochastic differential equation of Nelson's stochastic mechanics is integrated numerically for several simple quantum systems. The calculations are performed with use of Helfand and Greenside's method and pseudorandom numbers. The resulting trajectories are analyzed both individually and collectively to yield insight into momentum, uncertainty principles, interference, tunneling, quantum chaos, and common models of diatomic molecules from the stochastic quantization point of view. In addition to confirming Shucker's momentum theorem, these simulations illustrate, within the context of stochastic mechanics, the position-momentum and time-energy uncertainty relations, the two-slit diffraction pattern, exponential decay of an unstable system, and the greater degree of anticorrelation in a valence-bond model as compared with a molecular-orbital model of H2. The attempt to find exponential divergence of initially nearby trajectories, potentially useful as a criterion for quantum chaos, in a periodically forced oscillator is inconclusive. A way of computing excited energies from the ground-state motion is presented. In all of these studies the use of particle trajectories allows a more insightful interpretation of physical phenomena than is possible within traditional wave mechanics.

Near-Unity Internal Quantum Efficiency of Luminescent Silicon Nanocrystals with Ligand Passivation.

PubMed

Sangghaleh, Fatemeh; Sychugov, Ilya; Yang, Zhenyu; Veinot, Jonathan G C; Linnros, Jan

2015-07-28

Spectrally resolved photoluminescence (PL) decays were measured for samples of colloidal, ligand-passivated silicon nanocrystals. These samples have PL emission energies with peak positions in the range ∼1.4-1.8 eV and quantum yields of ∼30-70%. Their ensemble PL decays are characterized by a stretched-exponential decay with a dispersion factor of ∼0.8, which changes to an almost monoexponential character at fixed detection energies. The dispersion factors and decay rates for various detection energies were extracted from spectrally resolved curves using a mathematical approach that excluded the effect of homogeneous line width broadening. Since nonradiative recombination would introduce a random lifetime variation, leading to a stretched-exponential decay for an ensemble, we conclude that the observed monoexponential decay in size-selected ensembles signifies negligible nonradiative transitions of a similar strength to the radiative one. This conjecture is further supported as extracted decay rates agree with radiative rates reported in the literature, suggesting 100% internal quantum efficiency over a broad range of emission wavelengths. The apparent differences in the quantum yields can then be explained by a varying fraction of "dark" or blinking nanocrystals.

Photocounting distributions for exponentially decaying sources.

PubMed

Teich, M C; Card, H C

1979-05-01

Exact photocounting distributions are obtained for a pulse of light whose intensity is exponentially decaying in time, when the underlying photon statistics are Poisson. It is assumed that the starting time for the sampling interval (which is of arbitrary duration) is uniformly distributed. The probability of registering n counts in the fixed time T is given in terms of the incomplete gamma function for n >/= 1 and in terms of the exponential integral for n = 0. Simple closed-form expressions are obtained for the count mean and variance. The results are expected to be of interest in certain studies involving spontaneous emission, radiation damage in solids, and nuclear counting. They will also be useful in neurobiology and psychophysics, since habituation and sensitization processes may sometimes be characterized by the same stochastic model.

Thermal and active fluctuations of a compressible bilayer vesicle

NASA Astrophysics Data System (ADS)

Sachin Krishnan, T. V.; Yasuda, Kento; Okamoto, Ryuichi; Komura, Shigeyuki

2018-05-01

We discuss thermal and active fluctuations of a compressible bilayer vesicle by using the results of hydrodynamic theory for vesicles. Coupled Langevin equations for the membrane deformation and the density fields are employed to calculate the power spectral density matrix of membrane fluctuations. Thermal contribution is obtained by means of the fluctuation dissipation theorem, whereas active contribution is calculated from exponentially decaying time correlation functions of active random forces. We obtain the total power spectral density as a sum of thermal and active contributions. An apparent response function is further calculated in order to compare with the recent microrheology experiment on red blood cells. An enhanced response is predicted in the low-frequency regime for non-thermal active fluctuations.

Heterogenous fluorescence decay of (4→6)-and (4→8)-linked dimers of (+)-catechin and (-) epicatechin as a result of rotational isomerism.

Treesearch

Wolfgang R. Bergmann; Mary D. Barkley; Richard W. Hemingway; Wayne Mattice

1987-01-01

The time-resolved fluorescence of (+)-catechin and ( -)-epicatechin decays as a single exponential. In contrast dimers formed from (+)-catechin and (-)-epicatechin have more complex decays unless rotation about the interflavan bond is constrained by the introduction of a new ring. The fluorescence decay in unconstrained dimers is adequately described by the sum of two...

Turbulent flame propagation and combustion in spark ignition engines

NASA Technical Reports Server (NTRS)

Beretta, G. P.; Rashidi, M.; Keck, J. C.

1983-01-01

Pressure measurements synchronized with high-speed motion-picture records of flame propagation have been made in a transparent-piston engine. The data show that the initial expansion speed of the flame front is close to that of a laminar flame. As the flame expands, its speed rapidly accelerates to a quasi-steady value comparable with that of the turbulent velocity fluctuations in the unburned gas. During the quasi-steady propagation phase, a significant fraction of the gas behind the visible front is unburned. Final burnout of the charge may be approximated by an exponential decay in time. The data have been analyzed in a model-independent way to obtain a set of empirical equations for calculating mass burning rates in spark-ignition engines. The burning equations contain three parameters: the laminar burning speed, a characteristic speed (uT), and a characteristic length (lT). The laminar burning speed is known from laboratory measurements. Tentative correlations relating uT and lT to engine geometry and operating variables have been derived from the engine data.

Phonon transport in a curved aluminum thin film due to laser short pulse irradiation

NASA Astrophysics Data System (ADS)

Mansoor, Saad Bin; Yilbas, Bekir Sami

2018-05-01

Laser short-pulse heating of a curved aluminum thin film is investigated. The Boltzmann transport equation is incorporated to formulate the heating situation. A Gaussian laser intensity distribution is considered along the film arc and time exponentially decaying of pulse intensity is incorporated in the analysis. The governing equations of energy transport in the electron and lattice sub-systems are coupled through the electron-phonon coupling parameter. To quantify the phonon intensity distribution in the thin film, equivalent equilibrium temperature is introduced, which is associated with the average energy of all phonons around a local point when the phonon energies are redistributed adiabatically to an equilibrium state. It is found the numerical simulations that electron temperature follows similar trend to the spatial distribution of the laser pulse intensity at the film edge. Temporal variation of electron temperature does not follow the laser pulse intensity distribution. The rise of temperature in the electron sub-system is fast while it remains slow in the lattice sub-system.

Check the Lambert-Beer-Bouguer law: a simple trick to boost the confidence of students toward both exponential laws and the discrete approach to experimental physics

NASA Astrophysics Data System (ADS)

Di Capua, R.; Offi, F.; Fontana, F.

2014-07-01

Exponential decay is a prototypical functional behaviour for many physical phenomena, and therefore it deserves great attention in physics courses at an academic level. The absorption of the electromagnetic radiation that propagates in a dissipative medium provides an example of the decay of light intensity, as stated by the law of Lambert-Beer-Bourguer. We devised a very simple experiment to check this law. The experimental setup, its realization, and the data analysis of the experiment are definitely simple. Our main goal was to create an experiment that is accessible to all students, including those in their first year of academic courses and those with poorly equipped laboratories. As illustrated in this paper, our proposal allowed us to develop a deep discussion about some general mathematical and numerical features of exponential decay. Furthermore, the special setup of the absorbing medium (sliced in finite thickness slabs) and the experimental outcomes allow students to understand the transition from the discrete to the continuum approach in experimental physics.

On a class of unsteady three-dimensional Navier Stokes solutions relevant to rotating disc flows: Threshold amplitudes and finite time singularities

NASA Technical Reports Server (NTRS)

Hall, Philip; Balakumar, P.

1990-01-01

A class of exact steady and unsteady solutions of the Navier Stokes equations in cylindrical polar coordinates is given. The flows correspond to the motion induced by an infinite disc rotating with constant angular velocity about the z-axis in a fluid occupying a semi-infinite region which, at large distances from the disc, has velocity field proportional to (x,-y,O) with respect to a Cartesian coordinate system. It is shown that when the rate of rotation is large, Karman's exact solution for a disc rotating in an otherwise motionless fluid is recovered. In the limit of zero rotation rate a particular form of Howarth's exact solution for three-dimensional stagnation point flow is obtained. The unsteady form of the partial differential system describing this class of flow may be generalized to time-periodic equilibrium flows. In addition the unsteady equations are shown to describe a strongly nonlinear instability of Karman's rotating disc flow. It is shown that sufficiently large perturbations lead to a finite time breakdown of that flow whilst smaller disturbances decay to zero. If the stagnation point flow at infinity is sufficiently strong, the steady basic states become linearly unstable. In fact there is then a continuous spectrum of unstable eigenvalues of the stability equations but, if the initial value problem is considered, it is found that, at large values of time, the continuous spectrum leads to a velocity field growing exponentially in time with an amplitude decaying algebraically in time.

Correlation of conformational heterogeneity of the tryptophyl side chain and time-resolved fluorescence intensity decay kinetics

NASA Astrophysics Data System (ADS)

Laws, William R.; Ross, J. B. Alexander

1992-04-01

The time-resolved fluorescence properties of a tryptophan residue should be useful for probing protein structure, function, and dynamics. To date, however, the non-single exponential fluorescence intensity decay kinetics for numerous peptides and proteins having a single tryptophan residue have not been adequately explained. Many possibilities have been considered and include: (1) contributions from the 1La and 1Lb states of indole; (2) excited-state hydrogen exchange; and (3) environmental heterogeneity from (chi) 1 and (chi) 2 rotamers. In addition, it has been suggested that generally many factors contribute to the decay and a distribution of probabilities may be more appropriate. Two recent results support multiple species due to conformational heterogeneity as the major contributor to complex kinetics. First, a rotationally constrained tryptophan analogue has fluorescence intensity decay kinetics that can be described by the sum of two exponentials with amplitudes comparable to the relative populations of the two rotational isomers. Second, the multiple exponentials observed for tyrosine-containing model compounds and peptides correlate with the (chi) 1 rotamer populations independently determined by 1H NMR. We now report similar correlations between rotamer populations and fluorescence intensity decay kinetics for a tryptophan analogue of oxytocin. It appears for this compound that either (chi) 2 rotations do not appreciably alter the indole environment, (chi) 2 rotations are rapid enough to average the observed dependence, or only one of two possible (chi) 2 populations is associated with each (chi) 1 rotamer.

Comparison of kinetic model for biogas production from corn cob

NASA Astrophysics Data System (ADS)

Shitophyta, L. M.; Maryudi

2018-04-01

Energy demand increases every day, while the energy source especially fossil energy depletes increasingly. One of the solutions to overcome the energy depletion is to provide renewable energies such as biogas. Biogas can be generated by corn cob and food waste. In this study, biogas production was carried out by solid-state anaerobic digestion. The steps of biogas production were the preparation of feedstock, the solid-state anaerobic digestion, and the measurement of biogas volume. This study was conducted on TS content of 20%, 22%, and 24%. The aim of this research was to compare kinetic models of biogas production from corn cob and food waste as a co-digestion using the linear, exponential equation, and first-kinetic models. The result showed that the exponential equation had a better correlation than the linear equation on the ascending graph of biogas production. On the contrary, the linear equation had a better correlation than the exponential equation on the descending graph of biogas production. The correlation values on the first-kinetic model had the smallest value compared to the linear and exponential models.

Modeling the degradation kinetics of ascorbic acid.

PubMed

Peleg, Micha; Normand, Mark D; Dixon, William R; Goulette, Timothy R

2018-06-13

Most published reports on ascorbic acid (AA) degradation during food storage and heat preservation suggest that it follows first-order kinetics. Deviations from this pattern include Weibullian decay, and exponential drop approaching finite nonzero retention. Almost invariably, the degradation rate constant's temperature-dependence followed the Arrhenius equation, and hence the simpler exponential model too. A formula and freely downloadable interactive Wolfram Demonstration to convert the Arrhenius model's energy of activation, E a , to the exponential model's c parameter, or vice versa, are provided. The AA's isothermal and non-isothermal degradation can be simulated with freely downloadable interactive Wolfram Demonstrations in which the model's parameters can be entered and modified by moving sliders on the screen. Where the degradation is known a priori to follow first or other fixed order kinetics, one can use the endpoints method, and in principle the successive points method too, to estimate the reaction's kinetic parameters from considerably fewer AA concentration determinations than in the traditional manner. Freeware to do the calculations by either method has been recently made available on the Internet. Once obtained in this way, the kinetic parameters can be used to reconstruct the entire degradation curves and predict those at different temperature profiles, isothermal or dynamic. Comparison of the predicted concentration ratios with experimental ones offers a way to validate or refute the kinetic model and the assumptions on which it is based.

Decay of random correlation functions for unimodal maps

NASA Astrophysics Data System (ADS)

Baladi, Viviane; Benedicks, Michael; Maume-Deschamps, Véronique

2000-10-01

Since the pioneering results of Jakobson and subsequent work by Benedicks-Carleson and others, it is known that quadratic maps tfa( χ) = a - χ2 admit a unique absolutely continuous invariant measure for a positive measure set of parameters a. For topologically mixing tfa, Young and Keller-Nowicki independently proved exponential decay of correlation functions for this a.c.i.m. and smooth observables. We consider random compositions of small perturbations tf + ωt, with tf = tfa or another unimodal map satisfying certain nonuniform hyperbolicity axioms, and ωt chosen independently and identically in [-ɛ, ɛ]. Baladi-Viana showed exponential mixing of the associated Markov chain, i.e., averaging over all random itineraries. We obtain stretched exponential bounds for the random correlation functions of Lipschitz observables for the sample measure μωof almost every itinerary.

A decades-long fast-rise-exponential-decay flare in low-luminosity AGN NGC 7213

NASA Astrophysics Data System (ADS)

Yan, Zhen; Xie, Fu-Guo

2018-03-01

We analysed the four-decades-long X-ray light curve of the low-luminosity active galactic nucleus (LLAGN) NGC 7213 and discovered a fast-rise-exponential-decay (FRED) pattern, i.e. the X-ray luminosity increased by a factor of ≈4 within 200 d, and then decreased exponentially with an e-folding time ≈8116 d (≈22.2 yr). For the theoretical understanding of the observations, we examined three variability models proposed in the literature: the thermal-viscous disc instability model, the radiation pressure instability model, and the TDE model. We find that a delayed tidal disruption of a main-sequence star is most favourable; either the thermal-viscous disc instability model or radiation pressure instability model fails to explain some key properties observed, thus we argue them unlikely.

Measurement of magnetostatic mode excitation and relaxation in permalloy films using scanning Kerr imaging

NASA Astrophysics Data System (ADS)

Tamaru, S.; Bain, J. A.; van de Veerdonk, R. J. M.; Crawford, T. M.; Covington, M.; Kryder, M. H.

2004-09-01

This work presents experimental results of magnetostatic mode excitation using scanning Kerr microscopy under continuous sinusoidal excitation in the microwave frequency range. This technique was applied to 100nm thick permalloy coupons excited in two different ways. In the first experiment, the uniform (Kittel) mode was excited at frequencies in 2.24-8.00GHz . The resonant condition was effectively described with the conventional Kittel mode equation. The LLG damping parameter α increased significantly with decreasing bias field. It was confirmed that this increase was caused by multidomain structure and ripple domains formed under weak bias fields, as suggested by other studies. In the second experiment, propagating magnetostatic mode surface waves were excited. They showed an exponential amplitude decay and a linear phase variation with distance from the drive field source, consistent with a decaying plane wave. The Damon-Eshbach (DE) model was extended to include a finite energy damping and used to analyze the results. It was found that the wave number and the decay constant were reasonably well described by the extended DE model. In contrast to the first experiment, no significant variation of α with frequency or bias field was seen in this second experiment, where spatial inhomogeneities in the magnetization are less significant.

Doubling Time for Nonexponential Families of Functions

ERIC Educational Resources Information Center

Gordon, Sheldon P.

2010-01-01

One special characteristic of any exponential growth or decay function f(t) = Ab[superscript t] is its unique doubling time or half-life, each of which depends only on the base "b". The half-life is used to characterize the rate of decay of any radioactive substance or the rate at which the level of a medication in the bloodstream decays as it is…

Probing solvation decay length in order to characterize hydrophobicity-induced bead-bead attractive interactions in polymer chains.

PubMed

Das, Siddhartha; Chakraborty, Suman

2011-08-01

In this paper, we quantitatively demonstrate that exponentially decaying attractive potentials can effectively mimic strong hydrophobic interactions between monomer units of a polymer chain dissolved in aqueous solvent. Classical approaches to modeling hydrophobic solvation interactions are based on invariant attractive length scales. However, we demonstrate here that the solvation interaction decay length may need to be posed as a function of the relative separation distances and the sizes of the interacting species (or beads or monomers) to replicate the necessary physical interactions. As an illustrative example, we derive a universal scaling relationship for a given solute-solvent combination between the solvation decay length, the bead radius, and the distance between the interacting beads. With our formalism, the hydrophobic component of the net attractive interaction between monomer units can be synergistically accounted for within the unified framework of a simple exponentially decaying potential law, where the characteristic decay length incorporates the distinctive and critical physical features of the underlying interaction. The present formalism, even in a mesoscopic computational framework, is capable of incorporating the essential physics of the appropriate solute-size dependence and solvent-interaction dependence in the hydrophobic force estimation, without explicitly resolving the underlying molecular level details.

Scintillation properties of Ce-doped (Gd0.32Y0.68)3Al5O12 transparent ceramics

NASA Astrophysics Data System (ADS)

Hirano, Shotaro; Okada, Go; Kawaguchi, Noriaki; Yagi, Hideki; Yanagitani, Takagimi; Yanagida, Takayuki

2017-04-01

In this work, we have investigated optical and scintillation properties of 0.35-0.65% Ce:(Gd0.32Y0.68)3Al5O12 (Ce:GYAG) transparent ceramics prepared by the vacuum sintering method. Obtained samples showed high transmittance in the spectral region longer than 500 nm, and two strong absorption bands were clearly observed below 380 nm and between 400 and 500 nm due to the 4f-5d transitions of Ce3+. Under UV and X-rays, we have also observed emission due to the 5d-4f transitions of Ce3+ which appeared around 500-700 nm. The emission decay profile of PL consisted of a single exponential decay component with the decay time of 62.7-64.1 ns while the scintillation decay profile was approximated by a second-order exponential decay function with the decay times of 87.3-100 ns and 1.14-1.32 μs. In addition, it has been revealed that 0.65% Ce:GYAG transparent ceramic showed a notable light yield of 18,000 ph/MeV and low afterglow (13 ppm).

Characterization of plasma current quench during disruptions at HL-2A

NASA Astrophysics Data System (ADS)

Zhu, Jinxia; Zhang, Yipo; Dong, Yunbo; HL-2A Team

2017-05-01

The most essential assumptions of physics for the evaluation of electromagnetic forces on the plasma-facing components due to a disruption-induced eddy current are characteristics of plasma current quenches including the current quench rate or its waveforms. The characteristics of plasma current quenches at HL-2A have been analyzed during spontaneous disruptions. Both linear decay and exponential decay are found in the disruptions with the fastest current quenches. However, there are two stages of current quench in the slow current quench case. The first stage with an exponential decay and the second stage followed by a rapid linear decay. The faster current quench rate corresponds to the faster movement of plasma displacement. The parameter regimes on the current quench time and the current quench rates have been obtained from disruption statistics at HL-2A. There exists no remarkable difference for distributions obtained between the limiter and the divertor configuration. This data from HL-2A provides basic data of the derivation of design criteria for a large-sized machine during the current decay phase of the disruptions.

Origin of stretched-exponential photoluminescence relaxation in size-separated silicon nanocrystals

DOE PAGES

Brown, Samuel L.; Krishnan, Retheesh; Elbaradei, Ahmed; ...

2017-05-25

A detailed understanding of the photoluminescence (PL) from silicon nanocrystals (SiNCs) is convoluted by the complexity of the decay mechanism, including a stretched-exponential relaxation and the presence of both nanosecond and microsecond time scales. In this publication, we analyze the microsecond PL decay of size-resolved SiNC fractions in both full-spectrum (FS) and spectrally resolved (SR) configurations, where the stretching exponent and lifetime are used to deduce a probability distribution function (PDF) of decay rates. For the PL decay measured at peak emission, we find a systematic shift and narrowing of the PDF in comparison to the FS measurements. In amore » similar fashion, we resolve the PL lifetime of the ‘blue’, ‘peak’, and ‘red’ regions of the spectrum and map PL decays of different photon energy onto their corresponding location in the PDF. Furthermore, a general trend is observed where higher and lower photon energies are correlated with shorter and longer lifetimes, respectively, which we relate to the PL line width and electron-phonon coupling.« less

The discrete Fourier transform algorithm for determining decay constants—Implementation using a field programmable gate array

NASA Astrophysics Data System (ADS)

Bostrom, G.; Atkinson, D.; Rice, A.

2015-04-01

Cavity ringdown spectroscopy (CRDS) uses the exponential decay constant of light exiting a high-finesse resonance cavity to determine analyte concentration, typically via absorption. We present a high-throughput data acquisition system that determines the decay constant in near real time using the discrete Fourier transform algorithm on a field programmable gate array (FPGA). A commercially available, high-speed, high-resolution, analog-to-digital converter evaluation board system is used as the platform for the system, after minor hardware and software modifications. The system outputs decay constants at maximum rate of 4.4 kHz using an 8192-point fast Fourier transform by processing the intensity decay signal between ringdown events. We present the details of the system, including the modifications required to adapt the evaluation board to accurately process the exponential waveform. We also demonstrate the performance of the system, both stand-alone and incorporated into our existing CRDS system. Details of FPGA, microcontroller, and circuitry modifications are provided in the Appendix and computer code is available upon request from the authors.

Analytical model of coincidence resolving time in TOF-PET

NASA Astrophysics Data System (ADS)

Wieczorek, H.; Thon, A.; Dey, T.; Khanin, V.; Rodnyi, P.

2016-06-01

The coincidence resolving time (CRT) of scintillation detectors is the parameter determining noise reduction in time-of-flight PET. We derive an analytical CRT model based on the statistical distribution of photons for two different prototype scintillators. For the first one, characterized by single exponential decay, CRT is proportional to the decay time and inversely proportional to the number of photons, with a square root dependence on the trigger level. For the second scintillator prototype, characterized by exponential rise and decay, CRT is proportional to the square root of the product of rise time and decay time divided by the doubled number of photons, and it is nearly independent of the trigger level. This theory is verified by measurements of scintillation time constants, light yield and CRT on scintillator sticks. Trapping effects are taken into account by defining an effective decay time. We show that in terms of signal-to-noise ratio, CRT is as important as patient dose, imaging time or PET system sensitivity. The noise reduction effect of better timing resolution is verified and visualized by Monte Carlo simulation of a NEMA image quality phantom.

In vivo chlorine and sodium MRI of rat brain at 21.1 T.

PubMed

Schepkin, Victor D; Elumalai, Malathy; Kitchen, Jason A; Qian, Chunqi; Gor'kov, Peter L; Brey, William W

2014-02-01

MR imaging of low-gamma nuclei at the ultrahigh magnetic field of 21.1 T provides a new opportunity for understanding a variety of biological processes. Among these, chlorine and sodium are attracting attention for their involvement in brain function and cancer development. MRI of (35)Cl and (23)Na were performed and relaxation times were measured in vivo in normal rat (n = 3) and in rat with glioma (n = 3) at 21.1 T. The concentrations of both nuclei were evaluated using the center-out back-projection method. T 1 relaxation curve of chlorine in normal rat head was fitted by bi-exponential function (T 1a = 4.8 ms (0.7) T 1b = 24.4 ± 7 ms (0.3) and compared with sodium (T 1 = 41.4 ms). Free induction decays (FID) of chlorine and sodium in vivo were bi-exponential with similar rapidly decaying components of [Formula: see text] ms and [Formula: see text] ms, respectively. Effects of small acquisition matrix and bi-exponential FIDs were assessed for quantification of chlorine (33.2 mM) and sodium (44.4 mM) in rat brain. The study modeled a dramatic effect of the bi-exponential decay on MRI results. The revealed increased chlorine concentration in glioma (~1.5 times) relative to a normal brain correlates with the hypothesis asserting the importance of chlorine for tumor progression.

Spherical Ornstein-Uhlenbeck Processes

NASA Astrophysics Data System (ADS)

Wilkinson, Michael; Pumir, Alain

2011-10-01

The paper considers random motion of a point on the surface of a sphere, in the case where the angular velocity is determined by an Ornstein-Uhlenbeck process. The solution is fully characterised by only one dimensionless number, the persistence angle, which is the typical angle of rotation during the correlation time of the angular velocity. We first show that the two-dimensional case is exactly solvable. When the persistence angle is large, a series for the correlation function has the surprising property that its sum varies much more slowly than any of its individual terms. In three dimensions we obtain asymptotic forms for the correlation function, in the limits where the persistence angle is very small and very large. The latter case exhibits a complicated transient, followed by a much slower exponential decay. The decay rate is determined by the solution of a radial Schrödinger equation in which the angular momentum quantum number takes an irrational value, namely j=1/2(sqrt{17}-1). Possible applications of the model to objects tumbling in a turbulent environment are discussed.

A Reduced Model for the Magnetorotational Instability

NASA Astrophysics Data System (ADS)

Jamroz, Ben; Julien, Keith; Knobloch, Edgar

2008-11-01

The magnetorotational instability is investigated within the shearing box approximation in the large Elsasser number regime. In this regime, which is of fundamental importance to astrophysical accretion disk theory, shear is the dominant source of energy, but the instability itself requires the presence of a weaker vertical magnetic field. Dissipative effects are weaker still. However, they are sufficiently large to permit a nonlinear feedback mechanism whereby the turbulent stresses generated by the MRI act on and modify the local background shear in the angular velocity profile. To date this response has been omitted in shearing box simulations and is captured by a reduced pde model derived here from the global MHD fluid equations using multiscale asymptotic perturbation theory. Results from numerical simulations of the reduced pde model indicate a linear phase of exponential growth followed by a nonlinear adjustment to algebraic growth and decay in the fluctuating quantities. Remarkably, the velocity and magnetic field correlations associated with these algebraic growth and decay laws conspire to achieve saturation of the angular momentum transport. The inclusion of subdominant ohmic dissipation arrests the algebraic growth of the fluctuations on a longer, dissipative time scale.

Expanding sheath in a bounded plasma in the context of the post-arc phase of a vacuum arc

NASA Astrophysics Data System (ADS)

Sarrailh, P.; Garrigues, L.; Hagelaar, G. J. M.; Sandolache, G.; Rowe, S.; Jusselin, B.; Boeuf, J. P.

2008-01-01

A numerical model of sheath expansion and plasma decay in a bounded plasma subjected to a linearly increasing voltage has been developed. Numerical results obtained with a hybrid-MB model (Maxwell-Boltzmann electrons, particle ions and Poisson's equations) are compared with analytical theory and results from particle-in-cell (PIC) simulations. The hybrid-MB model is similar to models used for plasma immersion ion implantation except that plasma decay due to particle losses to the electrodes is taken into account. The comparisons with more accurate and much more time consuming PIC models show that the hybrid-MB model provides a very satisfactory description of the sheath expansion and plasma decay even for conditions where the grid spacing is much larger than the Debye length. The model is used for high plasma density conditions, corresponding to the post-arc phase of a vacuum arc circuit breaker where a vacuum gap is subject to a transient recovery voltage (TRV) after it has ceased to sustain a vacuum arc. The results show that the plasma sheath expansion is subsonic under these conditions, and that the plasma starts to decay exponentially after two rarefaction waves from the cathode and anode merge in the centre of the gap. A parametric study also shows the strong influence of the TRV rise rate and initial plasma density on the plasma decay time and on the ion current collected by each electrode. The effect of collisions between charged particles and metal atoms resulting for the electrode evaporation is also discussed.

Model evaluation of plant metal content and biomass yield for the phytoextraction of heavy metals by switchgrass.

PubMed

Chen, Bo-Ching; Lai, Hung-Yu; Juang, Kai-Wei

2012-06-01

To better understand the ability of switchgrass (Panicum virgatum L.), a perennial grass often relegated to marginal agricultural areas with minimal inputs, to remove cadmium, chromium, and zinc by phytoextraction from contaminated sites, the relationship between plant metal content and biomass yield is expressed in different models to predict the amount of metals switchgrass can extract. These models are reliable in assessing the use of switchgrass for phytoremediation of heavy-metal-contaminated sites. In the present study, linear and exponential decay models are more suitable for presenting the relationship between plant cadmium and dry weight. The maximum extractions of cadmium using switchgrass, as predicted by the linear and exponential decay models, approached 40 and 34 μg pot(-1), respectively. The log normal model was superior in predicting the relationship between plant chromium and dry weight. The predicted maximum extraction of chromium by switchgrass was about 56 μg pot(-1). In addition, the exponential decay and log normal models were better than the linear model in predicting the relationship between plant zinc and dry weight. The maximum extractions of zinc by switchgrass, as predicted by the exponential decay and log normal models, were about 358 and 254 μg pot(-1), respectively. To meet the maximum removal of Cd, Cr, and Zn, one can adopt the optimal timing of harvest as plant Cd, Cr, and Zn approach 450 and 526 mg kg(-1), 266 mg kg(-1), and 3022 and 5000 mg kg(-1), respectively. Due to the well-known agronomic characteristics of cultivation and the high biomass production of switchgrass, it is practicable to use switchgrass for the phytoextraction of heavy metals in situ. Copyright © 2012 Elsevier Inc. All rights reserved.

Real-Time Exponential Curve Fits Using Discrete Calculus

NASA Technical Reports Server (NTRS)

Rowe, Geoffrey

2010-01-01

An improved solution for curve fitting data to an exponential equation (y = Ae(exp Bt) + C) has been developed. This improvement is in four areas -- speed, stability, determinant processing time, and the removal of limits. The solution presented avoids iterative techniques and their stability errors by using three mathematical ideas: discrete calculus, a special relationship (be tween exponential curves and the Mean Value Theorem for Derivatives), and a simple linear curve fit algorithm. This method can also be applied to fitting data to the general power law equation y = Ax(exp B) + C and the general geometric growth equation y = Ak(exp Bt) + C.

Estimating outflow facility through pressure dependent pathways of the human eye

PubMed Central

Gardiner, Bruce S.

2017-01-01

We develop and test a new theory for pressure dependent outflow from the eye. The theory comprises three main parameters: (i) a constant hydraulic conductivity, (ii) an exponential decay constant and (iii) a no-flow intraocular pressure, from which the total pressure dependent outflow, average outflow facilities and local outflow facilities for the whole eye may be evaluated. We use a new notation to specify precisely the meaning of model parameters and so model outputs. Drawing on a range of published data, we apply the theory to animal eyes, enucleated eyes and in vivo human eyes, and demonstrate how to evaluate model parameters. It is shown that the theory can fit high quality experimental data remarkably well. The new theory predicts that outflow facilities and total pressure dependent outflow for the whole eye are more than twice as large as estimates based on the Goldman equation and fluorometric analysis of anterior aqueous outflow. It appears likely that this discrepancy can be largely explained by pseudofacility and aqueous flow through the retinal pigmented epithelium, while any residual discrepancy may be due to pathological processes in aged eyes. The model predicts that if the hydraulic conductivity is too small, or the exponential decay constant is too large, then intraocular eye pressure may become unstable when subjected to normal circadian changes in aqueous production. The model also predicts relationships between variables that may be helpful when planning future experiments, and the model generates many novel testable hypotheses. With additional research, the analysis described here may find application in the differential diagnosis, prognosis and monitoring of glaucoma. PMID:29261696

A study of perturbations in scalar-tensor theory using 1 + 3 covariant approach

NASA Astrophysics Data System (ADS)

Ntahompagaze, Joseph; Abebe, Amare; Mbonye, Manasse

This work discusses scalar-tensor theories of gravity, with a focus on the Brans-Dicke sub-class, and one that also takes note of the latter’s equivalence with f(R) gravitation theories. A 1 + 3 covariant formalism is used in this case to discuss covariant perturbations on a background Friedmann-Laimaître-Robertson-Walker (FLRW) spacetime. Linear perturbation equations are developed based on gauge-invariant gradient variables. Both scalar and harmonic decompositions are applied to obtain second-order equations. These equations can then be used for further analysis of the behavior of the perturbation quantities in such a scalar-tensor theory of gravitation. Energy density perturbations are studied for two systems, namely for a scalar fluid-radiation system and for a scalar fluid-dust system, for Rn models. For the matter-dominated era, it is shown that the dust energy density perturbations grow exponentially, a result which agrees with those already existing in the literatures. In the radiation-dominated era, it is found that the behavior of the radiation energy-density perturbations is oscillatory, with growing amplitudes for n > 1, and with decaying amplitudes for 0 < n < 1. This is a new result.

LP-stability for the strong solutions of the Navier-Stokes equations in the whole space

NASA Astrophysics Data System (ADS)

Beiraodaveiga, H.; Secchi, P.

1985-10-01

We consider the motion of a viscous fluid filling the whole space R3, governed by the classical Navier-Stokes equations (1). Existence of global (in time) regular solutions for that system of non-linear partial differential equations, is still an open problem. From either the mathematical and the physical point of view, an interesting property is the stability (or not) of the (eventual) global regular solutions. Here, we assume that v1(t,x) is a solution, with initial data a1(x). For small perturbations of a1, we want the solution v1(t,x) being slightly perturbed, too. Due to viscosity, it is even expected that the perturbed solution v2(t,x) approaches the unperturbed one, as time goes to + infinity. This is just the result proved in this paper. To measure the distance between v1(t,x) and v2(t,x), at each time t, suitable norms are introduced (LP-norms). For fluids filling a bounded vessel, exponential decay of the above distance, is expected. Such a strong result is not reasonable, for fluids filling the entire space.

An Exponential Stability Result of a Timoshenko System with Thermoelasticity with Second Sound and in the Presence of Delay

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

Apalara, Tijani A., E-mail: tijani@kfupm.edu.sa; Messaoudi, Salim A., E-mail: messaoud@kfupm.edu.sa

In this paper, we consider a one-dimensional linear thermoelastic system of Timoshenko type with a delay, where the heat flux is given by Cattaneo’s law. We prove an exponential decay result under a smallness condition on the delay and a stability number introduced first in Santos et al. (J Diff Eqs 253:2715–2733, 2012), using a method different from that of Santos et al. (J Diff Eqs 253:2715–2733, 2012). We also reproduce the polynomial decay of Santos et al. (J Diff Eqs 253:2715–2733, 2012) using the multiplier method in the case of absence of delay. The polynomial decay issue in themore » presence of a small delay is an open question.« less

Asymptotic decay and non-rupture of viscous sheets

NASA Astrophysics Data System (ADS)

Fontelos, Marco A.; Kitavtsev, Georgy; Taranets, Roman M.

2018-06-01

For a nonlinear system of coupled PDEs, that describes evolution of a viscous thin liquid sheet and takes account of surface tension at the free surface, we show exponential (H^1, L^2) asymptotic decay to the flat profile of its solutions considered with general initial data. Additionally, by transforming the system to Lagrangian coordinates we show that the minimal thickness of the sheet stays positive for all times. This result proves the conjecture formally accepted in the physical literature (cf. Eggers and Fontelos in Singularities: formation, structure, and propagation. Cambridge Texts in Applied Mathematics, Cambridge, 2015), that a viscous sheet cannot rupture in finite time in the absence of external forcing. Moreover, in the absence of surface tension we find a special class of initial data for which the Lagrangian solution exhibits L^2-exponential decay to the flat profile.

Gradient-based stochastic estimation of the density matrix

NASA Astrophysics Data System (ADS)

Wang, Zhentao; Chern, Gia-Wei; Batista, Cristian D.; Barros, Kipton

2018-03-01

Fast estimation of the single-particle density matrix is key to many applications in quantum chemistry and condensed matter physics. The best numerical methods leverage the fact that the density matrix elements f(H)ij decay rapidly with distance rij between orbitals. This decay is usually exponential. However, for the special case of metals at zero temperature, algebraic decay of the density matrix appears and poses a significant numerical challenge. We introduce a gradient-based probing method to estimate all local density matrix elements at a computational cost that scales linearly with system size. For zero-temperature metals, the stochastic error scales like S-(d+2)/2d, where d is the dimension and S is a prefactor to the computational cost. The convergence becomes exponential if the system is at finite temperature or is insulating.

The Kepler Light Curve of V344 LYR: Constraining the Thermal-Viscous Limit Cycle Instability

NASA Technical Reports Server (NTRS)

Cannizzo, J. K.; Still, M. D.; Howell, S. B.; Wood, M. A.; Smale, A. P.

2010-01-01

We present time dependent modeling based on the accretion disk limit cycle model for a 90 d light curve of the short period SU UMa-type dwarf nova V344 Lyr taken by Kepler. The unprecedented precision and cadence (1 minute) far surpass that generally available for long term light curves. The data encompass a super outburst, preceded by three normal (i.e., short) outbursts and followed by two normal outbursts. The main decay of the super outburst is nearly perfectly exponential, decaying at a rate approx.12 d/mag, while the much more rapid decays of the normal outbursts exhibit a faster-than-exponential shape. We show that the standard limit cycle model can account for the light curve, without the need for either the thermal-tidal instability or enhanced mass transfer.

Complex Degradation Processes Lead to Non-Exponential Decay Patterns and Age-Dependent Decay Rates of Messenger RNA

PubMed Central

Deneke, Carlus; Lipowsky, Reinhard; Valleriani, Angelo

2013-01-01

Experimental studies on mRNA stability have established several, qualitatively distinct decay patterns for the amount of mRNA within the living cell. Furthermore, a variety of different and complex biochemical pathways for mRNA degradation have been identified. The central aim of this paper is to bring together both the experimental evidence about the decay patterns and the biochemical knowledge about the multi-step nature of mRNA degradation in a coherent mathematical theory. We first introduce a mathematical relationship between the mRNA decay pattern and the lifetime distribution of individual mRNA molecules. This relationship reveals that the mRNA decay patterns at steady state expression level must obey a general convexity condition, which applies to any degradation mechanism. Next, we develop a theory, formulated as a Markov chain model, that recapitulates some aspects of the multi-step nature of mRNA degradation. We apply our theory to experimental data for yeast and explicitly derive the lifetime distribution of the corresponding mRNAs. Thereby, we show how to extract single-molecule properties of an mRNA, such as the age-dependent decay rate and the residual lifetime. Finally, we analyze the decay patterns of the whole translatome of yeast cells and show that yeast mRNAs can be grouped into three broad classes that exhibit three distinct decay patterns. This paper provides both a method to accurately analyze non-exponential mRNA decay patterns and a tool to validate different models of degradation using decay data. PMID:23408982

Strong feedback limit of the Goodwin circadian oscillator

NASA Astrophysics Data System (ADS)

Woller, Aurore; Gonze, Didier; Erneux, Thomas

2013-03-01

The three-variable Goodwin model constitutes a prototypical oscillator based on a negative feedback loop. It was used as a minimal model for circadian oscillations. Other core models for circadian clocks are variants of the Goodwin model. The Goodwin oscillator also appears in many studies of coupled oscillator networks because of its relative simplicity compared to other biophysical models involving a large number of variables and parameters. Because the synchronization properties of Goodwin oscillators still remain difficult to explore mathematically, further simplifications of the Goodwin model have been sought. In this paper, we investigate the strong negative feedback limit of Goodwin equations by using asymptotic techniques. We find that Goodwin oscillations approach a sequence of decaying exponentials that can be described in terms of a single-variable leaky integrated-and-fire model.

Quench dynamics of one-dimensional interacting bosons in a disordered potential: elastic dephasing and critical speeding-up of thermalization.

PubMed

Tavora, Marco; Rosch, Achim; Mitra, Aditi

2014-07-04

The dynamics of interacting bosons in one dimension following the sudden switching on of a weak disordered potential is investigated. On time scales before quasiparticles scatter (prethermalized regime), the dephasing from random elastic forward scattering causes all correlations to decay exponentially fast, but the system remains far from thermal equilibrium. For longer times, the combined effect of disorder and interactions gives rise to inelastic scattering and to thermalization. A novel quantum kinetic equation accounting for both disorder and interactions is employed to study the dynamics. Thermalization turns out to be most effective close to the superfluid-Bose-glass critical point where nonlinearities become more and more important. The numerically obtained thermalization times are found to agree well with analytic estimates.

Necessary conditions for weighted mean convergence of Lagrange interpolation for exponential weights

NASA Astrophysics Data System (ADS)

Damelin, S. B.; Jung, H. S.; Kwon, K. H.

2001-07-01

Given a continuous real-valued function f which vanishes outside a fixed finite interval, we establish necessary conditions for weighted mean convergence of Lagrange interpolation for a general class of even weights w which are of exponential decay on the real line or at the endpoints of (-1,1).

Quantum discord length is enhanced while entanglement length is not by introducing disorder in a spin chain.

PubMed

Sadhukhan, Debasis; Roy, Sudipto Singha; Rakshit, Debraj; Prabhu, R; Sen De, Aditi; Sen, Ujjwal

2016-01-01

Classical correlation functions of ground states typically decay exponentially and polynomially, respectively, for gapped and gapless short-range quantum spin systems. In such systems, entanglement decays exponentially even at the quantum critical points. However, quantum discord, an information-theoretic quantum correlation measure, survives long lattice distances. We investigate the effects of quenched disorder on quantum correlation lengths of quenched averaged entanglement and quantum discord, in the anisotropic XY and XYZ spin glass and random field chains. We find that there is virtually neither reduction nor enhancement in entanglement length while quantum discord length increases significantly with the introduction of the quenched disorder.

Time-resolved photoluminescence investigation of (Mg, Zn) O alloy growth on a non-polar plane

NASA Astrophysics Data System (ADS)

Mohammed Ali, Mohammed Jassim; Chauveau, J. M.; Bretagnon, T.

2018-04-01

Excitons recombination dynamics in ZnMgO alloy have been studied by time-resolved photoluminescence according to temperature. At low temperature, localisation effects of the exciton are found to play a significant role. The photoluminescence (PL) decays are bi-exponential. The short lifetime has a constant value, whereas the long lifetime shows a dependency with temperature. For temperature higher than 100 K the declines show a mono-exponential decay. The PL declines are dominated by non-radiative process at temperatures above 150 K. The PL lifetime dependancy with temperature is analysed using a model including localisation effects and non-radiative recombinations.

Analysis of projectile motion: A comparative study using fractional operators with power law, exponential decay and Mittag-Leffler kernel

NASA Astrophysics Data System (ADS)

Gómez-Aguilar, J. F.; Escobar-Jiménez, R. F.; López-López, M. G.; Alvarado-Martínez, V. M.

2018-03-01

In this paper, the two-dimensional projectile motion was studied; for this study two cases were considered, for the first one, we considered that there is no air resistance and, for the second case, we considered a resisting medium k . The study was carried out by using fractional calculus. The solution to this study was obtained by using fractional operators with power law, exponential decay and Mittag-Leffler kernel in the range of γ \\in (0,1] . These operators were considered in the Liouville-Caputo sense to use physical initial conditions with a known physical interpretation. The range and the maximum height of the projectile were obtained using these derivatives. With the aim of exploring the validity of the obtained results, we compared our results with experimental data given in the literature. A multi-objective particle swarm optimization approach was used for generating Pareto-optimal solutions for the parameters k and γ for different fixed values of velocity v0 and angle θ . The results showed some relevant qualitative differences between the use of power law, exponential decay and Mittag-Leffler law.

Rate laws of the self-induced aggregation kinetics of Brownian particles

NASA Astrophysics Data System (ADS)

Mondal, Shrabani; Sen, Monoj Kumar; Baura, Alendu; Bag, Bidhan Chandra

2016-03-01

In this paper we have studied the self induced aggregation kinetics of Brownian particles in the presence of both multiplicative and additive noises. In addition to the drift due to the self aggregation process, the environment may induce a drift term in the presence of a multiplicative noise. Then there would be an interplay between the two drift terms. It may account qualitatively the appearance of the different laws of aggregation process. At low strength of white multiplicative noise, the cluster number decreases as a Gaussian function of time. If the noise strength becomes appreciably large then the variation of cluster number with time is fitted well by the mono exponentially decaying function of time. For additive noise driven case, the decrease of cluster number can be described by the power law. But in case of multiplicative colored driven process, cluster number decays multi exponentially. However, we have explored how the rate constant (in the mono exponentially cluster number decaying case) depends on strength of interference of the noises and their intensity. We have also explored how the structure factor at long time depends on the strength of the cross correlation (CC) between the additive and the multiplicative noises.

Very slow lava extrusion continued for more than five years after the 2011 Shinmoedake eruption observed from SAR interferometry

NASA Astrophysics Data System (ADS)

Ozawa, T.; Miyagi, Y.

2017-12-01

Shinmoe-dake located to SW Japan erupted in January 2011 and lava accumulated in the crater (e.g., Ozawa and Kozono, EPS, 2013). Last Vulcanian eruption occurred in September 2011, and after that, no eruption has occurred until now. Miyagi et al. (GRL, 2014) analyzed TerraSAR-X and Radarsat-2 SAR data acquired after the last eruption and found continuous inflation in the crater. Its inflation decayed with time, but had not terminated in May 2013. Since the time-series of inflation volume change rate fitted well to the exponential function with the constant term, we suggested that lava extrusion had continued in long-term due to deflation of shallow magma source and to magma supply from deeper source. To investigate its deformation after that, we applied InSAR to Sentinel-1 and ALOS-2 SAR data. Inflation decayed further, and almost terminated in the end of 2016. It means that this deformation has continued more than five years from the last eruption. We have found that the time series of inflation volume change rate fits better to the double-exponential function than single-exponential function with the constant term. The exponential component with the short time constant has almost settled in one year from the last eruption. Although InSAR result from TerraSAR-X data of November 2011 and May 2013 indicated deflation of shallow source under the crater, such deformation has not been obtained from recent SAR data. It suggests that this component has been due to deflation of shallow magma source with excess pressure. In this study, we found the possibility that long-term component also decayed exponentially. Then this factor may be deflation of deep source or delayed vesiculation.

InP:Fe Photoconducting device

DOEpatents

Hammond, Robert B.; Paulter, Nicholas G.; Wagner, Ronald S.

1984-01-01

A photoconducting device fabricated from Fe-doped, semi-insulating InP crystals exhibits an exponential decay transient with decay time inversely related to Fe concentration. Photoconductive gain as high as 5 is demonstrated in photoconducting devices with AuGe and AuSn contacts. Response times from 150 to 1000 picoseconds can be achieved.

InP:Fe photoconducting device

DOEpatents

Hammond, R.B.; Paulter, N.G.; Wagner, R.S.

A photoconducting device fabricated from Fe-doped, semi-insulating InP crystals exhibits an exponential decay transient with decay time inversely related to Fe concentration. Photoconductive gain as high as 5 is demonstrated in photoconducting devices with AuGe and AuSn contacts. Response times from 150 to 1000 picoseconds can be achieved.

Convergence and stability of the exponential Euler method for semi-linear stochastic delay differential equations.

PubMed

Zhang, Ling

2017-01-01

The main purpose of this paper is to investigate the strong convergence and exponential stability in mean square of the exponential Euler method to semi-linear stochastic delay differential equations (SLSDDEs). It is proved that the exponential Euler approximation solution converges to the analytic solution with the strong order [Formula: see text] to SLSDDEs. On the one hand, the classical stability theorem to SLSDDEs is given by the Lyapunov functions. However, in this paper we study the exponential stability in mean square of the exact solution to SLSDDEs by using the definition of logarithmic norm. On the other hand, the implicit Euler scheme to SLSDDEs is known to be exponentially stable in mean square for any step size. However, in this article we propose an explicit method to show that the exponential Euler method to SLSDDEs is proved to share the same stability for any step size by the property of logarithmic norm.

A review of the matrix-exponential formalism in radiative transfer

NASA Astrophysics Data System (ADS)

Efremenko, Dmitry S.; Molina García, Víctor; Gimeno García, Sebastián; Doicu, Adrian

2017-07-01

This paper outlines the matrix exponential description of radiative transfer. The eigendecomposition method which serves as a basis for computing the matrix exponential and for representing the solution in a discrete ordinate setting is considered. The mathematical equivalence of the discrete ordinate method, the matrix operator method, and the matrix Riccati equations method is proved rigorously by means of the matrix exponential formalism. For optically thin layers, approximate solution methods relying on the Padé and Taylor series approximations to the matrix exponential, as well as on the matrix Riccati equations, are presented. For optically thick layers, the asymptotic theory with higher-order corrections is derived, and parameterizations of the asymptotic functions and constants for a water-cloud model with a Gamma size distribution are obtained.

In vivo chlorine and sodium MRI of rat brain at 21.1 T

PubMed Central

Elumalai, Malathy; Kitchen, Jason A.; Qian, Chunqi; Gor’kov, Peter L.; Brey, William W.

2017-01-01

Object MR imaging of low-gamma nuclei at the ultrahigh magnetic field of 21.1 T provides a new opportunity for understanding a variety of biological processes. Among these, chlorine and sodium are attracting attention for their involvement in brain function and cancer development. Materials and methods MRI of 35Cl and 23Na were performed and relaxation times were measured in vivo in normal rat (n = 3) and in rat with glioma (n = 3) at 21.1 T. The concentrations of both nuclei were evaluated using the center-out back-projection method. Results T1 relaxation curve of chlorine in normal rat head was fitted by bi-exponential function (T1a = 4.8 ms (0.7) T1b = 24.4 ± 7 ms (0.3) and compared with sodium (T1 = 41.4 ms). Free induction decays (FID) of chlorine and sodium in vivo were bi-exponential with similar rapidly decaying components of T2a∗=0.4 ms and T2a∗=0.53 ms, respectively. Effects of small acquisition matrix and bi-exponential FIDs were assessed for quantification of chlorine (33.2 mM) and sodium (44.4 mM) in rat brain. Conclusion The study modeled a dramatic effect of the bi-exponential decay on MRI results. The revealed increased chlorine concentration in glioma (~1.5 times) relative to a normal brain correlates with the hypothesis asserting the importance of chlorine for tumor progression. PMID:23748497

Optical coherence tomography assessment of vessel wall degradation in aneurysmatic thoracic aortas

NASA Astrophysics Data System (ADS)

Real, Eusebio; Eguizabal, Alma; Pontón, Alejandro; Val-Bernal, J. Fernando; Mayorga, Marta; Revuelta, José M.; López-Higuera, José; Conde, Olga M.

2013-06-01

Optical coherence tomographic images of ascending thoracic human aortas from aneurysms exhibit disorders on the smooth muscle cell structure of the media layer of the aortic vessel as well as elastin degradation. Ex-vivo measurements of human samples provide results that correlate with pathologist diagnosis in aneurysmatic and control aortas. The observed disorders are studied as possible hallmarks for aneurysm diagnosis. To this end, the backscattering profile along the vessel thickness has been evaluated by fitting its decay against two different models, a third order polynomial fitting and an exponential fitting. The discontinuities present on the vessel wall on aneurysmatic aortas are slightly better identified with the exponential approach. Aneurysmatic aortic walls present uneven reflectivity decay when compared with healthy vessels. The fitting error has revealed as the most favorable indicator for aneurysm diagnosis as it provides a measure of how uniform is the decay along the vessel thickness.

Human vertical eye movement responses to earth horizontal pitch

NASA Technical Reports Server (NTRS)

Wall, C. 3rd; Petropoulos, A. E.

1993-01-01

The vertical eye movements in humans produced in response to head-over-heels constant velocity pitch rotation about a horizontal axis resemble those from other species. At 60 degrees/s these are persistent and tend to have non-reversing slow components that are compensatory to the direction of rotation. In most, but not all subjects, the slow component velocity was well characterized by a rapid build-up followed by an exponential decay to a non-zero baseline. Super-imposed was a cyclic or modulation component whose frequency corresponded to the time for one revolution and whose maximum amplitude occurred during a specific head orientation. All response components (exponential decay, baseline and modulation) were larger during pitch backward compared to pitch forward runs. Decay time constants were shorter during the backward runs, thus, unlike left to right yaw axis rotation, pitch responses display significant asymmetries between paired forward and backward runs.

Light-induced biophotonic emission from plant tissues.

PubMed

Bajpai, R P; Bajpai, P K

1992-07-01

The emission of biophotons in the visible range, following a delay time of 2-200 seconds after exposure to light, has been measured in germinating seeds, roots, flowers, leaves, and cells. It was found that the biophotonic signals are reproducible and light-induced. The observed signals from germinating seeds of Phaseolus aures and decaying leaves of Eucalyptus are presented to show that the signals have characteristic kinetics and intensity. The kinetics of the signal was found to be independent of the stage of growth or decay, though its intensity varied with biological factors. The kinetics in the first minute is characterized by a single exponential decay term while that in the region t less than or equal to 200 s is characterized by two exponentials. The variation in the intensity of the signal with mass, state of hydration, and growth, and the effect of inhibitors in various systems (e.g. leaves, lichen, Chlorella) are reported.

Decaying and growing eigenmodes in open quantum systems: Biorthogonality and the Petermann factor

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

Lee, Soo-Young

2009-10-15

We study the biorthogonality between decaying and growing eigenmodes in one-dimensional potential barrier problems. It is shown that Petermann factors K{sub n} of the eigenmodes, a measure of nonorthogonality, are involved in decaying mechanism of an initially confined particle. We also show that the decay tail of the growing modes at an exceptional point (EP), where K{sub n} become infinite, is not exponential, but {approx}t{sup 2}e{sup -{gamma}{sub EP}t}, {gamma}{sub EP} the decay rate of the decaying mode at EP. In addition, the geometrical phase near an EP is illustrated by the evolution of wave function.

Centric scan SPRITE for spin density imaging of short relaxation time porous materials.

PubMed

Chen, Quan; Halse, Meghan; Balcom, Bruce J

2005-02-01

The single-point ramped imaging with T1 enhancement (SPRITE) imaging technique has proven to be a very robust and flexible method for the study of a wide range of systems with short signal lifetimes. As a pure phase encoding technique, SPRITE is largely immune to image distortions generated by susceptibility variations, chemical shift and paramagnetic impurities. In addition, it avoids the line width restrictions on resolution common to time-based sampling, frequency encoding methods. The standard SPRITE technique is however a longitudinal steady-state imaging method; the image intensity is related to the longitudinal steady state, which not only decreases the signal-to-noise ratio, but also introduces many parameters into the image signal equation. A centric scan strategy for SPRITE removes the longitudinal steady state from the image intensity equation and increases the inherent image intensity. Two centric scan SPRITE methods, that is, Spiral-SPRITE and Conical-SPRITE, with fast acquisition and greatly reduced gradient duty cycle, are outlined. Multiple free induction decay (FID) points may be acquired during SPRITE sampling for signal averaging to increase signal-to-noise ratio or for T2* and spin density mapping without an increase in acquisition time. Experimental results show that most porous sedimentary rock and concrete samples have a single exponential T2* decay due to susceptibility difference-induced field distortion. Inhomogeneous broadening thus dominates, which suggests that spin density imaging can be easily obtained by SPRITE.

Luminescence and transient lifetime studies for energy transfer of PbS QD films

NASA Astrophysics Data System (ADS)

Wang, Joanna S.; Ullrich, Bruno; Dass, Chandriker K.; Das, Anirban; Wai, Chien M.; Brown, Gail J.; Hendrickson, Joshua R.

2017-08-01

Quantum confined semiconductor materials in colloidal form have drawn great attention in scientific communities due to the size-tunability, which controls their optical properties. PbS quantum dots (QDs) are exciting candidates for quantum optics, particularly due to the control of the QD sizes during the synthetic process enabling the realization of precisely tunable emission properties in the near-infrared region. Differently sized pairs of PbS QDs were deposited onto glass substrates to form thin films using supercritical CO2 (sc-CO2) deposition and solvent deposition methods (SDM). The fluorescence and photoluminescence (PL) spectra obtained from these closely packed films prepared by the sc-CO2 method reveal effective Förster resonance energy transfer (FRET) between two different sized dots, while the films composed of three different QD sizes show an even more effective FRET from the smallest to the largest ones. Energy transfer can be observed more directly by temporally resolved PL decay of mixed dots. By means of transient lifetime measurements, a mixed PbS film with 3.1 and 4.7 nm QDs was studied for FRET by time correlated single photon counting. The PL peak of the 3.1 nm QDs is quenched with respect to the emission of the 4.7 nm QDs and decays faster, and the best fit for the lifetime (decay constant)-1 is a biexponential decay mode. The long wavelength decay (4.7 nm QDs) is best fit by a mono-exponential equation. More theoretical and experimental work is required for a thorough understanding of the radiative lifetimes of PbS QDs in mixed QD systems.

A new generalized exponential rational function method to find exact special solutions for the resonance nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Ghanbari, Behzad; Inc, Mustafa

2018-04-01

The present paper suggests a novel technique to acquire exact solutions of nonlinear partial differential equations. The main idea of the method is to generalize the exponential rational function method. In order to examine the ability of the method, we consider the resonant nonlinear Schrödinger equation (R-NLSE). Many variants of exact soliton solutions for the equation are derived by the proposed method. Physical interpretations of some obtained solutions is also included. One can easily conclude that the new proposed method is very efficient and finds the exact solutions of the equation in a relatively easy way.

Reverberation in a trapezoidal room

NASA Astrophysics Data System (ADS)

Kanev, N. G.

2013-09-01

The problem of sound decay in a trapezoidal room with a nonuniform distribution of wall absorption is considered. It is shown that the sound energy decay may be either anomalously slow, obeying the law ˜1/ t, or fast, obeying an exponential law. It is found that the type of the decay law depends on the presence of stable ray trajectories in the room. Manifestations of stable ray trajectories in both laboratory and field experiments are demonstrated.

Disordered Kitaev chains with long-range pairing.

PubMed

Cai, Xiaoming

2017-03-22

We study the competition of disorder and superconductivity for a generalized Kitaev model in incommensurate potentials. The generalized Kitaev model describes one dimensional spinless fermions with long-range p-wave superconducting pairing, which decays with distance l as a power law  ∼[Formula: see text]. We focus on the transition from the topological superconducting phase to the topologically trivial Anderson localized phase, and effects of the exponent α on this phase transition. In the topological superconducting phase, for a system under open boundary condition the amplitude of zero-mode Majorana fermion has a hybrid exponential-algebraic decay as the distance increases from the edge. In the Anderson localized phase, some single-particle states remain critical for very strong disorders and the number of critical states increases as α decreases. In addition, except for critical disorders, the correlation function always has an exponential decay at the short range and an algebraic decay at the long range. Phase transition points are also numerically determined and the topological phase transition happens earlier at a smaller disorder strength for a system with smaller α.

Use of Continuous Exponential Families to Link Forms via Anchor Tests. Research Report. ETS RR-11-11

ERIC Educational Resources Information Center

Haberman, Shelby J.; Yan, Duanli

2011-01-01

Continuous exponential families are applied to linking test forms via an internal anchor. This application combines work on continuous exponential families for single-group designs and work on continuous exponential families for equivalent-group designs. Results are compared to those for kernel and equipercentile equating in the case of chained…

Free response approach in a parametric system

NASA Astrophysics Data System (ADS)

Huang, Dishan; Zhang, Yueyue; Shao, Hexi

2017-07-01

In this study, a new approach to predict the free response in a parametric system is investigated. It is proposed in the special form of a trigonometric series with an exponentially decaying function of time, based on the concept of frequency splitting. By applying harmonic balance, the parametric vibration equation is transformed into an infinite set of homogeneous linear equations, from which the principal oscillation frequency can be computed, and all coefficients of harmonic components can be obtained. With initial conditions, arbitrary constants in a general solution can be determined. To analyze the computational accuracy and consistency, an approach error function is defined, which is used to assess the computational error in the proposed approach and in the standard numerical approach based on the Runge-Kutta algorithm. Furthermore, an example of a dynamic model of airplane wing flutter on a turbine engine is given to illustrate the applicability of the proposed approach. Numerical solutions show that the proposed approach exhibits high accuracy in mathematical expression, and it is valuable for theoretical research and engineering applications of parametric systems.

Scavenging of radioactive soluble gases from inhomogeneous atmosphere by evaporating rain droplets.

PubMed

Elperin, Tov; Fominykh, Andrew; Krasovitov, Boris

2015-05-01

We analyze effects of inhomogeneous concentration and temperature distributions in the atmosphere, rain droplet evaporation and radioactive decay of soluble gases on the rate of trace gas scavenging by rain. We employ a one-dimensional model of precipitation scavenging of radioactive soluble gaseous pollutants that is valid for small gradients and non-uniform initial altitudinal distributions of temperature and concentration in the atmosphere. We assume that conditions of equilibrium evaporation of rain droplets are fulfilled. It is demonstrated that transient altitudinal distribution of concentration under the influence of rain is determined by the linear wave equation that describes propagation of a scavenging wave front. The obtained equation is solved by the method of characteristics. Scavenging coefficients are calculated for wet removal of gaseous iodine-131 and tritiated water vapor (HTO) for the exponential initial distribution of trace gases concentration in the atmosphere and linear temperature distribution. Theoretical predictions of the dependence of the magnitude of the scavenging coefficient on rain intensity for tritiated water vapor are in good agreement with the available atmospheric measurements. Copyright © 2015 Elsevier Ltd. All rights reserved.

Local energy decay for linear wave equations with variable coefficients

NASA Astrophysics Data System (ADS)

Ikehata, Ryo

2005-06-01

A uniform local energy decay result is derived to the linear wave equation with spatial variable coefficients. We deal with this equation in an exterior domain with a star-shaped complement. Our advantage is that we do not assume any compactness of the support on the initial data, and its proof is quite simple. This generalizes a previous famous result due to Morawetz [The decay of solutions of the exterior initial-boundary value problem for the wave equation, Comm. Pure Appl. Math. 14 (1961) 561-568]. In order to prove local energy decay, we mainly apply two types of ideas due to Ikehata-Matsuyama [L2-behaviour of solutions to the linear heat and wave equations in exterior domains, Sci. Math. Japon. 55 (2002) 33-42] and Todorova-Yordanov [Critical exponent for a nonlinear wave equation with damping, J. Differential Equations 174 (2001) 464-489].

Re-examination of a Classic Experiment to Measure the Positronium-Helium Cross Section

NASA Technical Reports Server (NTRS)

Drachman, Richard J.; DiRienzi, Joseph

1998-01-01

In 1975, before the advent of positronium beams, a clever experiment was carried out in an attempt to measure low-energy Ps-atom scattering cross-sections, especially that of Ps-He. A series of parallel thin plates was placed in the vessel containing the sample of gas, and positrons were allowed to enter the chamber from a radioactive source. The time spectrum of annihilation radiation was observed in the traditional way, and the pickoff annihilation due to thermalized Ps striking one of the plates was to be the special feature of the experiment. Using a diffusion analysis the authors derived cross- sections for several gases, and for helium the value obtained was sigma = 0.0166 pi(alpha)(sub o, sup 2). Even then this value was thought to be very much too small, while recent measurements and some calculations suggest a more reasonable value would be sigma = 3 to 13 pi(alpha)(sub o,sup 2). It has always been puzzling that an apparently well-designed experiment should give such an unsatisfactory result. We have now re-examined the analysis of the data with some interesting consequences which may explain the discrepancy. Two main observations support our re-analysis. First, we note that the mean free path for Ps-He scattering would be quite long if the cross-section were as small as that quoted above; the diffusion method itself would seem to be questionable. For the larger values, however, there would be no such problem. Second, it was assumed that when the annihilation rate had settled down and was following an exponential decay curve the asymptotic solution of the diffusion equation had been reached. We find, instead, that a superposition of exponentials can accurately represent the decay curve, consistent with the higher cross-section value.

A model for hematopoietic death in man from irradiation of bone marrow during radioimmunotherapy.

PubMed

Scott, B R; Dillehay, L E

1990-11-01

There are numerous institutions worldwide performing clinical trials of radioimmunotherapy (RIT) for cancer. For RIT, an exponentially decaying radionuclide is attached by using a chelating agent to a specific monoclonal or polyclonal tumour antibody (e.g. antiferritin IgG). The major limitation to RIT is toxicity to normal tissue in organs other than the one containing the tumour (e.g. bone marrow). The focus of this manuscript is on modelling the risk (or probability) of hematopoietic death in man for exponentially decaying patterns of high-energy beta irradiation (e.g. 90Y) of bone marrow by radioimmunoglobulin injected into the blood. The analytical solutions presented are only applicable to protocols for which significant uptake of radioactivity by the bone marrow does not occur, and only for high energy beta emitters. However, the generic equation used to obtain the analytical solutions is applicable to any continuous pattern of high energy beta irradiation. A model called the "normalized dose model" was used to generate calculated values for the LD50 as a function of the effective half-time for the radioimmunoglobulin in the blood. A less complicated empirical model was used to describe the calculated values. This model is presumed to be valid for effective half-times in blood of up to about 20 days. For longer effective half-times, the LD50 can be estimated using the normalized-dose model presented. In this manuscript, we also provide a modified Weibull model that allows estimation of the risk of hematopoietic death for single or multiple injections (in one cycle) of radioimmunoglobulin, for patients with normal susceptibility to irradiation and for patients with heightened susceptibility. With the modified Weibull model, the risk of hematopoietic death depends on the level of medical treatment provided to mitigate radiation injuries.

Long-term creep characterization of Gr. 91 steel by modified creep constitutive equations

NASA Astrophysics Data System (ADS)

Kim, Woo-Gon; Kim, Sung-Ho; Lee, Chan-Bock

2011-06-01

This paper focuses on the long-term creep characterization of Gr. 91 steel using creep constitutive equations. The models of three such equations, a combination of power-law form and omega model (CPO), a combination of exponential form and omega model (CEO), and a combination of logarithmic form and omega model (CLO), which are described as sum decaying primary creep and accelerating tertiary creep, are proposed. A series of creep rupture data was obtained through creep tests with various applied loads at 600 °C. On the basis of the creep data, a nonlinear least-square fitting (NLSF) analysis was carried out to provide the best fit with the experimental data in optimizing the parameter constants of an individual equation. The results of the NLSF analysis showed that in the lower stress regions of 160 MPa (σ/σys <0.65), the CEO model showed a match with the experimental creep data comparable to those of the CPO and CLO models; however, in the higher stress regions of 160 MPa (σ/σy > 0.65), the CPO model showed better agreement than the other two models. It was found that the CEO model was superior to the CPO and CLO models in the modeling of long-term creep curves. Using the CEO model, the long-term creep curves of Gr. 91 steel were numerically characterized, and its creep life was predicted accurately.

Fast, purely growing collisionless reconnection as an eigenfunction problem related to but not involving linear whistler waves

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

Bellan, Paul M.

If either finite electron inertia or finite resistivity is included in 2D magnetic reconnection, the two-fluid equations become a pair of second-order differential equations coupling the out-of-plane magnetic field and vector potential to each other to form a fourth-order system. The coupling at an X-point is such that out-of-plane even-parity electric and odd-parity magnetic fields feed off each other to produce instability if the scale length on which the equilibrium magnetic field changes is less than the ion skin depth. The instability growth rate is given by an eigenvalue of the fourth-order system determined by boundary and symmetry conditions. Themore » instability is a purely growing mode, not a wave, and has growth rate of the order of the whistler frequency. The spatial profile of both the out-of-plane electric and magnetic eigenfunctions consists of an inner concave region having extent of the order of the electron skin depth, an intermediate convex region having extent of the order of the equilibrium magnetic field scale length, and a concave outer exponentially decaying region. If finite electron inertia and resistivity are not included, the inner concave region does not exist and the coupled pair of equations reduces to a second-order differential equation having non-physical solutions at an X-point.« less

Characterization of continuously distributed cortical water diffusion rates with a stretched-exponential model.

PubMed

Bennett, Kevin M; Schmainda, Kathleen M; Bennett, Raoqiong Tong; Rowe, Daniel B; Lu, Hanbing; Hyde, James S

2003-10-01

Experience with diffusion-weighted imaging (DWI) shows that signal attenuation is consistent with a multicompartmental theory of water diffusion in the brain. The source of this so-called nonexponential behavior is a topic of debate, because the cerebral cortex contains considerable microscopic heterogeneity and is therefore difficult to model. To account for this heterogeneity and understand its implications for current models of diffusion, a stretched-exponential function was developed to describe diffusion-related signal decay as a continuous distribution of sources decaying at different rates, with no assumptions made about the number of participating sources. DWI experiments were performed using a spin-echo diffusion-weighted pulse sequence with b-values of 500-6500 s/mm(2) in six rats. Signal attenuation curves were fit to a stretched-exponential function, and 20% of the voxels were better fit to the stretched-exponential model than to a biexponential model, even though the latter model had one more adjustable parameter. Based on the calculated intravoxel heterogeneity measure, the cerebral cortex contains considerable heterogeneity in diffusion. The use of a distributed diffusion coefficient (DDC) is suggested to measure mean intravoxel diffusion rates in the presence of such heterogeneity. Copyright 2003 Wiley-Liss, Inc.

Exponential Methods for the Time Integration of Schroedinger Equation

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

Cano, B.; Gonzalez-Pachon, A.

2010-09-30

We consider exponential methods of second order in time in order to integrate the cubic nonlinear Schroedinger equation. We are interested in taking profit of the special structure of this equation. Therefore, we look at symmetry, symplecticity and approximation of invariants of the proposed methods. That will allow to integrate till long times with reasonable accuracy. Computational efficiency is also our aim. Therefore, we make numerical computations in order to compare the methods considered and so as to conclude that explicit Lawson schemes projected on the norm of the solution are an efficient tool to integrate this equation.

Long-term radio and X-ray evolution of the tidal disruption event ASASSN-14li

NASA Astrophysics Data System (ADS)

Bright, J. S.; Fender, R. P.; Motta, S. E.; Mooley, K.; Perrott, Y. C.; van Velzen, S.; Carey, S.; Hickish, J.; Razavi-Ghods, N.; Titterington, D.; Scott, P.; Grainge, K.; Scaife, A.; Cantwell, T.; Rumsey, C.

2018-04-01

We report on late time radio and X-ray observations of the tidal disruption event candidate ASASSN-14li, covering the first 1000 d of the decay phase. For the first ˜200 d the radio and X-ray emission fade in concert. This phase is better fitted by an exponential decay at X-ray wavelengths, while the radio emission is well described by either an exponential or the canonical t-5/3 decay assumed for tidal disruption events. The correlation between radio and X-ray emission during this period can be fitted as L_R∝ L_X^{1.9± 0.2}. After 400 d the radio emission at 15.5 GHz has reached a plateau level of 244 ± 8 μJy which it maintains for at least the next 600 d, while the X-ray emission continues to fade exponentially. This steady level of radio emission is likely due to relic radio lobes from the weak AGN-like activity implied by historical radio observations. We note that while most existing models are based upon the evolution of ejecta which are decoupled from the central black hole, the radio-X-ray correlation during the declining phase is also consistent with core-jet emission coupled to a radiatively efficient accretion flow.

An exact formulation of the time-ordered exponential using path-sums

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

Giscard, P.-L., E-mail: p.giscard1@physics.ox.ac.uk; Lui, K.; Thwaite, S. J.

2015-05-15

We present the path-sum formulation for the time-ordered exponential of a time-dependent matrix. The path-sum formulation gives the time-ordered exponential as a branched continued fraction of finite depth and breadth. The terms of the path-sum have an elementary interpretation as self-avoiding walks and self-avoiding polygons on a graph. Our result is based on a representation of the time-ordered exponential as the inverse of an operator, the mapping of this inverse to sums of walks on a graphs, and the algebraic structure of sets of walks. We give examples demonstrating our approach. We establish a super-exponential decay bound for the magnitudemore » of the entries of the time-ordered exponential of sparse matrices. We give explicit results for matrices with commonly encountered sparse structures.« less

Matrix exponential-based closures for the turbulent subgrid-scale stress tensor.

PubMed

Li, Yi; Chevillard, Laurent; Eyink, Gregory; Meneveau, Charles

2009-01-01

Two approaches for closing the turbulence subgrid-scale stress tensor in terms of matrix exponentials are introduced and compared. The first approach is based on a formal solution of the stress transport equation in which the production terms can be integrated exactly in terms of matrix exponentials. This formal solution of the subgrid-scale stress transport equation is shown to be useful to explore special cases, such as the response to constant velocity gradient, but neglecting pressure-strain correlations and diffusion effects. The second approach is based on an Eulerian-Lagrangian change of variables, combined with the assumption of isotropy for the conditionally averaged Lagrangian velocity gradient tensor and with the recent fluid deformation approximation. It is shown that both approaches lead to the same basic closure in which the stress tensor is expressed as the matrix exponential of the resolved velocity gradient tensor multiplied by its transpose. Short-time expansions of the matrix exponentials are shown to provide an eddy-viscosity term and particular quadratic terms, and thus allow a reinterpretation of traditional eddy-viscosity and nonlinear stress closures. The basic feasibility of the matrix-exponential closure is illustrated by implementing it successfully in large eddy simulation of forced isotropic turbulence. The matrix-exponential closure employs the drastic approximation of entirely omitting the pressure-strain correlation and other nonlinear scrambling terms. But unlike eddy-viscosity closures, the matrix exponential approach provides a simple and local closure that can be derived directly from the stress transport equation with the production term, and using physically motivated assumptions about Lagrangian decorrelation and upstream isotropy.

Universal Long Ranged Correlations in Driven Binary Mixtures

NASA Astrophysics Data System (ADS)

Poncet, Alexis; Bénichou, Olivier; Démery, Vincent; Oshanin, Gleb

2017-03-01

When two populations of "particles" move in opposite directions, like oppositely charged colloids under an electric field or intersecting flows of pedestrians, they can move collectively, forming lanes along their direction of motion. The nature of this "laning transition" is still being debated and, in particular, the pair correlation functions, which are the key observables to quantify this phenomenon, have not been characterized yet. Here, we determine the correlations using an analytical approach based on a linearization of the stochastic equations for the density fields, which is valid for dense systems of soft particles. We find that the correlations decay algebraically along the direction of motion, and have a self-similar exponential profile in the transverse direction. Brownian dynamics simulations confirm our theoretical predictions and show that they also hold beyond the validity range of our analytical approach, pointing to a universal behavior.

Luminescence dating of quaternary deposits in geology in Brazil.

PubMed

Tatumi, Sonia Hatsue; Gozzi, Giuliano; Yee, Márcio; de Oliveira, Victor Inácio; Sallun, Alethéa Ernandes Martins; Suguio, Kenitiro

2006-01-01

In the present work, systematic dating by luminescence methods has been done on 50 Quaternary geological samples within the study area of São Paulo State, Brazil. Bleaching experiments showed that residual TL intensity of 375 degrees C peak, of the quartz, was obtained after 10 h of sunlight exposition. Intensities decays of the 325 and 375 degrees C TL peaks can be fitted using second order exponential equation. Paleodose values were evaluated using regeneration methods with multiple aliquots. Samples dated indicate preliminary ages varying from 9 +/- 1 to 935 +/- 130 ka for colluvio-elluvial deposits, and from 17 +/- 2 to 215 +/- 30 ka for alluvial deposits of the study area. They cover four peneplained surfaces shaped during the Quaternary: I (1000-400 ka), II (400-120 ka), III (120-10 ka) and IV (10 ka until today), in decreasing order.

Memory effects on a resonate-and-fire neuron model subjected to Ornstein-Uhlenbeck noise

NASA Astrophysics Data System (ADS)

Paekivi, S.; Mankin, R.; Rekker, A.

2017-10-01

We consider a generalized Langevin equation with an exponentially decaying memory kernel as a model for the firing process of a resonate-and-fire neuron. The effect of temporally correlated random neuronal input is modeled as Ornstein-Uhlenbeck noise. In the noise-induced spiking regime of the neuron, we derive exact analytical formulas for the dependence of some statistical characteristics of the output spike train, such as the probability distribution of the interspike intervals (ISIs) and the survival probability, on the parameters of the input stimulus. Particularly, on the basis of these exact expressions, we have established sufficient conditions for the occurrence of memory-time-induced transitions between unimodal and multimodal structures of the ISI density and a critical damping coefficient which marks a dynamical transition in the behavior of the system.

Kinetic analysis of simultaneous denitrification and biomineralization of novel Acinetobacter sp. CN86.

PubMed

Su, Jun-Feng; Shi, Jing-Xin; Huang, Ting-Lin; Ma, Fang

2016-08-15

A novel aerobic denitrification and biomineralization strain CN86 was isolated from the Qu Jiang artificial lake. Based on phylogenetic characteristics, the isolated strain was identified as Acinetobacter species. Strain CN86 was confirmed to have the ability to perform simultaneous denitrification and biomineralization. Exponential decay equation was used for the matching of kinetic processes on denitrification and biomineralization. A highest nitrate removal rate was achieved at the pH7.0, organic concentration of 1.5g/L and temperature of 30°C. An optimal hardness removal rate was obtained at the pH9.0, organic concentration of 2.0g/L and temperature of 30°C. Strain CN86 is a suitable candidate for the simultaneous removal of nitrate and hardness in groundwater treatment. Copyright © 2016 Elsevier Ltd. All rights reserved.

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

Yanai, Takeshi; Fann, George I.; Beylkin, Gregory

Using the fully numerical method for time-dependent Hartree–Fock and density functional theory (TD-HF/DFT) with the Tamm–Dancoff (TD) approximation we use a multiresolution analysis (MRA) approach to present our findings. From a reformulation with effective use of the density matrix operator, we obtain a general form of the HF/DFT linear response equation in the first quantization formalism. It can be readily rewritten as an integral equation with the bound-state Helmholtz (BSH) kernel for the Green's function. The MRA implementation of the resultant equation permits excited state calculations without virtual orbitals. Moreover, the integral equation is efficiently and adaptively solved using amore » numerical multiresolution solver with multiwavelet bases. Our implementation of the TD-HF/DFT methods is applied for calculating the excitation energies of H 2, Be, N 2, H 2O, and C 2H 4 molecules. The numerical errors of the calculated excitation energies converge in proportion to the residuals of the equation in the molecular orbitals and response functions. The energies of the excited states at a variety of length scales ranging from short-range valence excitations to long-range Rydberg-type ones are consistently accurate. It is shown that the multiresolution calculations yield the correct exponential asymptotic tails for the response functions, whereas those computed with Gaussian basis functions are too diffuse or decay too rapidly. Finally, we introduce a simple asymptotic correction to the local spin-density approximation (LSDA) so that in the TDDFT calculations, the excited states are correctly bound.« less

Decay Properties of Axially Symmetric D-Solutions to the Steady Navier-Stokes Equations

NASA Astrophysics Data System (ADS)

Weng, Shangkun

2018-03-01

We investigate the decay properties of smooth axially symmetric D-solutions to the steady Navier-Stokes equations. The achievements of this paper are two folds. One is improved decay rates of u_{θ } and \

On the nature of dissipative Timoshenko systems at light of the second spectrum of frequency

NASA Astrophysics Data System (ADS)

Almeida Júnior, D. S.; Ramos, A. J. A.

2017-12-01

In the present work, we prove that there exists a relation between a physical inconsistence known as second spectrum of frequency or non-physical spectrum and the exponential decay of a dissipative Timoshenko system where the damping mechanism acts on angle rotation. The so-called second spectrum is addressed into stabilization scenario and, in particular, we show that the second spectrum of the classical Timoshenko model can be truncated by taking a damping mechanism. Also, we show that dissipative Timoshenko type systems which are free of the second spectrum [based on important physical and historical observations made by Elishakoff (Advances mathematical modeling and experimental methods for materials and structures, solid mechanics and its applications, Springer, Berlin, pp 249-254, 2010), Elishakoff et al. (ASME Am Soc Mech Eng Appl Mech Rev 67(6):1-11 2015) and Elishakoff et al. (Int J Solids Struct 109:143-151, 2017)] are exponential stable for any values of the coefficients of system. In this direction, we provide physical explanations why weakly dissipative Timoshenko systems decay exponentially according to equality between velocity of wave propagation as proved in pioneering works by Soufyane (C R Acad Sci 328(8):731-734, 1999) and also by Muñoz Rivera and Racke (Discrete Contin Dyn Syst B 9:1625-1639, 2003). Therefore, the second spectrum of the classical Timoshenko beam model plays an important role in explaining some results on exponential decay and our investigations suggest to pay attention to the eventual consequences of this spectrum on stabilization setting for dissipative Timoshenko type systems.

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.

On the Claim of Modulations in 36Cl Beta Decay and Their Association with Solar Rotation

NASA Astrophysics Data System (ADS)

Pommé, S.; Kossert, K.; Nähle, O.

2017-11-01

Recently, claims were made by Sturrock et al. ( Astropart. Phys. 42, 62, 2013), Sturrock, Fischbach, and Scargle ( Solar Phys. 291, 3467, 2016; arXiv http://arxiv.org/abs/arXiv:1705.03010, 2017) that beta decay can be induced by interaction of the nucleus with solar neutrinos and that cyclic modulations in decay rates are indicative of the dynamics of the solar interior. Transient modulations in residuals from a purely exponential decay curve were observed at frequencies near 11 a^{-1} and 12.7 a^{-1} in repeated activity measurements of a 36Cl source by Alburger, Harbottle, and Norton ( Earth Planet Sci. Lett. 78, 168, 1986) at Brookhaven National Laboratory in a period from 1984 to 1985. Sturrock et al. have speculatively associated them with rotational influence on the solar neutrino flux. In this work, more accurate 36Cl decay-rate measurements - performed at the Physikalisch-Technische Bundesanstalt Braunschweig in the period 2010 - 2013 by means of the triple-to-double coincidence ratio measurement technique - are scrutinised. The residuals from an exponential decay curve were analysed by a weighted Lomb-Scargle periodogram. The existence of modulations in the frequency range between 0.2 a^{-1} and 20 a^{-1} could be excluded down to an amplitude of about 0.0016%. The invariability of the 36Cl decay constant contradicts the speculations made about the deep solar interior on the basis of instabilities in former activity measurements.

A method for nonlinear exponential regression analysis

NASA Technical Reports Server (NTRS)

Junkin, B. G.

1971-01-01

A computer-oriented technique is presented for performing a nonlinear exponential regression analysis on decay-type experimental data. The technique involves the least squares procedure wherein the nonlinear problem is linearized by expansion in a Taylor series. A linear curve fitting procedure for determining the initial nominal estimates for the unknown exponential model parameters is included as an integral part of the technique. A correction matrix was derived and then applied to the nominal estimate to produce an improved set of model parameters. The solution cycle is repeated until some predetermined criterion is satisfied.

Solvent and temperature effects on the decay dynamics of [p-N,N-(dialkylamino)benzylidene]malononitriles

NASA Astrophysics Data System (ADS)

Safarzadeh-Amiri, A.

1986-08-01

The effects of solvent and temperature on the decay kinetics of p-(dialkylamino)benzylidenemalononitrile (1) and julodinemalononitrile (3) has been studied in glycerol and triacetin. The fluorescence decay curves of these compounds were non-exponential and varied slightly with wavelength. This is attributed to the existence of two ground state conformers and to reorientation of the solvent cage around solute molecules. The results were explained in terms of trans → cisphotoisomerization.

Almost periodic solutions to difference equations

NASA Technical Reports Server (NTRS)

Bayliss, A.

1975-01-01

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

Exact calculations of survival probability for diffusion on growing lines, disks, and spheres: The role of dimension.

PubMed

Simpson, Matthew J; Baker, Ruth E

2015-09-07

Unlike standard applications of transport theory, the transport of molecules and cells during embryonic development often takes place within growing multidimensional tissues. In this work, we consider a model of diffusion on uniformly growing lines, disks, and spheres. An exact solution of the partial differential equation governing the diffusion of a population of individuals on the growing domain is derived. Using this solution, we study the survival probability, S(t). For the standard non-growing case with an absorbing boundary, we observe that S(t) decays to zero in the long time limit. In contrast, when the domain grows linearly or exponentially with time, we show that S(t) decays to a constant, positive value, indicating that a proportion of the diffusing substance remains on the growing domain indefinitely. Comparing S(t) for diffusion on lines, disks, and spheres indicates that there are minimal differences in S(t) in the limit of zero growth and minimal differences in S(t) in the limit of fast growth. In contrast, for intermediate growth rates, we observe modest differences in S(t) between different geometries. These differences can be quantified by evaluating the exact expressions derived and presented here.

Absorption dynamics and delay time in complex potentials

NASA Astrophysics Data System (ADS)

Villavicencio, Jorge; Romo, Roberto; Hernández-Maldonado, Alberto

2018-05-01

The dynamics of absorption is analyzed by using an exactly solvable model that deals with an analytical solution to Schrödinger’s equation for cutoff initial plane waves incident on a complex absorbing potential. A dynamical absorption coefficient which allows us to explore the dynamical loss of particles from the transient to the stationary regime is derived. We find that the absorption process is characterized by the emission of a series of damped periodic pulses in time domain, associated with damped Rabi-type oscillations with a characteristic frequency, ω = (E + ε)/ℏ, where E is the energy of the incident waves and ‑ε is energy of the quasidiscrete state of the system induced by the absorptive part of the Hamiltonian; the width γ of this resonance governs the amplitude of the pulses. The resemblance of the time-dependent absorption coefficient with a real decay process is discussed, in particular the transition from exponential to nonexponential regimes, a well-known feature of quantum decay. We have also analyzed the effect of the absorptive part of the potential on the dynamical delay time, which behaves differently from the one observed in attractive real delta potentials, exhibiting two regimes: time advance and time delay.

Resonance and decay phenomena lead to quantum mechanical time asymmetry

NASA Astrophysics Data System (ADS)

Bohm, A.; Bui, H. V.

2013-04-01

The states (Schrödinger picture) and observables (Heisenberg picture) in the standard quantum theory evolve symmetrically in time, given by the unitary group with time extending over -∞ < t < +∞. This time evolution is a mathematical consequence of the Hilbert space boundary condition for the dynamical differential equations. However, this unitary group evolution violates causality. Moreover, it does not solve an old puzzle of Wigner: How does one describe excited states of atoms which decay exponentially, and how is their lifetime τ related to the Lorentzian width Γ? These question can be answered if one replaces the Hilbert space boundary condition by new, Hardy space boundary conditions. These Hardy space boundary conditions allow for a distinction between states (prepared by a preparation apparatus) and observables (detected by a registration apparatus). The new Hardy space quantum theory is time asymmetric, i.e, the time evolution is given by the semigroup with t0 <= t < +∞, which predicts a finite "beginning of time" t0, where t0 is the ensemble of time at which each individual system has been prepared. The Hardy space axiom also leads to the new prediction: the width Γ and the lifetime τ are exactly related by τ = hslash/Γ.

Predicting the onset of high-frequency self-excited oscillations in a channel with an elastic wall

NASA Astrophysics Data System (ADS)

Ward, Thomas; Whittaker, Robert

2016-11-01

Flow-induced oscillations of fluid-conveying elastic-walled channels arise in many industrial and biological systems including the oscillation of the vocal cords during phonation. We derive a system of equations that describes the wall displacement in response to the steady and oscillatory components of the fluid pressure derived by Whittaker et al. (2010). We show that the steady pressure component results in a base state deformation assumed to be small in magnitude relative to the length of the channel. The oscillation frequency of the elastic wall is determined by an eigenvalue problem paramterised by the shape of the base state deformation, the strength of axial tension relative to azimuthal bending, F , and the size of non-linear stretching effects from the wall's initial deformation, K . We determine the slow growth or decay of the normal modes in each by considering the energy budget of the system. The amplitude of the oscillations grow or decay exponentially with a growth rate Λ, which may be expressed in terms of a critical Reynolds number Rec . We use numerical simulations to identify three distinct regions in parameter regimes space and determine the stability of oscillations in each.

Can the Earth be Dated from Decay of Its Magnetic Field?

ERIC Educational Resources Information Center

Dalrymple, G. Brent

1983-01-01

Thomas G. Barnes, geologist/creationist, argues that the geomagnetic field was created by unknown processes when earth was created and has been decaying (irreversibly/exponentially) with a half-life of about 1,400 years since then. Shows that Barnes' proposition is wrong and explains why the earth's age cannot be determined from magnetic-field…

Decomposition rates for hand-piled fuels

Treesearch

Clinton S. Wright; Alexander M. Evans; Joseph C. Restaino

2017-01-01

Hand-constructed piles in eastern Washington and north-central New Mexico were weighed periodically between October 2011 and June 2015 to develop decay-rate constants that are useful for estimating the rate of piled biomass loss over time. Decay-rate constants (k) were determined by fitting negative exponential curves to time series of pile weight for each site. Piles...

Profit Maximization Models for Exponential Decay Processes.

DTIC Science & Technology

1980-08-01

assumptions could easily be analyzed in similar fashion. References [1] Bensoussan, A., Hurst , E.G. and Nislund, B., Management Applications of Modern...TVIPe OF r 04PORNT A i M0 CiH O .V9RAE PROFIT MAXIMIZATION .ODELS FOR EXPONENT IAL Technical Report DECAY PROCESSES August 1990 ~~~I. PtA’OR~idNG ONqG

Decay of Correlations, Quantitative Recurrence and Logarithm Law for Contracting Lorenz Attractors

NASA Astrophysics Data System (ADS)

Galatolo, Stefano; Nisoli, Isaia; Pacifico, Maria Jose

2018-03-01

In this paper we prove that a class of skew products maps with non uniformly hyperbolic base has exponential decay of correlations. We apply this to obtain a logarithm law for the hitting time associated to a contracting Lorenz attractor at all the points having a well defined local dimension, and a quantitative recurrence estimation.

A new approach to interpretation of heterogeneity of fluorescence decay in complex biological systems

NASA Astrophysics Data System (ADS)

Wlodarczyk, Jakub; Kierdaszuk, Borys

2005-08-01

Decays of tyrosine fluorescence in protein-ligand complexes are described by a model of continuous distribution of fluorescence lifetimes. Resulted analytical power-like decay function provides good fits to highly complex fluorescence kinetics. Moreover, this is a manifestation of so-called Tsallis q-exponential function, which is suitable for description of the systems with long-range interactions, memory effect, as well as with fluctuations of the characteristic lifetime of fluorescence. The proposed decay functions were applied to analysis of fluorescence decays of tyrosine in a protein, i.e. the enzyme purine nucleoside phosphorylase from E. coli (the product of the deoD gene), free in aqueous solution and in a complex with formycin A (an inhibitor) and orthophosphate (a co-substrate). The power-like function provides new information about enzyme-ligand complex formation based on the physically justified heterogeneity parameter directly related to the lifetime distribution. A measure of the heterogeneity parameter in the enzyme systems is provided by a variance of fluorescence lifetime distribution. The possible number of deactivation channels and excited state mean lifetime can be easily derived without a priori knowledge of the complexity of studied system. Moreover, proposed model is simpler then traditional multi-exponential one, and better describes heterogeneous nature of studied systems.

Temporal binning of time-correlated single photon counting data improves exponential decay fits and imaging speed

PubMed Central

Walsh, Alex J.; Sharick, Joe T.; Skala, Melissa C.; Beier, Hope T.

2016-01-01

Time-correlated single photon counting (TCSPC) enables acquisition of fluorescence lifetime decays with high temporal resolution within the fluorescence decay. However, many thousands of photons per pixel are required for accurate lifetime decay curve representation, instrument response deconvolution, and lifetime estimation, particularly for two-component lifetimes. TCSPC imaging speed is inherently limited due to the single photon per laser pulse nature and low fluorescence event efficiencies (<10%) required to reduce bias towards short lifetimes. Here, simulated fluorescence lifetime decays are analyzed by SPCImage and SLIM Curve software to determine the limiting lifetime parameters and photon requirements of fluorescence lifetime decays that can be accurately fit. Data analysis techniques to improve fitting accuracy for low photon count data were evaluated. Temporal binning of the decays from 256 time bins to 42 time bins significantly (p<0.0001) improved fit accuracy in SPCImage and enabled accurate fits with low photon counts (as low as 700 photons/decay), a 6-fold reduction in required photons and therefore improvement in imaging speed. Additionally, reducing the number of free parameters in the fitting algorithm by fixing the lifetimes to known values significantly reduced the lifetime component error from 27.3% to 3.2% in SPCImage (p<0.0001) and from 50.6% to 4.2% in SLIM Curve (p<0.0001). Analysis of nicotinamide adenine dinucleotide–lactate dehydrogenase (NADH-LDH) solutions confirmed temporal binning of TCSPC data and a reduced number of free parameters improves exponential decay fit accuracy in SPCImage. Altogether, temporal binning (in SPCImage) and reduced free parameters are data analysis techniques that enable accurate lifetime estimation from low photon count data and enable TCSPC imaging speeds up to 6x and 300x faster, respectively, than traditional TCSPC analysis. PMID:27446663

A kinematic-based methodology for radiological protection: Runoff analysis to calculate the effective dose for internal exposure caused by ingestion of radioactive isotopes

NASA Astrophysics Data System (ADS)

Sasaki, Syota; Yamada, Tadashi; Yamada, Tomohito J.

2014-05-01

We aim to propose a kinematic-based methodology similar with runoff analysis for readily understandable radiological protection. A merit of this methodology is to produce sufficiently accurate effective doses by basic analysis. The great earthquake attacked the north-east area in Japan on March 11, 2011. The system of electrical facilities to control Fukushima Daiichi nuclear power plant was completely destroyed by the following tsunamis. From the damaged reactor containment vessels, an amount of radioactive isotopes had leaked and been diffused in the vicinity of the plant. Radiological internal exposure caused by ingestion of food containing radioactive isotopes has become an issue of great interest to the public, and has caused excessive anxiety because of a deficiency of fundamental knowledge concerning radioactivity. Concentrations of radioactivity in the human body and internal exposure have been studied extensively. Previous radiologic studies, for example, studies by International Commission on Radiological Protection(ICRP), employ a large-scale computational simulation including actual mechanism of metabolism in the human body. While computational simulation is a standard method for calculating exposure doses among radiology specialists, these methods, although exact, are too difficult for non-specialists to grasp the whole image owing to the sophistication. In this study, the human body is treated as a vessel. The number of radioactive atoms in the human body can be described by an equation of continuity, which is the only governing equation. Half-life, the period of time required for the amount of a substance decreases by half, is only parameter to calculate the number of radioactive isotopes in the human body. Half-life depends only on the kinds of nuclides, there are no arbitrary parameters. It is known that the number of radioactive isotopes decrease exponentially by radioactive decay (physical outflow). It is also known that radioactive isotopes decrease exponentially by excretion (biological outflow). The total outflow is the sum of physical outflow and biological outflow. As a result, the number of radioactive atoms in the human body also decreases exponentially. Half-life can be determined by outflow flux from the definition. Intensity of radioactivity is linear respect to the number of radioactive atoms, both are equivalent analytically. Internal total exposure can be calculated by the time integral of intensity of radioactivity. The absorbed energy into the human body per radioactive decay and the effective dose are calculated by aid of Fermi's theory of beta decay and special relativity. The effective doses calculated by the present method almost agree with those of a study by ICRP. The present method shows that standard limit in general foods for radioactive cesium enforced in Japan, 100 Bq/kg, is too excessive. When we eat foods which contain cesium-137 of 100 Bq/kg at 1 kg/d during 50 years, we receive the effective dose less than natural exposure. Similarly, it is shown that we cannot find significant health damage medically and statistically by ingestion of rice which is harvested from a paddy field deposited current (January, 2014) radioactive cesium.

Unusually large Stokes shift for a near-infrared emitting DNA-stabilized silver nanocluster

NASA Astrophysics Data System (ADS)

Ammitzbøll Bogh, Sidsel; Carro-Temboury, Miguel R.; Cerretani, Cecilia; Swasey, Steven M.; Copp, Stacy M.; Gwinn, Elisabeth G.; Vosch, Tom

2018-04-01

In this paper we present a new near-IR emitting silver nanocluster (NIR-DNA-AgNC) with an unusually large Stokes shift between absorption and emission maximum (211 nm or 5600 cm-1). We studied the effect of viscosity and temperature on the steady state and time-resolved emission. The time-resolved results on NIR-DNA-AgNC show that the relaxation dynamics slow down significantly with increasing viscosity of the solvent. In high viscosity solution, the spectral relaxation stretches well into the nanosecond scale. As a result of this slow spectral relaxation in high viscosity solutions, a multi-exponential fluorescence decay time behavior is observed, in contrast to the more mono-exponential decay in low viscosity solution.

Penetrating transmission zeros in the design of robust servomechanism systems

NASA Technical Reports Server (NTRS)

Wang, S. H.; Davison, E. J.

1981-01-01

In the design of a robust servomechanism system, it is well known that the system cannot track a reference signal whose frequency coincides with the transmission zeros of the system. This paper proposes a new design method for overcoming this difficulty. The controller to be used employs a sampler and holding device with exponential decay. It is shown that the transmission zeros of the discretized system can be shifted by changing the rate of the exponential decay of the holding device. Thus, it is possible to design a robust controller for the discretized system to track any reference signal of given frequency, even if the given frequency coincides with the transmission zeros of the original continuous-time system.

Using Differentials to Differentiate Trigonometric and Exponential Functions

ERIC Educational Resources Information Center

Dray, Tevian

2013-01-01

Starting from geometric definitions, we show how differentials can be used to differentiate trigonometric and exponential functions without limits, numerical estimates, solutions of differential equations, or integration.

On the Prony series representation of stretched exponential relaxation

NASA Astrophysics Data System (ADS)

Mauro, John C.; Mauro, Yihong Z.

2018-09-01

Stretched exponential relaxation is a ubiquitous feature of homogeneous glasses. The stretched exponential decay function can be derived from the diffusion-trap model, which predicts certain critical values of the fractional stretching exponent, β. In practical implementations of glass relaxation models, it is computationally convenient to represent the stretched exponential function as a Prony series of simple exponentials. Here, we perform a comprehensive mathematical analysis of the Prony series approximation of the stretched exponential relaxation, including optimized coefficients for certain critical values of β. The fitting quality of the Prony series is analyzed as a function of the number of terms in the series. With a sufficient number of terms, the Prony series can accurately capture the time evolution of the stretched exponential function, including its "fat tail" at long times. However, it is unable to capture the divergence of the first-derivative of the stretched exponential function in the limit of zero time. We also present a frequency-domain analysis of the Prony series representation of the stretched exponential function and discuss its physical implications for the modeling of glass relaxation behavior.

Phytoplankton productivity in relation to light intensity: A simple equation

USGS Publications Warehouse

Peterson, D.H.; Perry, M.J.; Bencala, K.E.; Talbot, M.C.

1987-01-01

A simple exponential equation is used to describe photosynthetic rate as a function of light intensity for a variety of unicellular algae and higher plants where photosynthesis is proportional to (1-e-??1). The parameter ?? (=Ik-1) is derived by a simultaneous curve-fitting method, where I is incident quantum-flux density. The exponential equation is tested against a wide range of data and is found to adequately describe P vs. I curves. The errors associated with photosynthetic parameters are calculated. A simplified statistical model (Poisson) of photon capture provides a biophysical basis for the equation and for its ability to fit a range of light intensities. The exponential equation provides a non-subjective simultaneous curve fitting estimate for photosynthetic efficiency (a) which is less ambiguous than subjective methods: subjective methods assume that a linear region of the P vs. I curve is readily identifiable. Photosynthetic parameters ?? and a are used widely in aquatic studies to define photosynthesis at low quantum flux. These parameters are particularly important in estuarine environments where high suspended-material concentrations and high diffuse-light extinction coefficients are commonly encountered. ?? 1987.

Solution of some types of differential equations: operational calculus and inverse differential operators.

PubMed

Zhukovsky, K

2014-01-01

We present a general method of operational nature to analyze and obtain solutions for a variety of equations of mathematical physics and related mathematical problems. We construct inverse differential operators and produce operational identities, involving inverse derivatives and families of generalised orthogonal polynomials, such as Hermite and Laguerre polynomial families. We develop the methodology of inverse and exponential operators, employing them for the study of partial differential equations. Advantages of the operational technique, combined with the use of integral transforms, generating functions with exponentials and their integrals, for solving a wide class of partial derivative equations, related to heat, wave, and transport problems, are demonstrated.

Photo-dynamics of roseoflavin and riboflavin in aqueous and organic solvents

NASA Astrophysics Data System (ADS)

Zirak, P.; Penzkofer, A.; Mathes, T.; Hegemann, P.

2009-03-01

Roseoflavin (8-dimethylamino-8-demethyl- D-riboflavin) and riboflavin in aqueous and organic solvents are studied by optical absorption spectroscopy, fluorescence spectroscopy, and fluorescence decay kinetics. Solvent polarity dependent absorption shifts are observed. The fluorescence quantum yields are solvent dependent. For roseoflavin the fluorescence decay shows a bi-exponential dependence (ps to sub-ps time constant, and 100 ps to a few ns time constant). The roseoflavin photo-dynamics is explained in terms of fast intra-molecular charge transfer (diabatic electron transfer) from the dimethylamino electron donor group to the pteridin carbonyl electron acceptor followed by intra-molecular charge recombination. The fast fluorescence component is due to direct locally-excited-state emission, and the slow fluorescence component is due to delayed locally-excited-state emission and charge transfer state emission. The fluorescence decay of riboflavin is mono-exponential. The S 1-state potential energy surface is determined by vibronic relaxation and solvation dynamics due to excited-state dipole moment changes (adiabatic optical electron transfer).

Studies on color-center formation in glass utilizing measurements made during 1 to 3 MeV electron irradiation

NASA Technical Reports Server (NTRS)

Swyler, K. J.; Levy, P. W.

1976-01-01

The coloring of NBS 710 glass was studied using a facility for making optical absorption measurements during and after electron irradiation. The induced absorption contains three Gaussian shaped bands. The color center growth curves contain two saturating exponential and one linear components. After irradiation the coloring decays can be described by three decreasing exponentials. At room temperature both the coloring curve plateau and coloring rate increases with increasing dose rate. Coloring measurements made at fixed dose rate but at increasing temperature indicate: (1) The coloring curve plateau decreases with increasing temperature and coloring is barely measurable near 400 C. (2) The plateau is reached more rapidly as the temperature increases. (3) The decay occurring after irradiation cannot be described by Arrhenius kinetics. At each temperature the coloring can be explained by simple kinetics. The temperature dependence of the decay can be explained if it is assumed that the thermal untrapping is controlled by a distribution of activation energies.

All-sky monitor observations of the decay of A0620-00 (Nova monocerotis 1975)

NASA Technical Reports Server (NTRS)

Kaluzienski, L. J.; Holt, S. S.; Boldt, E. A.; Serlemitsos, P. J.

1976-01-01

The All-Sky X-ray Monitor onboard Ariel 5 has observed the 3-6 keV decline of the bright transient X-ray source A0620-00 on a virtually continuous basis during the period September 1975 - March 1976. The source behavior on timescales 100 minutes is characterized by smooth, exponential decays interrupted by substantial increases in October and February. The latter increase was an order-of-magnitude rise above the extrapolated exponential fall-off, and was followed by a final rapid decline. Upper limits of 2.5% and 10% were found for any periodicities in the range 0d.2 - 10d during the early and later decay phases, respectively. A probable correlation between the optical and 3-6 keV emission from A0620-00 was noted, effectively ruling out models involving traditional optical novae in favor of Roche-lobe overflow in a binary system. The existing data on the transient X-ray sources is consistent with two distinct luminosity-lifetime classes of these objects.

Optical spectroscopy of BaY2F8:Dy3+

NASA Astrophysics Data System (ADS)

Parisi, Daniela; Toncelli, Alessandra; Tonelli, Mauro; Cavalli, Enrico; Bovero, Enrico; Belletti, Alessandro

2005-05-01

The optical spectra of the BaY2F8:Dy3+ laser crystal have been investigated in the 5000-30 000 cm-1 range. The Judd-Ofelt parametrization scheme has been applied to the analysis of the room temperature absorption spectra. The calculated radiative lifetime of the 4F9/2 state is 1.48 ms. Decay curves of the visible emission have been measured as a function of the temperature for two different Dy3+ concentrations (0.5 and 4.4%). In the case of the diluted crystal the emission profiles are single exponential with decay times consistent with the radiative lifetime. The decay curves of the concentrated crystal are not exponential and they obey the Inokuti-Hirayama model for energy transfer for an electric dipole-dipole interaction in the absence of diffusion among the donors. The emission cross section at 575 nm has been estimated using the integral β-τ method in order to assess the potentialities of this compound as a solid state laser material in the yellow region.

Temperature dependence of laser induced insulator-metal transition in VO2

NASA Astrophysics Data System (ADS)

Wang, Siming; Bar-Ad, Shimshon; Ramirez, Juan Gabriel; Huppert, Dan; Schuller, Ivan K.

2013-03-01

We performed optical pump-probe experiments on VO2 thin films with low laser fluence at temperatures ranging across the insulator-metal transition (IMT). At room temperature, the reflectivity of VO2 increases in the first 400-500 fs when pumped by 150 fs laser pulses. An exponential decay of the reflectivity is observed in the following 1 ps. Interestingly, as the temperature approaches the transition temperature (340 K), the reflectivity shows a second increase on an 80 ps time scale following the exponential decay, indicating an IMT. We propose that the decay of the reflectivity is due to electron-phonon thermalization, which raises the phonon temperature and causes a superheating of the lattice. This process provides the latent heat and induces the IMT on the 80 ps time scale. The coexistence of the insulating and metallic phases is observed in the reflectivity measurements for temperatures above 340 K. This work is supported by the Air Force Office of Scientific Research No. FA9550-12-1-0381.

In situ passivation of GaAsP nanowires.

PubMed

Himwas, C; Collin, S; Rale, P; Chauvin, N; Patriarche, G; Oehler, F; Julien, F H; Travers, L; Harmand, J-C; Tchernycheva, M

2017-12-08

We report on the structural and optical properties of GaAsP nanowires (NWs) grown by molecular-beam epitaxy. By adjusting the alloy composition in the NWs, the transition energy was tuned to the optimal value required for tandem III-V/silicon solar cells. We discovered that an unintentional shell was also formed during the GaAsP NW growth. The NW surface was passivated by an in situ deposition of a radial Ga(As)P shell. Different shell compositions and thicknesses were investigated. We demonstrate that the optimal passivation conditions for GaAsP NWs (with a gap of 1.78 eV) are obtained with a 5 nm thick GaP shell. This passivation enhances the luminescence intensity of the NWs by 2 orders of magnitude and yields a longer luminescence decay. The luminescence dynamics changes from single exponential decay with a 4 ps characteristic time in non-passivated NWs to a bi-exponential decay with characteristic times of 85 and 540 ps in NWs with GaP shell passivation.

Enhanced Elliptic Grid Generation

NASA Technical Reports Server (NTRS)

Kaul, Upender K.

2007-01-01

An enhanced method of elliptic grid generation has been invented. Whereas prior methods require user input of certain grid parameters, this method provides for these parameters to be determined automatically. "Elliptic grid generation" signifies generation of generalized curvilinear coordinate grids through solution of elliptic partial differential equations (PDEs). Usually, such grids are fitted to bounding bodies and used in numerical solution of other PDEs like those of fluid flow, heat flow, and electromagnetics. Such a grid is smooth and has continuous first and second derivatives (and possibly also continuous higher-order derivatives), grid lines are appropriately stretched or clustered, and grid lines are orthogonal or nearly so over most of the grid domain. The source terms in the grid-generating PDEs (hereafter called "defining" PDEs) make it possible for the grid to satisfy requirements for clustering and orthogonality properties in the vicinity of specific surfaces in three dimensions or in the vicinity of specific lines in two dimensions. The grid parameters in question are decay parameters that appear in the source terms of the inhomogeneous defining PDEs. The decay parameters are characteristic lengths in exponential- decay factors that express how the influences of the boundaries decrease with distance from the boundaries. These terms govern the rates at which distance between adjacent grid lines change with distance from nearby boundaries. Heretofore, users have arbitrarily specified decay parameters. However, the characteristic lengths are coupled with the strengths of the source terms, such that arbitrary specification could lead to conflicts among parameter values. Moreover, the manual insertion of decay parameters is cumbersome for static grids and infeasible for dynamically changing grids. In the present method, manual insertion and user specification of decay parameters are neither required nor allowed. Instead, the decay parameters are determined automatically as part of the solution of the defining PDEs. Depending on the shape of the boundary segments and the physical nature of the problem to be solved on the grid, the solution of the defining PDEs may provide for rates of decay to vary along and among the boundary segments and may lend itself to interpretation in terms of one or more physical quantities associated with the problem.

Exponential fading to white of black holes in quantum gravity

NASA Astrophysics Data System (ADS)

Barceló, Carlos; Carballo-Rubio, Raúl; Garay, Luis J.

2017-05-01

Quantization of the gravitational field may allow the existence of a decay channel of black holes into white holes with an explicit time-reversal symmetry. The definition of a meaningful decay probability for this channel is studied in spherically symmetric situations. As a first nontrivial calculation, we present the functional integration over a set of geometries using a single-variable function to interpolate between black-hole and white-hole geometries in a bounded region of spacetime. This computation gives a finite result which depends only on the Schwarzschild mass and a parameter measuring the width of the interpolating region. The associated probability distribution displays an exponential decay law on the latter parameter, with a mean lifetime inversely proportional to the Schwarzschild mass. In physical terms this would imply that matter collapsing to a black hole from a finite radius bounces back elastically and instantaneously, with negligible time delay as measured by external observers. These results invite to reconsider the ultimate nature of astrophysical black holes, providing a possible mechanism for the formation of black stars instead of proper general relativistic black holes. The existence of both this decay channel and black stars can be tested in future observations of gravitational waves.

Efficient full decay inversion of MRS data with a stretched-exponential approximation of the ? distribution

NASA Astrophysics Data System (ADS)

Behroozmand, Ahmad A.; Auken, Esben; Fiandaca, Gianluca; Christiansen, Anders Vest; Christensen, Niels B.

2012-08-01

We present a new, efficient and accurate forward modelling and inversion scheme for magnetic resonance sounding (MRS) data. MRS, also called surface-nuclear magnetic resonance (surface-NMR), is the only non-invasive geophysical technique that directly detects free water in the subsurface. Based on the physical principle of NMR, protons of the water molecules in the subsurface are excited at a specific frequency, and the superposition of signals from all protons within the excited earth volume is measured to estimate the subsurface water content and other hydrological parameters. In this paper, a new inversion scheme is presented in which the entire data set is used, and multi-exponential behaviour of the NMR signal is approximated by the simple stretched-exponential approach. Compared to the mono-exponential interpretation of the decaying NMR signal, we introduce a single extra parameter, the stretching exponent, which helps describe the porosity in terms of a single relaxation time parameter, and helps to determine correct initial amplitude and relaxation time of the signal. Moreover, compared to a multi-exponential interpretation of the MRS data, the decay behaviour is approximated with considerably fewer parameters. The forward response is calculated in an efficient numerical manner in terms of magnetic field calculation, discretization and integration schemes, which allows fast computation while maintaining accuracy. A piecewise linear transmitter loop is considered for electromagnetic modelling of conductivities in the layered half-space providing electromagnetic modelling of arbitrary loop shapes. The decaying signal is integrated over time windows, called gates, which increases the signal-to-noise ratio, particularly at late times, and the data vector is described with a minimum number of samples, that is, gates. The accuracy of the forward response is investigated by comparing a MRS forward response with responses from three other approaches outlining significant differences between the three approaches. All together, a full MRS forward response is calculated in about 20 s and scales so that on 10 processors the calculation time is reduced to about 3-4 s. The proposed approach is examined through synthetic data and through a field example, which demonstrate the capability of the scheme. The results of the field example agree well the information from an in-site borehole.

The effect of convective boundary condition on MHD mixed convection boundary layer flow over an exponentially stretching vertical sheet

NASA Astrophysics Data System (ADS)

Isa, Siti Suzilliana Putri Mohamed; Arifin, Norihan Md.; Nazar, Roslinda; Bachok, Norfifah; Ali, Fadzilah Md

2017-12-01

A theoretical study that describes the magnetohydrodynamic mixed convection boundary layer flow with heat transfer over an exponentially stretching sheet with an exponential temperature distribution has been presented herein. This study is conducted in the presence of convective heat exchange at the surface and its surroundings. The system is controlled by viscous dissipation and internal heat generation effects. The governing nonlinear partial differential equations are converted into ordinary differential equations by a similarity transformation. The converted equations are then solved numerically using the shooting method. The results related to skin friction coefficient, local Nusselt number, velocity and temperature profiles are presented for several sets of values of the parameters. The effects of the governing parameters on the features of the flow and heat transfer are examined in detail in this study.

Transient hydrodynamic finite-size effects in simulations under periodic boundary conditions

NASA Astrophysics Data System (ADS)

Asta, Adelchi J.; Levesque, Maximilien; Vuilleumier, Rodolphe; Rotenberg, Benjamin

2017-06-01

We use lattice-Boltzmann and analytical calculations to investigate transient hydrodynamic finite-size effects induced by the use of periodic boundary conditions. These effects are inevitable in simulations at the molecular, mesoscopic, or continuum levels of description. We analyze the transient response to a local perturbation in the fluid and obtain the local velocity correlation function via linear response theory. This approach is validated by comparing the finite-size effects on the steady-state velocity with the known results for the diffusion coefficient. We next investigate the full time dependence of the local velocity autocorrelation function. We find at long times a crossover between the expected t-3 /2 hydrodynamic tail and an oscillatory exponential decay, and study the scaling with the system size of the crossover time, exponential rate and amplitude, and oscillation frequency. We interpret these results from the analytic solution of the compressible Navier-Stokes equation for the slowest modes, which are set by the system size. The present work not only provides a comprehensive analysis of hydrodynamic finite-size effects in bulk fluids, which arise regardless of the level of description and simulation algorithm, but also establishes the lattice-Boltzmann method as a suitable tool to investigate such effects in general.

Variable δD values among major biochemicals in plants: Implications for environmental studies

NASA Astrophysics Data System (ADS)

DeBond, Nicole; Fogel, Marilyn L.; Morrill, Penny L.; Benner, Ronald; Bowden, Roxane; Ziegler, Susan

2013-06-01

The stable hydrogen isotope composition (δD) of major plant biochemicals is variable. We present δD values for cellulose, hemicelluloses and lignin of six plant species. The δD value for lignin is consistently lower than that of bulk tissue (by ˜50‰) and cellulose (by ˜100‰). We show that these differences can be used to assess the extent of degradation of organic matter from a single source. A decrease in the δDbulk of decomposing Spartina alterniflora roots and rhizomes from -72‰ to -87‰ was observed over 18 months, reflecting a relative enrichment of lignin content due to the preferential removal of polysaccharides from the detrital material. Similar changes in δ13C were observed previously during the degradation of these plant tissues. These findings indicate that the extent of organic matter degradation should be considered when using stable isotope approaches to assess possible sources of organic matter in soils and sediments. We show that the change in δDbulk of plant detritus is best described by an exponential equation, which is simpler than the multiple exponential decay (multi-G) model which best describes the change in δ13Cbulk of plant detritus. Therefore correcting for isotopic shifts caused by decomposition may be more easily accomplished using δD.

The decay width of stringy hadrons

NASA Astrophysics Data System (ADS)

Sonnenschein, Jacob; Weissman, Dorin

2018-02-01

In this paper we further develop a string model of hadrons by computing their strong decay widths and comparing them to experiment. The main decay mechanism is that of a string splitting into two strings. The corresponding total decay width behaves as Γ = π/2 ATL where T and L are the tension and length of the string and A is a dimensionless universal constant. We show that this result holds for a bosonic string not only in the critical dimension. The partial width of a given decay mode is given by Γi / Γ =Φi exp ⁡ (- 2 πCmsep2 / T) where Φi is a phase space factor, msep is the mass of the "quark" and "antiquark" created at the splitting point, and C is a dimensionless coefficient close to unity. Based on the spectra of hadrons we observe that their (modified) Regge trajectories are characterized by a negative intercept. This implies a repulsive Casimir force that gives the string a "zero point length". We fit the theoretical decay width to experimental data for mesons on the trajectories of ρ, ω, π, η, K*, ϕ, D, and Ds*, and of the baryons N, Δ, Λ, and Σ. We examine both the linearity in L and the exponential suppression factor. The linearity was found to agree with the data well for mesons but less for baryons. The extracted coefficient for mesons A = 0.095 ± 0.015 is indeed quite universal. The exponential suppression was applied to both strong and radiative decays. We discuss the relation with string fragmentation and jet formation. We extract the quark-diquark structure of baryons from their decays. A stringy mechanism for Zweig suppressed decays of quarkonia is proposed and is shown to reproduce the decay width of ϒ states. The dependence of the width on spin and flavor symmetry is discussed. We further apply this model to the decays of glueballs and exotic hadrons.

Universality in stochastic exponential growth.

PubMed

Iyer-Biswas, Srividya; Crooks, Gavin E; Scherer, Norbert F; Dinner, Aaron R

2014-07-11

Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.

Universality in Stochastic Exponential Growth

NASA Astrophysics Data System (ADS)

Iyer-Biswas, Srividya; Crooks, Gavin E.; Scherer, Norbert F.; Dinner, Aaron R.

2014-07-01

Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.

Direct measurement of electron transfer distance decay constants of single redox proteins by electrochemical tunneling spectroscopy.

PubMed

Artés, Juan M; Díez-Pérez, Ismael; Sanz, Fausto; Gorostiza, Pau

2011-03-22

We present a method to measure directly and at the single-molecule level the distance decay constant that characterizes the rate of electron transfer (ET) in redox proteins. Using an electrochemical tunneling microscope under bipotentiostatic control, we obtained current−distance spectroscopic recordings of individual redox proteins confined within a nanometric tunneling gap at a well-defined molecular orientation. The tunneling current decays exponentially, and the corresponding decay constant (β) strongly supports a two-step tunneling ET mechanism. Statistical analysis of decay constant measurements reveals differences between the reduced and oxidized states that may be relevant to the control of ET rates in enzymes and biological electron transport chains.

Nonlinear stability of the 1D Boltzmann equation in a periodic box

NASA Astrophysics Data System (ADS)

Wu, Kung-Chien

2018-05-01

We study the nonlinear stability of the Boltzmann equation in the 1D periodic box with size , where is the Knudsen number. The convergence rate is for small time region and exponential for large time region. Moreover, the exponential rate depends on the size of the domain (Knudsen number). This problem is highly nonlinear and hence we need more careful analysis to control the nonlinear term.

The mechanism of double-exponential growth in hyper-inflation

NASA Astrophysics Data System (ADS)

Mizuno, T.; Takayasu, M.; Takayasu, H.

2002-05-01

Analyzing historical data of price indices, we find an extraordinary growth phenomenon in several examples of hyper-inflation in which, price changes are approximated nicely by double-exponential functions of time. In order to explain such behavior we introduce the general coarse-graining technique in physics, the Monte Carlo renormalization group method, to the price dynamics. Starting from a microscopic stochastic equation describing dealers’ actions in open markets, we obtain a macroscopic noiseless equation of price consistent with the observation. The effect of auto-catalytic shortening of characteristic time caused by mob psychology is shown to be responsible for the double-exponential behavior.

An efficiency-decay model for Lumen maintenance

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

Bobashev, Georgiy; Baldasaro, Nicholas G.; Mills, Karmann C.

Proposed is a multicomponent model for the estimation of light-emitting diode (LED) lumen maintenance using test data that were acquired in accordance with the test standards of the Illumination Engineering Society of North America, i.e., LM-80-08. Lumen maintenance data acquired with this test do not always follow exponential decay, particularly data collected in the first 1000 h or under low-stress (e.g., low temperature) conditions. This deviation from true exponential behavior makes it difficult to use the full data set in models for the estimation of lumen maintenance decay coefficient. As a result, critical information that is relevant to the earlymore » life or low-stress operation of LED light sources may be missed. We present an efficiency-decay model approach, where all lumen maintenance data can be used to provide an alternative estimate of the decay rate constant. The approach considers a combined model wherein one part describes an initial “break-in” period and another part describes the decay in lumen maintenance. During the break-in period, several mechanisms within the LED can act to produce a small (typically <; 10%) increase in luminous flux. The effect of the break-in period and its longevity is more likely to be present at low-ambient temperatures and currents, where the discrepancy between a standard TM-21 approach and our proposed model is the largest. For high temperatures and currents, the difference between the estimates becomes nonsubstantial. Finally, our approach makes use of all the collected data and avoids producing unrealistic estimates of the decay coefficient.« less

An efficiency-decay model for Lumen maintenance

DOE PAGES

Bobashev, Georgiy; Baldasaro, Nicholas G.; Mills, Karmann C.; ...

2016-08-25

Proposed is a multicomponent model for the estimation of light-emitting diode (LED) lumen maintenance using test data that were acquired in accordance with the test standards of the Illumination Engineering Society of North America, i.e., LM-80-08. Lumen maintenance data acquired with this test do not always follow exponential decay, particularly data collected in the first 1000 h or under low-stress (e.g., low temperature) conditions. This deviation from true exponential behavior makes it difficult to use the full data set in models for the estimation of lumen maintenance decay coefficient. As a result, critical information that is relevant to the earlymore » life or low-stress operation of LED light sources may be missed. We present an efficiency-decay model approach, where all lumen maintenance data can be used to provide an alternative estimate of the decay rate constant. The approach considers a combined model wherein one part describes an initial “break-in” period and another part describes the decay in lumen maintenance. During the break-in period, several mechanisms within the LED can act to produce a small (typically <; 10%) increase in luminous flux. The effect of the break-in period and its longevity is more likely to be present at low-ambient temperatures and currents, where the discrepancy between a standard TM-21 approach and our proposed model is the largest. For high temperatures and currents, the difference between the estimates becomes nonsubstantial. Finally, our approach makes use of all the collected data and avoids producing unrealistic estimates of the decay coefficient.« less

MRI quantification of diffusion and perfusion in bone marrow by intravoxel incoherent motion (IVIM) and non-negative least square (NNLS) analysis.

PubMed

Marchand, A J; Hitti, E; Monge, F; Saint-Jalmes, H; Guillin, R; Duvauferrier, R; Gambarota, G

2014-11-01

To assess the feasibility of measuring diffusion and perfusion fraction in vertebral bone marrow using the intravoxel incoherent motion (IVIM) approach and to compare two fitting methods, i.e., the non-negative least squares (NNLS) algorithm and the more commonly used Levenberg-Marquardt (LM) non-linear least squares algorithm, for the analysis of IVIM data. MRI experiments were performed on fifteen healthy volunteers, with a diffusion-weighted echo-planar imaging (EPI) sequence at five different b-values (0, 50, 100, 200, 600 s/mm2), in combination with an STIR module to suppress the lipid signal. Diffusion signal decays in the first lumbar vertebra (L1) were fitted to a bi-exponential function using the LM algorithm and further analyzed with the NNLS algorithm to calculate the values of the apparent diffusion coefficient (ADC), pseudo-diffusion coefficient (D*) and perfusion fraction. The NNLS analysis revealed two diffusion components only in seven out of fifteen volunteers, with ADC=0.60±0.09 (10(-3) mm(2)/s), D*=28±9 (10(-3) mm2/s) and perfusion fraction=14%±6%. The values obtained by the LM bi-exponential fit were: ADC=0.45±0.27 (10(-3) mm2/s), D*=63±145 (10(-3) mm2/s) and perfusion fraction=27%±17%. Furthermore, the LM algorithm yielded values of perfusion fraction in cases where the decay was not bi-exponential, as assessed by NNLS analysis. The IVIM approach allows for measuring diffusion and perfusion fraction in vertebral bone marrow; its reliability can be improved by using the NNLS, which identifies the diffusion decays that display a bi-exponential behavior. Copyright © 2014 Elsevier Inc. All rights reserved.

A note on free and forced Rossby wave solutions: The case of a straight coast and a channel

NASA Astrophysics Data System (ADS)

Graef, Federico

2017-03-01

The free Rossby wave (RW) solutions in an ocean with a straight coast when the offshore wavenumber of incident (l1) and reflected (l2) wave are equal or complex are discussed. If l1 = l2 the energy streams along the coast and a uniformly valid solution cannot be found; if l1,2 are complex it yields the sum of an exponentially decaying and growing (away from the coast) Rossby wave. The channel does not admit these solutions as free modes. If the wavenumber vectors of the RWs are perpendicular to the coast, the boundary condition of no normal flow is trivially satisfied and the value of the streamfunction does not need to vanish at the coast. A solution that satisfies Kelvin's theorem of time-independent circulation at the coast is proposed. The forced RW solutions when the ocean's forcing is a single Fourier component are studied. If the forcing is resonant, i.e. a free Rossby wave (RW), the linear response will depend critically on whether the wave carries energy perpendicular to the channel or not. In the first case, the amplitude of the response is linear in the direction normal to the channel, y, and in the second it has a parabolic profile in y. Examples of these solutions are shown for channels with parameters resembling the Mozambique Channel, the Tasman Sea, the Denmark Strait and the English Channel. The solutions for the single coast are unbounded, except when the forcing is a RW trapped against the coast. If the forcing is non-resonant, exponentially decaying or trapped RWs could be excited in the coast and both the exponentially ;decaying; and exponentially ;growing; RW could be excited in the channel.

Obstructive sleep apnea alters sleep stage transition dynamics.

PubMed

Bianchi, Matt T; Cash, Sydney S; Mietus, Joseph; Peng, Chung-Kang; Thomas, Robert

2010-06-28

Enhanced characterization of sleep architecture, compared with routine polysomnographic metrics such as stage percentages and sleep efficiency, may improve the predictive phenotyping of fragmented sleep. One approach involves using stage transition analysis to characterize sleep continuity. We analyzed hypnograms from Sleep Heart Health Study (SHHS) participants using the following stage designations: wake after sleep onset (WASO), non-rapid eye movement (NREM) sleep, and REM sleep. We show that individual patient hypnograms contain insufficient number of bouts to adequately describe the transition kinetics, necessitating pooling of data. We compared a control group of individuals free of medications, obstructive sleep apnea (OSA), medical co-morbidities, or sleepiness (n = 374) with mild (n = 496) or severe OSA (n = 338). WASO, REM sleep, and NREM sleep bout durations exhibited multi-exponential temporal dynamics. The presence of OSA accelerated the "decay" rate of NREM and REM sleep bouts, resulting in instability manifesting as shorter bouts and increased number of stage transitions. For WASO bouts, previously attributed to a power law process, a multi-exponential decay described the data well. Simulations demonstrated that a multi-exponential process can mimic a power law distribution. OSA alters sleep architecture dynamics by decreasing the temporal stability of NREM and REM sleep bouts. Multi-exponential fitting is superior to routine mono-exponential fitting, and may thus provide improved predictive metrics of sleep continuity. However, because a single night of sleep contains insufficient transitions to characterize these dynamics, extended monitoring of sleep, probably at home, would be necessary for individualized clinical application.

Behavior of hollow balls containing granules bouncing repeatedly off the ground

NASA Astrophysics Data System (ADS)

Hu, Min; Mu, Qing-song; Luo, Ning; Li, Gang; Peng, Ning-bo

2013-07-01

An experimental study of the behavior of hollow balls filled with some granules (mung beans or millets) bouncing repeatedly off a static flat horizontal surface is presented. We observed that the bounce number of the ball is limited and decreases regularly with an increasing number of granules. Moreover, for two balls containing a different kind of granules, their bounce numbers are basically equal when the two balls have the same mass of granules. While there is no clear relationship between the first rebound height of one ball and the number of granules, there appears an exponential decay of the second rebound height with an increase of the granule number. Furthermore, a two-dimensional numerical model has been created to find out the law of the ball's rebound height and the dissipation law of the granule nested system. A generalized prediction equation to reasonably explain the law of the bounce number has also been proposed.

Kinetics of ultraweak light emission from human erythroleukemia K562 cells upon electroporation.

PubMed

Maccarrone, M; Fantini, C; Agrò, A F; Rosato, N

1998-11-11

Electroporation involves the application of an electric pulse that creates transient aqueous channels (electropores) across the lipid bilayer membranes. Here, we describe an instrument set up suitable to record ultraweak light emission from human erythroleukemia K562 cells during and immediately after delivery of electric pulses. Most of light was emitted in the first seconds after each pulse, following a complex decay which can be fitted by a double exponential equation characterized by two different time constants (T1 and T2), both in the order of seconds. T1 was approximately 10-fold shorter than T2 and both time constants were dependent on field strength of the electric pulse. The effect of various antioxidants on the amount of emitted photons and on T1 and T2 values was investigated, in order to shed some light on the chemical species responsible for cellular luminescence.

New Mathematical Functions for Vacuum System Analysis

NASA Technical Reports Server (NTRS)

Woronowicz, Michael S.

2017-01-01

A new bivariate function has been found that provides solutions of integrals having the form u (sup minus eta) e (sup u) du which arise when developing predictions for the behavior of pressure within a rigid volume under high vacuum conditions in the presence of venting as well as sources characterized by power law transient decay over the range [0,1] for eta and for u greater than or equal to 0. A few properties of the new function are explored in this work. For instance the eta equals 1/2 case reproduces the Dawson function. In addition, a slight variation of the solution technique reproduces the exponential integral for eta equals 1. The technique used to generate these functions leads to an approach for solving a more general class of nonlinear ordinary differential equations, with the potential for identifying other new functions that solve other integrals.

Slow domain reconfiguration causes power-law kinetics in a two-state enzyme.

PubMed

Grossman-Haham, Iris; Rosenblum, Gabriel; Namani, Trishool; Hofmann, Hagen

2018-01-16

Protein dynamics are typically captured well by rate equations that predict exponential decays for two-state reactions. Here, we describe a remarkable exception. The electron-transfer enzyme quiescin sulfhydryl oxidase (QSOX), a natural fusion of two functionally distinct domains, switches between open- and closed-domain arrangements with apparent power-law kinetics. Using single-molecule FRET experiments on time scales from nanoseconds to milliseconds, we show that the unusual open-close kinetics results from slow sampling of an ensemble of disordered domain orientations. While substrate accelerates the kinetics, thus suggesting a substrate-induced switch to an alternative free energy landscape of the enzyme, the power-law behavior is also preserved upon electron load. Our results show that the slow sampling of open conformers is caused by a variety of interdomain interactions that imply a rugged free energy landscape, thus providing a generic mechanism for dynamic disorder in multidomain enzymes.

Kinetic modelling of the optically stimulated conversion of peaks 5a and 5 to peak 4 in LiF:Mg,Ti (TLD-100).

PubMed

Weizman, Y; Horowitz, Y S; Oster, L

2002-01-01

The TC/LC conversion model for peaks 4, 5a and 5 in LiF:Mg,Ti (TLD-100) has been studied by solution of the coupled differential equations describing the charge carrier traffic following optical stimulation. Aspects of the model investigated were (i) the two-component exponential decay of the composite peak 5 TL intensity following the bleach, (ii) the role of retrapping during bleaching, (iii) the hole nature of peak 4 and (iv) the conversion of peak 5a traps to peak 4 traps. The high conversion efficiency is naturally explained due to the absence of conduction band competitive mechanisms in the optical ionisation of the electron in the e-h occupied structure corresponding to peak 5a and thereby leading to the hole-only occupied TC/LC leading to peak 4.

Recurrent epidemic cycles driven by intervention in a population of two susceptibility types

NASA Astrophysics Data System (ADS)

Juanico, Drandreb Earl O.

2014-03-01

Epidemics have been known to persist in the form of recurrence cycles. Despite intervention efforts through vaccination and targeted social distancing, infectious diseases like influenza continue to appear intermittently over time. I have undertaken an analysis of a stochastic epidemic model to explore the hypothesis that intervention efforts actually drive epidemic cycles. Time series from simulations of the model reveal oscillations exhibiting a similar temporal signature as influenza epidemics. The power-spectral density indicates a resonant frequency, which approximately corresponds to the apparent annual seasonality of influenza in temperate zones. Asymptotic solution to the backward Kolmogorov equation of the dynamics corresponds to an exponentially-decaying mean-exit time as a function of the intervention rate. Intervention must be implemented at a sufficiently high rate to extinguish the infection. The results demonstrate that intervention efforts can induce epidemic cycles, and that the temporal signature of cycles can provide early warning of imminent outbreaks.

Persistence and changes in bioavailability of dieldrin, DDE and heptachlor epoxide in earthworms over 45 years

USGS Publications Warehouse

Beyer, W. Nelson; Gale, Robert W.

2013-01-01

The finding of dieldrin (88 ng/g), DDE (52 ng/g), and heptachlor epoxide (19 ng/g) in earthworms from experimental plots after a single moderate application (9 kg/ha) 45 years earlier attests to the remarkable persistence of these compounds in soil and their continued uptake by soil organisms. Half-lives (with 95 % confidence intervals) in earthworms, estimated from exponential decay equations, were as follows: dieldrin 4.9 (4.3-5.7) years, DDE 5.3 (4.7-6.1) years, and heptachlor epoxide 4.3 (3.8-4.9) years. These half-lives were not significantly different from those estimated after 20 years. Concentration factors (dry weight earthworm tissue/dry weight soil) were initially high and decreased mainly during the first 11 years after application. By the end of the study, average concentration factors were 1.5 (dieldrin), 4.0 (DDE), and 1.8 (heptachlor epoxide), respectively.

The time-course of protection of the RTS,S vaccine against malaria infections and clinical disease.

PubMed

Penny, Melissa A; Pemberton-Ross, Peter; Smith, Thomas A

2015-11-04

Recent publications have reported follow-up of the RTS,S/AS01 malaria vaccine candidate Phase III trials at 11 African sites for 32 months (or longer). This includes site- and time-specific estimates of incidence and efficacy against clinical disease with four different vaccination schedules. These data allow estimation of the time-course of protection against infection associated with two different ages of vaccination, both with and without a booster dose. Using an ensemble of individual-based stochastic models, each trial cohort in the Phase III trial was simulated assuming many different hypothetical profiles for the vaccine efficacy against infection in time, for both the primary course and boosting dose and including the potential for either exponential or non-exponential decay. The underlying profile of protection was determined by Bayesian fitting of these model predictions to the site- and time-specific incidence of clinical malaria over 32 months (or longer) of follow-up. Using the same stochastic models, projections of clinical efficacy in each of the sites were modelled and compared to available observed trial data. The initial protection of RTS,S immediately following three doses is estimated as providing an efficacy against infection of 65 % (when immunizing infants aged 6-12 weeks old) and 91 % (immunizing children aged 5-17 months old at first vaccination). This protection decays relatively rapidly, with an approximately exponential decay for the 6-12 weeks old cohort (with a half-life of 7.2 months); for the 5-17 months old cohort a biphasic decay with a similar half-life is predicted, with an initial rapid decay followed by a slower decay. The boosting dose was estimated to return protection to an efficacy against infection of 50-55 % for both cohorts. Estimates of clinical efficacy by trial site are consistent with those reported in the trial for all cohorts. The site- and time-specific clinical observations from the RTS,S/AS01 trial data allowed a reasonably precise estimation of the underlying vaccine protection against infection which is consistent with common underlying efficacy and decay rates across the trial sites. This calibration suggests that the decay in efficacy against clinical disease is more rapid than that against infection because of age-shifts in the incidence of disease. The dynamical models predict that clinical effectiveness will continue to decay and that likely effects beyond the time-scale of the trial will be small.

Generalization of the event-based Carnevale-Hines integration scheme for integrate-and-fire models.

PubMed

van Elburg, Ronald A J; van Ooyen, Arjen

2009-07-01

An event-based integration scheme for an integrate-and-fire neuron model with exponentially decaying excitatory synaptic currents and double exponential inhibitory synaptic currents has been introduced by Carnevale and Hines. However, the integration scheme imposes nonphysiological constraints on the time constants of the synaptic currents, which hamper its general applicability. This letter addresses this problem in two ways. First, we provide physical arguments demonstrating why these constraints on the time constants can be relaxed. Second, we give a formal proof showing which constraints can be abolished. As part of our formal proof, we introduce the generalized Carnevale-Hines lemma, a new tool for comparing double exponentials as they naturally occur in many cascaded decay systems, including receptor-neurotransmitter dissociation followed by channel closing. Through repeated application of the generalized lemma, we lift most of the original constraints on the time constants. Thus, we show that the Carnevale-Hines integration scheme for the integrate-and-fire model can be employed for simulating a much wider range of neuron and synapse types than was previously thought.

Double slip effects of Magnetohydrodynamic (MHD) boundary layer flow over an exponentially stretching sheet with radiation, heat source and chemical reaction

NASA Astrophysics Data System (ADS)

Shaharuz Zaman, Azmanira; Aziz, Ahmad Sukri Abd; Ali, Zaileha Md

2017-09-01

The double slips effect on the magnetohydrodynamic boundary layer flow over an exponentially stretching sheet with suction/blowing, radiation, chemical reaction and heat source is presented in this analysis. By using the similarity transformation, the governing partial differential equations of momentum, energy and concentration are transformed into the non-linear ordinary equations. These equations are solved using Runge-Kutta-Fehlberg method with shooting technique in MAPLE software environment. The effects of the various parameter on the velocity, temperature and concentration profiles are graphically presented and discussed.

Multiresolution quantum chemistry in multiwavelet bases: excited states from time-dependent Hartree–Fock and density functional theory via linear response

DOE PAGES

Yanai, Takeshi; Fann, George I.; Beylkin, Gregory; ...

2015-02-25

Using the fully numerical method for time-dependent Hartree–Fock and density functional theory (TD-HF/DFT) with the Tamm–Dancoff (TD) approximation we use a multiresolution analysis (MRA) approach to present our findings. From a reformulation with effective use of the density matrix operator, we obtain a general form of the HF/DFT linear response equation in the first quantization formalism. It can be readily rewritten as an integral equation with the bound-state Helmholtz (BSH) kernel for the Green's function. The MRA implementation of the resultant equation permits excited state calculations without virtual orbitals. Moreover, the integral equation is efficiently and adaptively solved using amore » numerical multiresolution solver with multiwavelet bases. Our implementation of the TD-HF/DFT methods is applied for calculating the excitation energies of H 2, Be, N 2, H 2O, and C 2H 4 molecules. The numerical errors of the calculated excitation energies converge in proportion to the residuals of the equation in the molecular orbitals and response functions. The energies of the excited states at a variety of length scales ranging from short-range valence excitations to long-range Rydberg-type ones are consistently accurate. It is shown that the multiresolution calculations yield the correct exponential asymptotic tails for the response functions, whereas those computed with Gaussian basis functions are too diffuse or decay too rapidly. Finally, we introduce a simple asymptotic correction to the local spin-density approximation (LSDA) so that in the TDDFT calculations, the excited states are correctly bound.« less

Structural, optical absorption and photoluminescence spectral studies of Sm3+ ions in Alkaline-Earth Boro Tellurite glasses

NASA Astrophysics Data System (ADS)

Siva Rama Krishna Reddy, K.; Swapna, K.; Mahamuda, Sk.; Venkateswarlu, M.; Srinivas Prasad, M. V. V. K.; Rao, A. S.; Prakash, G. Vijaya

2018-05-01

Sm3+ ions doped Alkaline-Earth Boro Tellurite (AEBT) glasses were prepared by using conventional melt quenching technique and characterized using the spectroscopic techniques such as FT-IR, optical absorption, emission and decay spectral measurements to understand their utility in optoelectronic devices. From absorption spectra, the bonding parameters, nephelauxetic ratios were determined to know the nature of bonding between Sm3+ ions and its surrounding ligands. From the measured oscillator strengths, the Judd-Ofelt (J-O) intensity parameters were evaluated and in turn used to estimate various radiative parameters for the fluorescent levels of Sm3+ ions in AEBT glasses. The PL spectra of Sm3+ ions exhibit three emission bands corresponding to the transitions 4G5/2 → 6H5/2, 6H7/2 and 6H9/2 in the visible region for which the emission cross-sections and branching ratios were evaluated. The decay spectral profiles measured for 4G5/2 → 6H7/2 transition showed single exponential for lower concentration and non-exponential for higher concentration of doped rare earth ion in the as prepared glasses. Conversion of decay spectral profiles from single to non-exponential have been analyzed using Inokuti-Hirayama (I-H) model to understand the energy transfer mechanism involved in the decay process. CIE Chromaticity coordinates were measured using emission spectral data to identify the exact region of emission from the as-prepared glasses. From the evaluated radiative parameters, emission cross-sections and quantum efficiencies, it was observed that AEBT glass with 1 mol% of Sm3+ ions is more suitable for designing optoelectronic devices.

Optical and luminescence properties of Dy3+ ions in phosphate based glasses

NASA Astrophysics Data System (ADS)

Rasool, Sk. Nayab; Rama Moorthy, L.; Jayasankar, C. K.

2013-08-01

Phosphate glasses with compositions of 44P2O5 + 17K2O + 9Al2O3 + (30 - x)CaF2 + xDy2O3 (x = 0.05, 0.1, 0.5, 1.0, 2.0, 3.0 and 4.0 mol %) were prepared and characterized by X-ray diffraction (XRD), differential thermal analysis (DTA), Fourier transform infrared (FTIR), optical absorption, emission and decay measurements. The observed absorption bands were analyzed by using the free-ion Hamiltonian (HFI) model. The Judd-Ofelt (JO) analysis has been performed and the intensity parameters (Ωλ, λ = 2, 4, 6) were evaluated in order to predict the radiative properties of the excited states. From the emission spectra, the effective band widths (Δλeff), stimulated emission cross-sections (σ(λp)), yellow to blue (Y/B) intensity ratios and chromaticity color coordinates (x, y) have been determined. The fluorescence decays from the 4F9/2 level of Dy3+ ions were measured by monitoring the intense 4F9/2 → 6H15/2 transition (486 nm). The experimental lifetimes (τexp) are found to decrease with the increase of Dy3+ ions concentration due to the quenching process. The decay curves are perfectly single exponential at lower concentrations and gradually changes to non-exponential for higher concentrations. The non-exponential decay curves are well fitted to the Inokuti-Hirayama (IH) model for S = 6, which indicates that the energy transfer between the donor and acceptor is of dipole-dipole type. The systematic analysis of revealed that the energy transfer mechanism strongly depends on Dy3+ ions concentration and the host glass composition.

An iterative phase-space explicit discontinuous Galerkin method for stellar radiative transfer in extended atmospheres

NASA Astrophysics Data System (ADS)

de Almeida, Valmor F.

2017-07-01

A phase-space discontinuous Galerkin (PSDG) method is presented for the solution of stellar radiative transfer problems. It allows for greater adaptivity than competing methods without sacrificing generality. The method is extensively tested on a spherically symmetric, static, inverse-power-law scattering atmosphere. Results for different sizes of atmospheres and intensities of scattering agreed with asymptotic values. The exponentially decaying behavior of the radiative field in the diffusive-transparent transition region, and the forward peaking behavior at the surface of extended atmospheres were accurately captured. The integrodifferential equation of radiation transfer is solved iteratively by alternating between the radiative pressure equation and the original equation with the integral term treated as an energy density source term. In each iteration, the equations are solved via an explicit, flux-conserving, discontinuous Galerkin method. Finite elements are ordered in wave fronts perpendicular to the characteristic curves so that elemental linear algebraic systems are solved quickly by sweeping the phase space element by element. Two implementations of a diffusive boundary condition at the origin are demonstrated wherein the finite discontinuity in the radiation intensity is accurately captured by the proposed method. This allows for a consistent mechanism to preserve photon luminosity. The method was proved to be robust and fast, and a case is made for the adequacy of parallel processing. In addition to classical two-dimensional plots, results of normalized radiation intensity were mapped onto a log-polar surface exhibiting all distinguishing features of the problem studied.

Molecular Basis of Paralytic Neurotoxin Action on Voltage-Sensitive Sodium Channels

DTIC Science & Technology

1987-10-20

reaching a new steady state rate of inactivation after 5 min. Fig. 6C shows a family of sodium currents elicited by depolarizations to test potentials...Fig. 7 compares time courses of decay of sodium currents during test pulses to +10 mV for 70 msec in the presence or absence of I x 10-7 CsTx on semi...logarithmic coordinates. The decay of the sodium currents in the absence of toxin was described by a single exponential with a decay constant of 0.7

Tensor tomography on Cartan–Hadamard manifolds

NASA Astrophysics Data System (ADS)

Lehtonen, Jere; Railo, Jesse; Salo, Mikko

2018-04-01

We study the geodesic x-ray transform on Cartan–Hadamard manifolds, generalizing the x-ray transforms on Euclidean and hyperbolic spaces that arise in medical and seismic imaging. We prove solenoidal injectivity of this transform acting on functions and tensor fields of any order. The functions are assumed to be exponentially decaying if the sectional curvature is bounded, and polynomially decaying if the sectional curvature decays at infinity. This work extends the results of Lehtonen (2016 arXiv:1612.04800) to dimensions n ≥slant 3 and to the case of tensor fields of any order.

Asymptotic Analysis of Time-Dependent Neutron Transport Coupled with Isotopic Depletion and Radioactive Decay

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

Brantley, P S

2006-09-27

We describe an asymptotic analysis of the coupled nonlinear system of equations describing time-dependent three-dimensional monoenergetic neutron transport and isotopic depletion and radioactive decay. The classic asymptotic diffusion scaling of Larsen and Keller [1], along with a consistent small scaling of the terms describing the radioactive decay of isotopes, is applied to this coupled nonlinear system of equations in a medium of specified initial isotopic composition. The analysis demonstrates that to leading order the neutron transport equation limits to the standard time-dependent neutron diffusion equation with macroscopic cross sections whose number densities are determined by the standard system of ordinarymore » differential equations, the so-called Bateman equations, describing the temporal evolution of the nuclide number densities.« less

On the performance of exponential integrators for problems in magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Einkemmer, Lukas; Tokman, Mayya; Loffeld, John

2017-02-01

Exponential integrators have been introduced as an efficient alternative to explicit and implicit methods for integrating large stiff systems of differential equations. Over the past decades these methods have been studied theoretically and their performance was evaluated using a range of test problems. While the results of these investigations showed that exponential integrators can provide significant computational savings, the research on validating this hypothesis for large scale systems and understanding what classes of problems can particularly benefit from the use of the new techniques is in its initial stages. Resistive magnetohydrodynamic (MHD) modeling is widely used in studying large scale behavior of laboratory and astrophysical plasmas. In many problems numerical solution of MHD equations is a challenging task due to the temporal stiffness of this system in the parameter regimes of interest. In this paper we evaluate the performance of exponential integrators on large MHD problems and compare them to a state-of-the-art implicit time integrator. Both the variable and constant time step exponential methods of EPIRK-type are used to simulate magnetic reconnection and the Kevin-Helmholtz instability in plasma. Performance of these methods, which are part of the EPIC software package, is compared to the variable time step variable order BDF scheme included in the CVODE (part of SUNDIALS) library. We study performance of the methods on parallel architectures and with respect to magnitudes of important parameters such as Reynolds, Lundquist, and Prandtl numbers. We find that the exponential integrators provide superior or equal performance in most circumstances and conclude that further development of exponential methods for MHD problems is warranted and can lead to significant computational advantages for large scale stiff systems of differential equations such as MHD.

Determination of the thermal stress wave propagation in orthotropic hollow cylinder based on classical theory of thermoelasticity

NASA Astrophysics Data System (ADS)

Shahani, Amir Reza; Sharifi Torki, Hamid

2018-01-01

The thermoelasticity problem in a thick-walled orthotropic hollow cylinder is solved analytically using finite Hankel transform and Laplace transform. Time-dependent thermal and mechanical boundary conditions are applied on the inner and the outer surfaces of the cylinder. For solving the energy equation, the temperature itself is considered as boundary condition to be applied on both the inner and the outer surfaces of the orthotropic cylinder. Two different cases are assumed for solving the equation of motion: traction-traction problem (tractions are prescribed on both the inner and the outer surfaces) and traction-displacement (traction is prescribed on the inner surface and displacement is prescribed on the outer surface of the hollow orthotropic cylinder). Due to considering uncoupled theory, after obtaining temperature distribution, the dynamical structural problem is solved and closed-form relations are derived for radial displacement, radial and hoop stress. As a case study, exponentially decaying temperature with respect to time is prescribed on the inner surface of the cylinder and the temperature of the outer surface is considered to be zero. Owing to solving dynamical problem, the stress wave propagation and its reflections were observed after plotting the results in both cases.

On the nonlinear three dimensional instability of Stokes layers and other shear layers to pairs of oblique waves

NASA Technical Reports Server (NTRS)

Wu, Xuesong; Lee, Sang Soo; Cowley, Stephen J.

1992-01-01

The nonlinear evolution of a pair of initially oblique waves in a high Reynolds Number Stokes layer is studied. Attention is focused on times when disturbances of amplitude epsilon have O(epsilon(exp 1/3)R) growth rates, where R is the Reynolds number. The development of a pair of oblique waves is then controlled by nonlinear critical-layer effects. Viscous effects are included by studying the distinguished scaling epsilon = O(R(exp -1)). This leads to a complicated modification of the kernel function in the integro-differential amplitude equation. When viscosity is not too large, solutions to the amplitude equation develop a finite-time singularity, indicating that an explosive growth can be introduced by nonlinear effects; we suggest that such explosive growth can lead to the bursts observed in experiments. Increasing the importance of viscosity generally delays the occurrence of the finite-time singularity, and sufficiently large viscosity may lead to the disturbance decaying exponentially. For the special case when the streamwise and spanwise wavenumbers are equal, the solution can evolve into a periodic oscillation. A link between the unsteady critical-layer approach to high-Reynolds-number flow instability, and the wave vortex approach is identified.

Statistical Mechanics and the Climatology of the Arctic Sea Ice Thickness Distribution

NASA Astrophysics Data System (ADS)

Wettlaufer, John; Toppaladoddi, Srikanth

We study the seasonal changes in the thickness distribution of Arctic sea ice, g (h) , under climate forcing. Our analytical and numerical approach is based on a Fokker-Planck equation for g (h) , in which the thermodynamic growth growth rates are determined using observed climatology. In particular, the Fokker-Planck equation is coupled to an observationally consistent thermodynamic model. We find that due to the combined effects of thermodynamics and mechanics, g (h) spreads during winter and contracts during summer. This behavior is in agreement with recent satellite observations from CryoSat-2. Because g (h) is a probability density function, we quantify all of the key moments (e.g., mean thickness, fraction of thin/thick ice, mean albedo, relaxation time scales) as greenhouse-gas radiative forcing, ΔF0 , increases. The mean ice thickness decays exponentially with ΔF0 , but much slower than do solely thermodynamic models. This exhibits the crucial role that ice mechanics plays in maintaining the ice cover, by redistributing thin ice to thick ice-far more rapidly than can thermal growth alone. NASA Grant NNH13ZDA001N-CRYO and Swedish Research Council Grant No. 638-2013-9243.

A theoretical study of the relaxation of a phenyl group chemisorbed to an RDX freestanding thin film

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

Pereverzev, Andrey, E-mail: pereverzeva@missouri.edu; Sewell, Thomas D., E-mail: sewellt@missouri.edu

Energy relaxation from an excited phenyl group chemisorbed to the surface of a crystalline thin film of α-1,3,5-trinitro-1,3,5-triazacyclohexane (α-RDX) at 298 K and 1 atm is simulated using molecular dynamics. Two schemes are used to excite the phenyl group. In the first scheme, the excitation energy is added instantaneously as kinetic energy by rescaling momenta of the 11 atoms in the phenyl group. In the second scheme, the phenyl group is equilibrated at a higher temperature in the presence of static RDX geometries representative of the 298 K thin film. An analytical model based on ballistic phonon transport that requiresmore » only the harmonic part of the total Hamiltonian and includes no adjustable parameters is shown to predict, essentially quantitatively, the short-time dynamics of the kinetic energy relaxation (∼200 fs). The dynamics of the phenyl group for times longer than about 6 ps follows exponential decay and agrees qualitatively with the dynamics described by a master equation. Long-time heat propagation within the bulk of the crystal film is consistent with the heat equation.« less

Rotating flow of a nanofluid due to an exponentially stretching surface with suction

NASA Astrophysics Data System (ADS)

Salleh, Siti Nur Alwani; Bachok, Norfifah; Arifin, Norihan Md

2017-08-01

An analysis of the rotating nanofluid flow past an exponentially stretched surface with the presence of suction is studied in this work. Three different types of nanoparticles, namely, copper, titania and alumina are considered. The system of ordinary differential equations is computed numerically using a shooting method in Maple software after being transformed from the partial differential equations. This transformation has considered the similarity transformations in exponential form. The physical effect of the rotation, suction and nanoparticle volume fraction parameters on the rotating flow and heat transfer phenomena is investigated and has been described in detail through graphs. The dual solutions are found to appear when the governing parameters reach a certain range.

A de Sitter tachyon thick braneworld

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

Germán, Gabriel; Herrera-Aguilar, Alfredo; Malagón-Morejón, Dagoberto

2013-02-01

Among the multiple 5D thick braneworld models that have been proposed in the last years, in order to address several open problems in modern physics, there is a specific one involving a tachyonic bulk scalar field. Delving into this framework, a thick braneworld with a cosmological background induced on the brane is here investigated. The respective field equations — derived from the model with a warped 5D geometry — are highly non-linear equations, admitting a non-trivial solution for the warp factor and the tachyon scalar field as well, in a de Sitter 4D cosmological background. Moreover, the non-linear tachyonic scalarmore » field, that generates the brane in complicity with warped gravity, has the form of a kink-like configuration. Notwithstanding, the non-linear field equations restricting character does not allow one to easily find thick brane solutions with a decaying warp factor which leads to the localization of 4D gravity and other matter fields. We derive such a thick brane configuration altogether in this tachyon-gravity setup. When analyzing the spectrum of gravity fluctuations in the transverse traceless sector, the 4D gravity is shown to be localized due to the presence of a single zero mode bound state, separated by a continuum of massive Kaluza-Klein (KK) modes by a mass gap. It contrasts with previous results, where there is a KK massive bound excitation providing no clear physical interpretation. The mass gap is determined by the scale of the metric parameter H. Finally, the corrections to Newton's law in this model are computed and shown to decay exponentially. It is in full compliance to corrections reported in previous results (up to a constant factor) within similar braneworlds with induced 4D de Sitter metric, despite the fact that the warp factor and the massive modes have a different form.« less

Attractors of three-dimensional fast-rotating Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Trahe, Markus

The three-dimensional (3-D) rotating Navier-Stokes equations describe the dynamics of rotating, incompressible, viscous fluids. In this work, they are considered with smooth, time-independent forces and the original statements implied by the classical "Taylor-Proudman Theorem" of geophysics are rigorously proved. It is shown that fully developed turbulence of 3-D fast-rotating fluids is essentially characterized by turbulence of two-dimensional (2-D) fluids in terms of numbers of degrees of freedom. In this context, the 3-D nonlinear "resonant limit equations", which arise in a non-linear averaging process as the rotation frequency O → infinity, are studied and optimal (2-D-type) upper bounds for fractal box and Hausdorff dimensions of the global attractor as well as upper bounds for box dimensions of exponential attractors are determined. Then, the convergence of exponential attractors for the full 3-D rotating Navier-Stokes equations to exponential attractors for the resonant limit equations as O → infinity in the sense of full Hausdorff-metric distances is established. This provides upper and lower semi-continuity of exponential attractors with respect to the rotation frequency and implies that the number of degrees of freedom (attractor dimension) of 3-D fast-rotating fluids is close to that of 2-D fluids. Finally, the algebraic-geometric structure of the Poincare curves, which control the resonances and small divisor estimates for partial differential equations, is further investigated; the 3-D nonlinear limit resonant operators are characterized by three-wave interactions governed by these curves. A new canonical transformation between those curves is constructed; with far-reaching consequences on the density of the latter.

Exponential propagators for the Schrödinger equation with a time-dependent potential.

PubMed

Bader, Philipp; Blanes, Sergio; Kopylov, Nikita

2018-06-28

We consider the numerical integration of the Schrödinger equation with a time-dependent Hamiltonian given as the sum of the kinetic energy and a time-dependent potential. Commutator-free (CF) propagators are exponential propagators that have shown to be highly efficient for general time-dependent Hamiltonians. We propose new CF propagators that are tailored for Hamiltonians of the said structure, showing a considerably improved performance. We obtain new fourth- and sixth-order CF propagators as well as a novel sixth-order propagator that incorporates a double commutator that only depends on coordinates, so this term can be considered as cost-free. The algorithms require the computation of the action of exponentials on a vector similar to the well-known exponential midpoint propagator, and this is carried out using the Lanczos method. We illustrate the performance of the new methods on several numerical examples.

Large-Time Behavior of Solutions to Vlasov-Poisson-Fokker-Planck Equations: From Evanescent Collisions to Diffusive Limit

NASA Astrophysics Data System (ADS)

Herda, Maxime; Rodrigues, L. Miguel

2018-03-01

The present contribution investigates the dynamics generated by the two-dimensional Vlasov-Poisson-Fokker-Planck equation for charged particles in a steady inhomogeneous background of opposite charges. We provide global in time estimates that are uniform with respect to initial data taken in a bounded set of a weighted L^2 space, and where dependencies on the mean-free path τ and the Debye length δ are made explicit. In our analysis the mean free path covers the full range of possible values: from the regime of evanescent collisions τ → ∞ to the strongly collisional regime τ → 0. As a counterpart, the largeness of the Debye length, that enforces a weakly nonlinear regime, is used to close our nonlinear estimates. Accordingly we pay a special attention to relax as much as possible the τ -dependent constraint on δ ensuring exponential decay with explicit τ -dependent rates towards the stationary solution. In the strongly collisional limit τ → 0, we also examine all possible asymptotic regimes selected by a choice of observation time scale. Here also, our emphasis is on strong convergence, uniformity with respect to time and to initial data in bounded sets of a L^2 space. Our proofs rely on a detailed study of the nonlinear elliptic equation defining stationary solutions and a careful tracking and optimization of parameter dependencies of hypocoercive/hypoelliptic estimates.

A General Exponential Framework for Dimensionality Reduction.

PubMed

Wang, Su-Jing; Yan, Shuicheng; Yang, Jian; Zhou, Chun-Guang; Fu, Xiaolan

2014-02-01

As a general framework, Laplacian embedding, based on a pairwise similarity matrix, infers low dimensional representations from high dimensional data. However, it generally suffers from three issues: 1) algorithmic performance is sensitive to the size of neighbors; 2) the algorithm encounters the well known small sample size (SSS) problem; and 3) the algorithm de-emphasizes small distance pairs. To address these issues, here we propose exponential embedding using matrix exponential and provide a general framework for dimensionality reduction. In the framework, the matrix exponential can be roughly interpreted by the random walk over the feature similarity matrix, and thus is more robust. The positive definite property of matrix exponential deals with the SSS problem. The behavior of the decay function of exponential embedding is more significant in emphasizing small distance pairs. Under this framework, we apply matrix exponential to extend many popular Laplacian embedding algorithms, e.g., locality preserving projections, unsupervised discriminant projections, and marginal fisher analysis. Experiments conducted on the synthesized data, UCI, and the Georgia Tech face database show that the proposed new framework can well address the issues mentioned above.

Mathematics of thermal diffusion in an exponential temperature field

NASA Astrophysics Data System (ADS)

Zhang, Yaqi; Bai, Wenyu; Diebold, Gerald J.

2018-04-01

The Ludwig-Soret effect, also known as thermal diffusion, refers to the separation of gas, liquid, or solid mixtures in a temperature gradient. The motion of the components of the mixture is governed by a nonlinear, partial differential equation for the density fractions. Here solutions to the nonlinear differential equation for a binary mixture are discussed for an externally imposed, exponential temperature field. The equation of motion for the separation without the effects of mass diffusion is reduced to a Hamiltonian pair from which spatial distributions of the components of the mixture are found. Analytical calculations with boundary effects included show shock formation. The results of numerical calculations of the equation of motion that include both thermal and mass diffusion are given.

THE TEMPORAL AND SPECTRAL CHARACTERISTICS OF 'FAST RISE AND EXPONENTIAL DECAY' GAMMA-RAY BURST PULSES

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

Peng, Z. Y.; Ma, L.; Yin, Y.

2010-08-01

In this paper, we have analyzed the temporal and spectral behavior of 52 fast rise and exponential decay (FRED) pulses in 48 long-duration gamma-ray bursts (GRBs) observed by the CGRO/BATSE, using a pulse model with two shape parameters and the Band model with three shape parameters, respectively. It is found that these FRED pulses are distinguished both temporally and spectrally from those in the long-lag pulses. In contrast to the long-lag pulses, only one parameter pair indicates an evident correlation among the five parameters, which suggests that at least four parameters are needed to model burst temporal and spectral behavior.more » In addition, our studies reveal that these FRED pulses have the following correlated properties: (1) long-duration pulses have harder spectra and are less luminous than short-duration pulses and (2) the more asymmetric the pulses are, the steeper are the evolutionary curves of the peak energy (E{sub p}) in the {nu}f{sub {nu}} spectrum within the pulse decay phase. Our statistical results give some constraints on the current GRB models.« less

Model-based analysis of multi-shell diffusion MR data for tractography: How to get over fitting problems

PubMed Central

Jbabdi, Saad; Sotiropoulos, Stamatios N; Savio, Alexander M; Graña, Manuel; Behrens, Timothy EJ

2012-01-01

In this article, we highlight an issue that arises when using multiple b-values in a model-based analysis of diffusion MR data for tractography. The non-mono-exponential decay, commonly observed in experimental data, is shown to induce over-fitting in the distribution of fibre orientations when not considered in the model. Extra fibre orientations perpendicular to the main orientation arise to compensate for the slower apparent signal decay at higher b-values. We propose a simple extension to the ball and stick model based on a continuous Gamma distribution of diffusivities, which significantly improves the fitting and reduces the over-fitting. Using in-vivo experimental data, we show that this model outperforms a simpler, noise floor model, especially at the interfaces between brain tissues, suggesting that partial volume effects are a major cause of the observed non-mono-exponential decay. This model may be helpful for future data acquisition strategies that may attempt to combine multiple shells to improve estimates of fibre orientations in white matter and near the cortex. PMID:22334356

Normal Mode Analysis on the Relaxation of AN Excited Nitromethane Molecule in Argon Bath

NASA Astrophysics Data System (ADS)

Rivera-Rivera, Luis A.; Wagner, Albert F.

2017-06-01

In our previous work [Rivera-Rivera et al. J. Chem. Phys. 142, 014303 (2015).] classical molecular dynamics simulations followed, in an Ar bath, the relaxation of nitromethane (CH_3NO_2) instantaneously excited by statistically distributing 50 kcal/mol among all its internal degrees of freedom. The 300 K Ar bath was at pressures of 10 to 400 atm. Both rotational and vibrational energies exhibited multi-exponential decay. This study explores mode-specific mechanisms at work in the decay process. With the separation of rotation and vibration developed by Rhee and Kim [J. Chem. Phys. 107, 1394 (1997).], one can show that the vibrational kinetic energy decomposes only into vibrational normal modes while the rotational and Coriolis energies decompose into both vibrational and rotational normal modes. Then the saved CH_3NO_2 positions and momenta can be converted into mode-specific energies whose decay over 1000 ps can be monitored. The results identify vibrational and rotational modes that promote/resist energy lost and drive multi-exponential behavior. In addition to mode-specificity, the results show disruption of IVR with increasing pressure.

Saturation of the magnetorotational instability at large Elsasser number

NASA Astrophysics Data System (ADS)

Jamroz, B.; Julien, K.; Knobloch, E.

2008-09-01

The magnetorotational instability is investigated within the shearing box approximation in the large Elsasser number regime. In this regime, which is of fundamental importance to astrophysical accretion disk theory, shear is the dominant source of energy, but the instability itself requires the presence of a weaker vertical magnetic field. Dissipative effects are weaker still but not negligible. The regime explored retains the condition that (viscous and ohmic) dissipative forces do not play a role in the leading order linear instability mechanism. However, they are sufficiently large to permit a nonlinear feedback mechanism whereby the turbulent stresses generated by the MRI act on and modify the local background shear in the angular velocity profile. To date this response has been omitted in shearing box simulations and is captured by a reduced pde model derived here from the global MHD fluid equations using multiscale asymptotic perturbation theory. Results from numerical simulations of the reduced pde model indicate a linear phase of exponential growth followed by a nonlinear adjustment to algebraic growth and decay in the fluctuating quantities. Remarkably, the velocity and magnetic field correlations associated with these algebraic growth and decay laws conspire to achieve saturation of the angular momentum transport. The inclusion of subdominant ohmic dissipation arrests the algebraic growth of the fluctuations on a longer, dissipative time scale.

Saturation of the Magnetorotational Instability at Large Elssaser Number

NASA Astrophysics Data System (ADS)

Julien, Keith; Jamroz, Benjamin; Knobloch, Edgar

2009-11-01

The MRI is believed to play an important role in accretion disk physics in extracting angular momentum from the disk and allowing accretion to take place. The instability is investigated within the shearing box approximation under conditions of fundamental importance to astrophysical accretion disk theory. The shear is taken to be the dominant source of energy, but the instability itself requires the presence of a weaker vertical magnetic field. Dissipative effects are suffiently weak that the Elsasser number is large. Thus dissipative forces do not play a role in the leading order linear instability mechanism. However, they are sufficiently large to permit a nonlinear feedback mechanism whereby the turbulent stresses generated by the MRI act on and modify the local background shear in the angular velocity profile. To date this response has been omitted in shearing box simulations and is captured by a reduced pde model derived from the global MHD fluid equations using multiscale asymptotic perturbation theory. Results from simulations of the model indicate a linear phase of exponential growth followed by a nonlinear adjustment to algebraic growth and decay in the fluctuating quantities. Remarkably, the velocity and magnetic field correlations associated with these growth and decay laws conspire to achieve saturation of angular momentum transport.

Multi-exponential analysis of magnitude MR images using a quantitative multispectral edge-preserving filter.

PubMed

Bonny, Jean Marie; Boespflug-Tanguly, Odile; Zanca, Michel; Renou, Jean Pierre

2003-03-01

A solution for discrete multi-exponential analysis of T(2) relaxation decay curves obtained in current multi-echo imaging protocol conditions is described. We propose a preprocessing step to improve the signal-to-noise ratio and thus lower the signal-to-noise ratio threshold from which a high percentage of true multi-exponential detection is detected. It consists of a multispectral nonlinear edge-preserving filter that takes into account the signal-dependent Rician distribution of noise affecting magnitude MR images. Discrete multi-exponential decomposition, which requires no a priori knowledge, is performed by a non-linear least-squares procedure initialized with estimates obtained from a total least-squares linear prediction algorithm. This approach was validated and optimized experimentally on simulated data sets of normal human brains.

Time since death and decay rate constants of Norway spruce and European larch deadwood in subalpine forests determined using dendrochronology and radiocarbon dating

NASA Astrophysics Data System (ADS)

Petrillo, M.; Cherubini, P.; Fravolini, G.; Ascher, J.; Schärer, M.; Synal, H.-A.; Bertoldi, D.; Camin, F.; Larcher, R.; Egli, M.

2015-09-01

Due to the large size and highly heterogeneous spatial distribution of deadwood, the time scales involved in the coarse woody debris (CWD) decay of Picea abies (L.) Karst. and Larix decidua Mill. in Alpine forests have been poorly investigated and are largely unknown. We investigated the CWD decay dynamics in an Alpine valley in Italy using the five-decay class system commonly employed for forest surveys, based on a macromorphological and visual assessment. For the decay classes 1 to 3, most of the dendrochronological samples were cross-dated to assess the time that had elapsed since tree death, but for decay classes 4 and 5 (poorly preserved tree rings) and some others not having enough tree rings, radiocarbon dating was used. In addition, density, cellulose and lignin data were measured for the dated CWD. The decay rate constants for spruce and larch were estimated on the basis of the density loss using a single negative exponential model. In the decay classes 1 to 3, the ages of the CWD were similar varying between 1 and 54 years for spruce and 3 and 40 years for larch with no significant differences between the classes; classes 1-3 are therefore not indicative for deadwood age. We found, however, distinct tree species-specific differences in decay classes 4 and 5, with larch CWD reaching an average age of 210 years in class 5 and spruce only 77 years. The mean CWD rate constants were 0.012 to 0.018 yr-1 for spruce and 0.005 to 0.012 yr-1 for larch. Cellulose and lignin time trends half-lives (using a multiple-exponential model) could be derived on the basis of the ages of the CWD. The half-lives for cellulose were 21 yr for spruce and 50 yr for larch. The half-life of lignin is considerably higher and may be more than 100 years in larch CWD.

False-vacuum decay in generalized extended inflation

NASA Technical Reports Server (NTRS)

Holman, Richard; Kolb, Edward W.; Vadas, Sharon L.; Wang, Yun

1990-01-01

False-vacuum decay was studied in context of generalized extended inflationary theories, and the bubble nucleation rates was computed for these theories in the limit of G(sub N) yields 0. It was found that the time dependence of the nucleation rate can be exponentially strong through the time dependence of the Jordan-Brans-Dicke field. This can have a pronounced effect on whether extended inflation can be successfully implemented.

VizieR Online Data Catalog: Catalog of Kepler flare stars (Van Doorsselaere+, 2017)

NASA Astrophysics Data System (ADS)

van Doorsselaere, T.; Shariati, H.; Debosscher, J.

2017-11-01

With an automated detection method, we have identified stellar flares in the long cadence observations of Kepler during quarter 15. We list each flare time for the respective Kepler objects. Furthermore, we list the flare amplitude and decay time after fitting the flare light curve with an exponential decay. Flare start times in long cadence data of Kepler during quarter 15. (1 data file).

Disorder in Protein Crystals.

NASA Astrophysics Data System (ADS)

Clarage, James Braun, II

1990-01-01

Methods have been developed for analyzing the diffuse x-ray scattering in the halos about a crystal's Bragg reflections as a means of determining correlations in atomic displacements in protein crystals. The diffuse intensity distribution for rhombohedral insulin, tetragonal lysozyme, and triclinic lysozyme crystals was best simulated in terms of exponential displacement correlation functions. About 90% of the disorder can be accounted for by internal movements correlated with a decay distance of about 6A; the remaining 10% corresponds to intermolecular movements that decay in a distance the order of size of the protein molecule. The results demonstrate that protein crystals fit into neither the Einstein nor the Debye paradigms for thermally fluctuating crystalline solids. Unlike the Einstein model, there are correlations in the atomic displacements, but these correlations decay more steeply with distance than predicted by the Debye-Waller model for an elastic solid. The observed displacement correlations are liquid -like in the sense that they decay exponentially with the distance between atoms, just as positional correlations in a liquid. This liquid-like disorder is similar to the disorder observed in 2-D crystals of polystyrene latex spheres, and similar systems where repulsive interactions dominate; hence, these colloidal crystals appear to provide a better analogy for the dynamics of protein crystals than perfectly elastic lattices.

Depth-Penetrating Temperature Measurements of Thermal Barrier Coatings Incorporating Thermographic Phosphors

NASA Technical Reports Server (NTRS)

Eldridge, Jeffrey I.; Bencic, Timothy J..; Allison, Stephen W.; Beshears, David L.

2003-01-01

Thermographic phosphors have been previously demonstrated to provide effective non-contact, emissivity-independent surface temperature measurements. Because of the translucent nature of thermal barrier coatings (TBCs), thermographic phosphor-based temperature measurements can be extended beyond the surface to provide depth-selective temperature measurements by incorporating the thermographic phosphor layer at the depth where the temperature measurement is desired. In this paper, thermographic phosphor (Y2O3:Eu) fluorescence decay time measurements are demonstrated to provide through-the-coating thickness temperature readings up to 1100 C with the phosphor layer residing beneath a 100 micron thick TBC (plasma-sprayed 8wt% yttria-stabilized zirconia). With an appropriately chosen excitation wavelength and detection configuration, it is shown that sufficient phosphor emission is generated to provide effective temperature measurements, despite the attenuation of both the excitation and emission intensities by the overlying TBC. This depth-penetrating temperature measurement capability should prove particularly useful for TBC diagnostics where a large thermal gradient is typically present across the TBC thickness. The fluorescence decay from the Y2O3:Eu layer exhibited both an initial short-term exponential rise and a longer-term exponential decay. The rise time constant was demonstrated to provide better temperature indication below 500 C while the decay time constant was a better indicator at higher temperatures.

Recurrence time statistics for finite size intervals

NASA Astrophysics Data System (ADS)

Altmann, Eduardo G.; da Silva, Elton C.; Caldas, Iberê L.

2004-12-01

We investigate the statistics of recurrences to finite size intervals for chaotic dynamical systems. We find that the typical distribution presents an exponential decay for almost all recurrence times except for a few short times affected by a kind of memory effect. We interpret this effect as being related to the unstable periodic orbits inside the interval. Although it is restricted to a few short times it changes the whole distribution of recurrences. We show that for systems with strong mixing properties the exponential decay converges to the Poissonian statistics when the width of the interval goes to zero. However, we alert that special attention to the size of the interval is required in order to guarantee that the short time memory effect is negligible when one is interested in numerically or experimentally calculated Poincaré recurrence time statistics.

Numerical investigation of MHD flow with Soret and Dufour effect

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Nasir, Tehreem; Khan, Muhammad Ijaz; Alsaedi, Ahmed

2018-03-01

This paper describes the flow due to an exponentially curved surface subject to Soret and Dufour effects. Nonlinear velocity is considered. Exponentially curved stretchable sheet induced the flow. Fluid is electrical conducting through constant applied magnetic field. The governing flow expressions are reduced to ordinary ones and then tackled by numerical technique (Built-in-Shooting). Impacts of various flow variables on the dimensionless velocity, concentration and temperature fields are graphically presented and discussed in detail. Skin friction coefficient and Sherwood and Nusselt numbers are studied through graphs. Furthermore it is observed that Soret and Dufour variables regulate heat and mass transfer rates. It is also noteworthy that velocity decays for higher magnetic variable. Skin friction magnitude decays via curvature and magnetic variables. Also mass transfer gradient or rate of mass transport enhances for higher estimations of curvature parameter and Schmidt number.

Thermodynamics and kinetics of the sulfation of porous calcium silicate

NASA Technical Reports Server (NTRS)

Miller, R. A.; Kohl, F. J.

1981-01-01

The sulfation of plasma sprayed calcium silicate in flowing SO2/air mixtures at 900 and 1000 C was investigated thermogravimetrically. Reaction products were analyzed using electron microprobe and X-ray diffraction analysis techniques, and results were compared with thermodynamic predictions. The percentage, by volume, of SO2 in air was varied between 0.036 and 10 percent. At 10 percent SO2 the weight gain curve displays a concave downward shoulder early in the sulfation process. An analytical model was developed which treats the initial process as one which decays exponentially with increasing time and the subsequent process as one which decays exponentially with increasing weight gain. At lower SO2 levels the initial rate is controlled by the reactant flow rate. At 1100 C and 0.036 percent SO2 there is no reaction, in agreement with thermodynamic predictions.

Stimulation Efficiency With Decaying Exponential Waveforms in a Wirelessly Powered Switched-Capacitor Discharge Stimulation System.

PubMed

Lee, Hyung-Min; Howell, Bryan; Grill, Warren M; Ghovanloo, Maysam

2018-05-01

The purpose of this study was to test the feasibility of using a switched-capacitor discharge stimulation (SCDS) system for electrical stimulation, and, subsequently, determine the overall energy saved compared to a conventional stimulator. We have constructed a computational model by pairing an image-based volume conductor model of the cat head with cable models of corticospinal tract (CST) axons and quantified the theoretical stimulation efficiency of rectangular and decaying exponential waveforms, produced by conventional and SCDS systems, respectively. Subsequently, the model predictions were tested in vivo by activating axons in the posterior internal capsule and recording evoked electromyography (EMG) in the contralateral upper arm muscles. Compared to rectangular waveforms, decaying exponential waveforms with time constants >500 μs were predicted to require 2%-4% less stimulus energy to activate directly models of CST axons and 0.4%-2% less stimulus energy to evoke EMG activity in vivo. Using the calculated wireless input energy of the stimulation system and the measured stimulus energies required to evoke EMG activity, we predict that an SCDS implantable pulse generator (IPG) will require 40% less input energy than a conventional IPG to activate target neural elements. A wireless SCDS IPG that is more energy efficient than a conventional IPG will reduce the size of an implant, require that less wireless energy be transmitted through the skin, and extend the lifetime of the battery in the external power transmitter.

Spectroscopic investigations of Nd3+ doped Lithium Lead Alumino Borate glasses for 1.06 μm laser applications

NASA Astrophysics Data System (ADS)

Deopa, Nisha; Rao, A. S.; Gupta, Mohini; Vijaya Prakash, G.

2018-01-01

Neodymium doped lithium lead alumino borate glasses were synthesized with the molar composition 10Li2Osbnd 10PbOsbnd (10-x) Al2O3sbnd 70B2O3sbnd x Nd2O3 (where, x = 0.1, 0.5, 1.0, 1.5, 2.0 and 2.5 mol %) via conventional melt quenching technique to understand their lasing potentialities using the absorption, emission and photoluminescence decay spectral measurements. The oscillator strengths measured from the absorption spectra were used to estimate the Judd-Ofelt intensity parameters using least square fitting procedure. The emission spectra recorded for the as-prepared glasses under investigation exhibit two emission transitions 4F3/2 → 4I11/2 (1063 nm) and 4F3/2 → 4I9/2 (1350 nm) for which radiative parameters have been evaluated. The emission intensity increases with increase in Nd3+ ion concentration up to 1 mol % and beyond concentration quenching took place. The decay profile shows single exponential nature for lower Nd3+ ion concentration and non-exponential for higher concentration. To elucidate the nature of energy transfer process, the non-exponential decay curves were well fitted to Inokuti-Hirayama model. The relatively higher values of emission cross-sections, branching ratios and quantum efficiency values obtained for 1.0 mol% of Nd3+ ions in LiPbAlB glass suggests it's aptness in generating lasing action at 1063 nm in NIR region.

General solution of the Bagley-Torvik equation with fractional-order derivative

NASA Astrophysics Data System (ADS)

Wang, Z. H.; Wang, X.

2010-05-01

This paper investigates the general solution of the Bagley-Torvik equation with 1/2-order derivative or 3/2-order derivative. This fractional-order differential equation is changed into a sequential fractional-order differential equation (SFDE) with constant coefficients. Then the general solution of the SFDE is expressed as the linear combination of fundamental solutions that are in terms of α-exponential functions, a kind of functions that play the same role of the classical exponential function. Because the number of fundamental solutions of the SFDE is greater than 2, the general solution of the SFDE depends on more than two free (independent) constants. This paper shows that the general solution of the Bagley-Torvik equation involves actually two free constants only, and it can be determined fully by the initial displacement and initial velocity.

Experimental Magnetohydrodynamic Energy Extraction from a Pulsed Detonation

DTIC Science & Technology

2015-03-01

experimental data taken in this thesis will follow voltage profiles similar to Fig. 2. Notice the initial section in Fig. 2 shows exponential decay consistent...equal that time constant. The exponential curves in Fig. 2 show how changing the time constant can change the charge and/or discharge rate of the...see Fig. 1), at a sampling rate of 1 MHz. Shielded wire and a common ground were used throughout the DAQ system to avoid capacitive issues in the

On the decay of solutions to the 2D Neumann exterior problem for the wave equation

NASA Astrophysics Data System (ADS)

Secchi, Paolo; Shibata, Yoshihiro

We consider the exterior problem in the plane for the wave equation with a Neumann boundary condition and study the asymptotic behavior of the solution for large times. For possible application we are interested to show a decay estimate which does not involve weighted norms of the initial data. In the paper we prove such an estimate, by a combination of the estimate of the local energy decay and decay estimates for the free space solution.

Inference of the ring current ion composition by means of charge exchange decay

NASA Technical Reports Server (NTRS)

Smith, P. H.; Bewtra, N. K.; Hoffman, R. A.

1978-01-01

The analysis of the measured ion fluxes during the several day storm recovery period and the assumption that beside hydrogen other ions were present and that the decays were exponential in nature, it was possible to establish three separate lifetimes for the ions. These fitted decay lifetimes are in excellent agreement with the expected charge exchange decay lifetimes for H(+), O(+), and He(+) in the energy and L-value range of the data. This inference technique, thus, establishes the presence of measurable and appreciable quantities of oxygen and helium ions as well as protons in the storm-time ring current. Indications that He(+) may also be present under these same conditions were found.

Bound-preserving modified exponential Runge-Kutta discontinuous Galerkin methods for scalar hyperbolic equations with stiff source terms

NASA Astrophysics Data System (ADS)

Huang, Juntao; Shu, Chi-Wang

2018-05-01

In this paper, we develop bound-preserving modified exponential Runge-Kutta (RK) discontinuous Galerkin (DG) schemes to solve scalar hyperbolic equations with stiff source terms by extending the idea in Zhang and Shu [43]. Exponential strong stability preserving (SSP) high order time discretizations are constructed and then modified to overcome the stiffness and preserve the bound of the numerical solutions. It is also straightforward to extend the method to two dimensions on rectangular and triangular meshes. Even though we only discuss the bound-preserving limiter for DG schemes, it can also be applied to high order finite volume schemes, such as weighted essentially non-oscillatory (WENO) finite volume schemes as well.

Development of a ReaxFF Potential for Carbon Condensed Phases and Its Application to the Thermal Fragmentation of a Large Fullerene

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

Srinivasan, Sriram Goverapet; van Duin, Adri C. T.; Ganesh, P.

2015-01-20

In this article, we report the development of a ReaxFF reactive potential that can accurately describe the chemistry and dynamics of carbon condensed phases. Density functional theory (DFT)-based calculations were performed to obtain the equation of state for graphite and diamond and the formation energies of defects in graphene and amorphous phases from fullerenes. The DFT data were used to reparametrize ReaxFFCHO, resulting in a new potential called ReaxFFC-2013. ReaxFFC-2013 accurately predicts the atomization energy of graphite and closely reproduces the DFT-based energy difference between graphite and diamond, and the barrier for transition from graphite to diamond. ReaxFFC-2013 also accuratelymore » predicts the DFT-based energy barrier for Stone–Wales transformation in a C60(Ih) fullerene through the concerted rotation of a C2 unit. Later, MD simulations of a C180 fullerene using ReaxFFC-2013 suggested that the thermal fragmentation of these giant fullerenes is an exponential function of time. An Arrhenius-type equation was fit to the decay rate, giving an activation energy of 7.66 eV for the loss of carbon atoms from the fullerene. Although the decay of the molecule occurs primarily via the loss of C2 units, we observed that, with an increase in temperature, the probability of loss of larger fragments increases. The ReaxFFC-2013 potential developed in this work, and the results obtained on fullerene fragmentation, provide an important step toward the full computational chemical modeling of coal pyrolysis, soot incandescence, high temperature erosion of graphitic rocket nozzles, and ablation of carbon-based spacecraft materials during atmospheric reentry.« less

Development of a ReaxFF potential for carbon condensed phases and its application to the thermal fragmentation of a large fullerene

DOE PAGES

Srinivasan, Sriram Goverapet; Adri C. T. van Duin; Ganesh, Panchapakesan

2015-01-06

In this paper, we report the development of a ReaxFF reactive potential that can accurately describe the chemistry and dynamics of carbon condensed phases. Density functional theory (DFT)-based calculations were performed to obtain the equation of state for graphite and diamond and the formation energies of defects in graphene and amorphous phases from fullerenes. The DFT data were used to reparametrize ReaxFF CHO, resulting in a new potential called ReaxFF C-2013. ReaxFF C-2013 accurately predicts the atomization energy of graphite and closely reproduces the DFT-based energy difference between graphite and diamond, and the barrier for transition from graphite to diamond.more » ReaxFF C-2013 also accurately predicts the DFT-based energy barrier for Stone–Wales transformation in a C 60(I h) fullerene through the concerted rotation of a C 2 unit. Later, MD simulations of a C 180 fullerene using ReaxFF C-2013 suggested that the thermal fragmentation of these giant fullerenes is an exponential function of time. An Arrhenius-type equation was fit to the decay rate, giving an activation energy of 7.66 eV for the loss of carbon atoms from the fullerene. Although the decay of the molecule occurs primarily via the loss of C 2 units, we observed that, with an increase in temperature, the probability of loss of larger fragments increases. Finally, the ReaxFF C-2013 potential developed in this work, and the results obtained on fullerene fragmentation, provide an important step toward the full computational chemical modeling of coal pyrolysis, soot incandescence, high temperature erosion of graphitic rocket nozzles, and ablation of carbon-based spacecraft materials during atmospheric reentry.« less

Inference of the ring current ion composition by means of charge exchange decay

NASA Technical Reports Server (NTRS)

Smith, P. H.; Hoffman, R. A.; Bewtra, N. K.

1981-01-01

The analysis of data from the Explorer 45 (S3-A) electrostatic analyzer in the energy range 5-30 keV has provided some new results on the ring current ion composition. It has been well established that the storm time ring current has a decay time of several days, during which the particle fluxes decrease nearly monotonically. By analyzing the measured ion fluxes during the several day storm recovery period and assuming that beside hydrogen other ions were present and that the decays were exponential in nature, three separate lifetimes for the ions were established. These fitted decay lifetimes are in excellent agreement with the expected charge exchange decay lifetimes for H(+), O(+) and He(+) in the energy and L value range of the data.

On the decay of outbursts in dwarf novae nad X-ray novae

NASA Technical Reports Server (NTRS)

Cannizzo, John K.

1994-01-01

We perform computations using a time-dependent model for the accretion disk limit-cycle mechanism to examine the decay of the optical light following the peak of a dwarf nova outburst. We present the results of a parameter study of the physical input variables which affect the decay rate. In the model, the decay is brought about by a cooling transition front which begins at large radii in the disk and moves inward. The nature of the decay is strongly influenced by the radial dependence of the accretion disk viscosity parameter alpha. To obtain exponential decays for typical dwarf nova parameters, we require alpha proportional to r(exp epsilon(sub 0)), where epsilon(sub 0) approximately = 0.3-0.4. The exact value of epsilon(sub 0) which produces exponential decays depends on factors such as the mass of the accreting star and the inner radius of the accretion disk. Therefore, the observed ubiquity of exponential decays in two different types of systems (dwarf novae and X-ray novae) leads us to believe that alpha is an unnatural scaling for the viscosity. The physics of the cooling transition front must be self-regulating in that the timescale (-parital derivative of lnSigma(r)/partial derivative +)(exp -1) (where Sigma is the surface density) for mass extraction across the front remains constant. This may be consistent with a scaling alpha proportional to (h/r)(exp n), where h is the local disk semi-thickness and n approximately 1-2. As regards the speed of the cooling front, we find v(sub F)(r) proportional to r(exp p), where p approximately 3 at large radii, with an abrupt transition to p approximately 0 at some smaller radius. The r(exp 3) dependence is much steeper than has been found by previous workers and appears to result from the strong variation of specific heat within the cooling front when the front resides at a large radius in the disk. The outflow of disk material across the cooling front causes a significant departure of dln T(sub dff0/dln r from the standard value of -0.75 (expected from steady state accretion) within about 0.2 dex in radius of the break associated with the cooling front -- T(sub eff) aproximately 10(exp 3.9) K (r/10(exp 10 cm)) (exp -0.1). These effects should be observable with eclipse mapping. Finally, it appears that the relatively slow decay rate for the optical flux in the 1975 outburst of A0620-00 can be accounted for if the primary is a approximately 10 Solar mass black hole.

Mechanisms of chaos in billiards: dispersing, defocusing and nothing else

NASA Astrophysics Data System (ADS)

Bunimovich, Leonid A.

2018-02-01

We explain and justify that the only mechanisms of chaotic dynamics for billiards are dispersing and defocusing. We also introduce boomerang billiards which dynamics demonstrate that two rather broadly accepted views about some features of nonlinear dynamics are actually wrong. Namely correlations in billiards having focusing components of the boundary can decay exponentially, and continuous time correlations for a billiard flow may decay faster than discrete time correlations for a billiard map.

Theoretical analysis of exponential transversal method of lines for the diffusion equation

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

Salazar, A.; Raydan, M.; Campo, A.

1996-12-31

Recently a new approximate technique to solve the diffusion equation was proposed by Campo and Salazar. This new method is inspired on the Method of Lines (MOL) with some insight coming from the method of separation of variables. The proposed method, the Exponential Transversal Method of Lines (ETMOL), utilizes an exponential variation to improve accuracy in the evaluation of the time derivative. Campo and Salazar have implemented this method in a wide range of heat/mass transfer applications and have obtained surprisingly good numerical results. In this paper, the authors study the theoretical properties of ETMOL in depth. In particular, consistency,more » stability and convergence are established in the framework of the heat/mass diffusion equation. In most practical applications the method presents a very reduced truncation error in time and its different versions are proven to be unconditionally stable in the Fourier sense. Convergence of the solutions is then established. The theory is corroborated by several analytical/numerical experiments.« less

A Fourier method for the analysis of exponential decay curves.

PubMed

Provencher, S W

1976-01-01

A method based on the Fourier convolution theorem is developed for the analysis of data composed of random noise, plus an unknown constant "base line," plus a sum of (or an integral over a continuous spectrum of) exponential decay functions. The Fourier method's usual serious practical limitation of needing high accuracy data over a very wide range is eliminated by the introduction of convergence parameters and a Gaussian taper window. A computer program is described for the analysis of discrete spectra, where the data involves only a sum of exponentials. The program is completely automatic in that the only necessary inputs are the raw data (not necessarily in equal intervals of time); no potentially biased initial guesses concerning either the number or the values of the components are needed. The outputs include the number of components, the amplitudes and time constants together with their estimated errors, and a spectral plot of the solution. The limiting resolving power of the method is studied by analyzing a wide range of simulated two-, three-, and four-component data. The results seem to indicate that the method is applicable over a considerably wider range of conditions than nonlinear least squares or the method of moments.

Heavy tailed bacterial motor switching statistics define macroscopic transport properties during upstream contamination by E. coli

NASA Astrophysics Data System (ADS)

Figueroa-Morales, N.; Rivera, A.; Altshuler, E.; Darnige, T.; Douarche, C.; Soto, R.; Lindner, A.; Clément, E.

The motility of E. Coli bacteria is described as a run and tumble process. Changes of direction correspond to a switch in the flagellar motor rotation. The run time distribution is described as an exponential decay of characteristic time close to 1s. Remarkably, it has been demonstrated that the generic response for the distribution of run times is not exponential, but a heavy tailed power law decay, which is at odds with the motility findings. We investigate the consequences of the motor statistics in the macroscopic bacterial transport. During upstream contamination processes in very confined channels, we have identified very long contamination tongues. Using a stochastic model considering bacterial dwelling times on the surfaces related to the run times, we are able to reproduce qualitatively and quantitatively the evolution of the contamination profiles when considering the power law run time distribution. However, the model fails to reproduce the qualitative dynamics when the classical exponential run and tumble distribution is considered. Moreover, we have corroborated the existence of a power law run time distribution by means of 3D Lagrangian tracking. We then argue that the macroscopic transport of bacteria is essentially determined by the motor rotation statistics.

Floquet states of a kicked particle in a singular potential: Exponential and power-law profiles

NASA Astrophysics Data System (ADS)

Paul, Sanku; Santhanam, M. S.

2018-03-01

It is well known that, in the chaotic regime, all the Floquet states of kicked rotor system display an exponential profile resulting from dynamical localization. If the kicked rotor is placed in an additional stationary infinite potential well, its Floquet states display power-law profile. It has also been suggested in general that the Floquet states of periodically kicked systems with singularities in the potential would have power-law profile. In this work, we study the Floquet states of a kicked particle in finite potential barrier. By varying the height of finite potential barrier, the nature of transition in the Floquet state from exponential to power-law decay profile is studied. We map this system to a tight-binding model and show that the nature of decay profile depends on energy band spanned by the Floquet states (in unperturbed basis) relative to the potential height. This property can also be inferred from the statistics of Floquet eigenvalues and eigenvectors. This leads to an unusual scenario in which the level spacing distribution, as a window in to the spectral correlations, is not a unique characteristic for the entire system.

Nanoconfined ionic liquids: Disentangling electrostatic and viscous forces

NASA Astrophysics Data System (ADS)

Lhermerout, Romain; Perkin, Susan

2018-01-01

Recent reports of surface forces across nanoconfined ionic liquids have revealed the existence of an anomalously long-ranged interaction apparently of electrostatic origin. Ionic liquids are viscous, and therefore it is important to inspect rigorously whether the observed repulsive forces are indeed equilibrium forces or, rather, arise from the viscous force during drainage of the fluid between two confining surfaces. In this paper we present our direct measurements of surface forces between mica sheets approaching in the ionic liquid [C2C1Im ] [NTf2] , exploring three orders of magnitude in approach velocity. Trajectories are systematically fitted by solving the equation of motion, allowing us to disentangle the viscous and equilibrium contributions. First, we find that the drainage obeys classical hydrodynamics with a negative slip boundary condition in the range of the structural force, implying that a nanometer -thick portion of the liquid in the vicinity of the solid surface is composed of ordered molecules that do not contribute to the flow. Second, we show that a long-range static force must indeed be invoked, in addition to the viscous force, in order to describe the data quantitatively. This equilibrium interaction decays exponentially and with decay length in agreement with the screening length reported for the same system in previous studies. In those studies the decay was simply checked to be independent of velocity and measured at a low approach rate, rather than explicitly taking account of viscous effects: we explain why this gives indistinguishable outcomes for the screening length by noting that the viscous force is linear to very good approximation over a wide range of distances.

Exponential decline of aftershocks of the M7.9 1868 great Kau earthquake, Hawaii, through the 20th century

USGS Publications Warehouse

Klein, F.W.; Wright, Tim

2008-01-01

The remarkable catalog of Hawaiian earthquakes going back to the 1820s is based on missionary diaries, newspaper accounts, and instrumental records and spans the great M7.9 Kau earthquake of April 1868 and its aftershock sequence. The earthquake record since 1868 defines a smooth curve complete to M5.2 of the declining rate into the 21st century, after five short volcanic swarms are removed. A single aftershock curve fits the earthquake record, even with numerous M6 and 7 main shocks and eruptions. The timing of some moderate earthquakes may be controlled by magmatic stresses, but their overall long-term rate reflects one of aftershocks of the Kau earthquake. The 1868 earthquake is, therefore, the largest and most controlling stress event in the 19th and 20th centuries. We fit both the modified Omori (power law) and stretched exponential (SE) functions to the earthquakes. We found that the modified Omori law is a good fit to the M ??? 5.2 earthquake rate for the first 10 years or so and the more rapidly declining SE function fits better thereafter, as supported by three statistical tests. The switch to exponential decay suggests that a possible change in aftershock physics may occur from rate and state fault friction, with no change in the stress rate, to viscoelastic stress relaxation. The 61-year exponential decay constant is at the upper end of the range of geodetic relaxation times seen after other global earthquakes. Modeling deformation in Hawaii is beyond the scope of this paper, but a simple interpretation of the decay suggests an effective viscosity of 1019 to 1020 Pa s pertains in the volcanic spreading of Hawaii's flanks. The rapid decline in earthquake rate poses questions for seismic hazard estimates in an area that is cited as one of the most hazardous in the United States.

Rapid Global Fitting of Large Fluorescence Lifetime Imaging Microscopy Datasets

PubMed Central

Warren, Sean C.; Margineanu, Anca; Alibhai, Dominic; Kelly, Douglas J.; Talbot, Clifford; Alexandrov, Yuriy; Munro, Ian; Katan, Matilda

2013-01-01

Fluorescence lifetime imaging (FLIM) is widely applied to obtain quantitative information from fluorescence signals, particularly using Förster Resonant Energy Transfer (FRET) measurements to map, for example, protein-protein interactions. Extracting FRET efficiencies or population fractions typically entails fitting data to complex fluorescence decay models but such experiments are frequently photon constrained, particularly for live cell or in vivo imaging, and this leads to unacceptable errors when analysing data on a pixel-wise basis. Lifetimes and population fractions may, however, be more robustly extracted using global analysis to simultaneously fit the fluorescence decay data of all pixels in an image or dataset to a multi-exponential model under the assumption that the lifetime components are invariant across the image (dataset). This approach is often considered to be prohibitively slow and/or computationally expensive but we present here a computationally efficient global analysis algorithm for the analysis of time-correlated single photon counting (TCSPC) or time-gated FLIM data based on variable projection. It makes efficient use of both computer processor and memory resources, requiring less than a minute to analyse time series and multiwell plate datasets with hundreds of FLIM images on standard personal computers. This lifetime analysis takes account of repetitive excitation, including fluorescence photons excited by earlier pulses contributing to the fit, and is able to accommodate time-varying backgrounds and instrument response functions. We demonstrate that this global approach allows us to readily fit time-resolved fluorescence data to complex models including a four-exponential model of a FRET system, for which the FRET efficiencies of the two species of a bi-exponential donor are linked, and polarisation-resolved lifetime data, where a fluorescence intensity and bi-exponential anisotropy decay model is applied to the analysis of live cell homo-FRET data. A software package implementing this algorithm, FLIMfit, is available under an open source licence through the Open Microscopy Environment. PMID:23940626

The Impact of Water Loading on Estimates of Postglacial Decay Times in Hudson Bay

NASA Astrophysics Data System (ADS)

Han, H. K.; Gomez, N. A.

2016-12-01

Ongoing glacial isostatic adjustment (GIA) due to surface loading (ice and water) variations since the Last Glacial Maximum (LGM) has been contributing to sea level changes globally throughout the Holocene, especially in regions like the Canada that were heavily glaciated during the LGM. The spatial and temporal distribution of GIA and relative sea level change are attributed to the ice history and the rheological structure of the solid Earth, both of which are uncertain. It has been shown that relative sea level curves in previously glaciated regions follow an exponential-like form, and the post glacial decay times associated with that form have weak sensitivity to the details of the ice loading history (Andrews 1970, Walcott 1980, Mitrovica & Peltier 1995). Post glacial decay time estimates may therefore be used to constrain the Earth's structure and improve GIA predictions. However, estimates of decay times in Hudson Bay in the literature differ significantly due to a number of sources of uncertainty and bias (Mitrovica et al. 2000). Previous decay time analyses have not considered the potential bias that surface loading associated with Holocene sea level changes can introduce in decay time estimates derived from nearby relative sea level observations. We explore the spatial patterns of post glacial decay time predictions in previously glaciated regions, and their sensitivity to ice and water loading history. We compute post glacial sea level changes over the last deglaciation from 21ka to the modern associated with the ICE5G (Peltier, 2004) and ICE6G (Argus et al. 2014, Peltier et al. 2015) ice history models. We fit exponential curves to the modeled relative sea level changes, and compute maps of post glacial decay time predictions across North America and the Arctic. In addition, we decompose the modeled relative sea level changes into contributions from water and ice loading effects, and compute the impact of water loading redistribution since the LGM on present day decay times. We show that Holocene water loading in the Hudson Bay may introduce significant bias in decay time estimates and we highlight locations where biases are minimized.

Impact of oxide thickness on the density distribution of near-interface traps in 4H-SiC MOS capacitors

NASA Astrophysics Data System (ADS)

Zhang, Xufang; Okamoto, Dai; Hatakeyama, Tetsuo; Sometani, Mitsuru; Harada, Shinsuke; Iwamuro, Noriyuki; Yano, Hiroshi

2018-06-01

The impact of oxide thickness on the density distribution of near-interface traps (NITs) in SiO2/4H-SiC structure was investigated. We used the distributed circuit model that had successfully explained the frequency-dependent characteristics of both capacitance and conductance under strong accumulation conditions for SiO2/4H-SiC MOS capacitors with thick oxides by assuming an exponentially decaying distribution of NITs. In this work, it was found that the exponentially decaying distribution is the most plausible approximation of the true NIT distribution because it successfully explained the frequency dependences of capacitance and conductance under strong accumulation conditions for various oxide thicknesses. The thickness dependence of the NIT density distribution was also characterized. It was found that the NIT density increases with increasing oxide thickness, and a possible physical reason was discussed.

Transdermal delivery of therapeutic agent

NASA Technical Reports Server (NTRS)

Kwiatkowski, Krzysztof C. (Inventor); Hayes, Ryan T. (Inventor); Magnuson, James W. (Inventor); Giletto, Anthony (Inventor)

2008-01-01

A device for the transdermal delivery of a therapeutic agent to a biological subject that includes a first electrode comprising a first array of electrically conductive microprojections for providing electrical communication through a skin portion of the subject to a second electrode comprising a second array of electrically conductive microprojections. Additionally, a reservoir for holding the therapeutic agent surrounding the first electrode and a pulse generator for providing an exponential decay pulse between the first and second electrodes may be provided. A method includes the steps of piercing a stratum corneum layer of skin with two arrays of conductive microprojections, encapsulating the therapeutic agent into biocompatible charged carriers, surrounding the conductive microprojections with the therapeutic agent, generating an exponential decay pulse between the two arrays of conductive microprojections to create a non-uniform electrical field and electrokinetically driving the therapeutic agent through the stratum corneum layer of skin.

Edge Extraction by an Exponential Function Considering X-ray Transmission Characteristics

NASA Astrophysics Data System (ADS)

Kim, Jong Hyeong; Youp Synn, Sang; Cho, Sung Man; Jong Joo, Won

2011-04-01

3-D radiographic methodology has been into the spotlight for quality inspection of mass product or in-service inspection of aging product. To locate a target object in 3-D space, its characteristic contours such as edge length, edge angle, and vertices are very important. In spite of a simple geometry product, it is very difficult to get clear shape contours from a single radiographic image. The image contains scattering noise at the edges and ambiguity coming from X-Ray absorption within the body. This article suggests a concise method to extract whole edges from a single X-ray image. At the edge point of the object, the intensity of the X-ray decays exponentially as the X-ray penetrates the object. Considering this X-Ray decaying property, edges are extracted by using the least square fitting with the control of Coefficient of Determination.

Simulation and prediction of the thuringiensin abiotic degradation processes in aqueous solution by a radius basis function neural network model.

PubMed

Zhou, Jingwen; Xu, Zhenghong; Chen, Shouwen

2013-04-01

The thuringiensin abiotic degradation processes in aqueous solution under different conditions, with a pH range of 5.0-9.0 and a temperature range of 10-40°C, were systematically investigated by an exponential decay model and a radius basis function (RBF) neural network model, respectively. The half-lives of thuringiensin calculated by the exponential decay model ranged from 2.72 d to 16.19 d under the different conditions mentioned above. Furthermore, an RBF model with accuracy of 0.1 and SPREAD value 5 was employed to model the degradation processes. The results showed that the model could simulate and predict the degradation processes well. Both the half-lives and the prediction data showed that thuringiensin was an easily degradable antibiotic, which could be an important factor in the evaluation of its safety. Copyright © 2012 Elsevier Ltd. All rights reserved.

Exponentially varying viscosity of magnetohydrodynamic mixed convection Eyring-Powell nanofluid flow over an inclined surface

NASA Astrophysics Data System (ADS)

Khan, Imad; Fatima, Sumreen; Malik, M. Y.; Salahuddin, T.

2018-03-01

This paper explores the theoretical study of the steady incompressible two dimensional MHD boundary layer flow of Eyring-Powell nanofluid over an inclined surface. The fluid is considered to be electrically conducting and the viscosity of the fluid is assumed to be varying exponentially. The governing partial differential equations (PDE's) are reduced into ordinary differential equations (ODE's) by applying similarity approach. The resulting ordinary differential equations are solved successfully by using Homotopy analysis method. The impact of pertinent parameters on velocity, concentration and temperature profiles are examined through graphs and tables. Also coefficient of skin friction, Sherwood and Nusselt numbers are illustrated in tabular and graphical form.

Fourth order exponential time differencing method with local discontinuous Galerkin approximation for coupled nonlinear Schrodinger equations

DOE PAGES

Liang, Xiao; Khaliq, Abdul Q. M.; Xing, Yulong

2015-01-23

In this paper, we study a local discontinuous Galerkin method combined with fourth order exponential time differencing Runge-Kutta time discretization and a fourth order conservative method for solving the nonlinear Schrödinger equations. Based on different choices of numerical fluxes, we propose both energy-conserving and energy-dissipative local discontinuous Galerkin methods, and have proven the error estimates for the semi-discrete methods applied to linear Schrödinger equation. The numerical methods are proven to be highly efficient and stable for long-range soliton computations. Finally, extensive numerical examples are provided to illustrate the accuracy, efficiency and reliability of the proposed methods.

Fast decay of solutions for linear wave equations with dissipation localized near infinity in an exterior domain

NASA Astrophysics Data System (ADS)

Ryo, Ikehata

Uniform energy and L2 decay of solutions for linear wave equations with localized dissipation will be given. In order to derive the L2-decay property of the solution, a useful device whose idea comes from Ikehata-Matsuyama (Sci. Math. Japon. 55 (2002) 33) is used. In fact, we shall show that the L2-norm and the total energy of solutions, respectively, decay like O(1/ t) and O(1/ t2) as t→+∞ for a kind of the weighted initial data.

Stretched-to-compressed-exponential crossover observed in the electrical degradation kinetics of some spinel-metallic screen-printed structures

NASA Astrophysics Data System (ADS)

Balitska, V.; Shpotyuk, O.; Brunner, M.; Hadzaman, I.

2018-02-01

Thermally-induced (170 °C) degradation-relaxation kinetics is examined in screen-printed structures composed of spinel Cu0.1Ni0.1Co1.6Mn1.2O4 ceramics with conductive Ag or Ag-Pd layered electrodes. Structural inhomogeneities due to Ag and Ag-Pd diffusants in spinel phase environment play a decisive role in non-exponential kinetics of negative relative resistance drift. If Ag migration in spinel is inhibited by Pd addition due to Ag-Pd alloy, the kinetics attains stretched exponential behavior with ∼0.58 exponent, typical for one-stage diffusion in structurally-dispersive media. Under deep Ag penetration into spinel ceramics, as for thick films with Ag-layered electrodes, the degradation kinetics drastically changes, attaining features of two-step diffusing process governed by compressed-exponential dependence with power index of ∼1.68. Crossover from stretched- to compressed-exponential kinetics in spinel-metallic structures is mapped on free energy landscape of non-barrier multi-well system under strong perturbation from equilibrium, showing transition with a character downhill scenario resulting in faster than exponential decaying.

Europium containing red light-emitting fibers made by electrohydrodynamic casting

NASA Astrophysics Data System (ADS)

Gan, Yong X.; Panahi, Niousha; Yu, Christina; Gan, Jeremy B.; Cheng, Wanli

2018-05-01

Red light-emitting polymeric micro- and nanofibers were made by electrohydrodynamic co-casting of two fluids. One fluid contains a 10 wt% concentration europium (III) complex dissolved in a dimethylformamide (DMF) solvent. The europium complex, an Eu3+ compound with the nominal formula of Eu(BA)3phen/PAN, consists of polyacrylonitrile (PAN), 1,10-phenanthroline (phen), and benzoic acid (BA). The other fluid consists of iron metal oxide nanoparticles dispersed in a solution containing 10 wt% polyacrylonitrile polymer in DMF solvent. The two fluids were electrohydrodynamically co-cast onto a soft tissue paper using a stainless steel coaxial nozzle. The intensity of the electric field used for the co-casting was 1.5 kV/cm. Scanning electron microscopic observation on the fibers obtained from the co-casting was made. The size of the fibers ranges from several hundreds of nanometers to several microns. Energy dispersive X-ray spectroscopic analysis of the fibers confirmed that the major elements included C, O, Fe, and Eu. The fluorescence of the two types of fibers was tested under the excitation of a UV light source. It was found that when the europium complex-containing solution was the sheath fluid and the iron-containing solution was the core, the prepared fibers showed red light-emitting behavior under ultraviolet light. Time-dependent fluorescence shows the two-stage decaying behavior. The first stage lasts about 2000 s and the intensity of fluorescence decreases linearly. The second stage reveals the slow decaying behavior and it lasts longer than 3 h. Based on the bi-exponential data fitting using a processing MATLAB code, the fluorescence-related constants were extracted. A bi-exponential formula was proposed to describe the time-dependent fluorescence behavior of the fiber made by the europium complex-containing solution as the sheath fluid. The decaying in the fluorescence shows two different stages. The first stage lasts about 2000 s and it is characterized by a fast decaying model. The intensity of fluorescence decreases linearly. The second stage has a slow decaying feature. It takes over 3 h for the fluorescence to die out completely. Bi-exponential data fitting shows that the time constant for the decay of fluorescence is about 10,000 s.

Exponential decay of GC content detected by strand-symmetric substitution rates influences the evolution of isochore structure.

PubMed

Karro, J E; Peifer, M; Hardison, R C; Kollmann, M; von Grünberg, H H

2008-02-01

The distribution of guanine and cytosine nucleotides throughout a genome, or the GC content, is associated with numerous features in mammals; understanding the pattern and evolutionary history of GC content is crucial to our efforts to annotate the genome. The local GC content is decaying toward an equilibrium point, but the causes and rates of this decay, as well as the value of the equilibrium point, remain topics of debate. By comparing the results of 2 methods for estimating local substitution rates, we identify 620 Mb of the human genome in which the rates of the various types of nucleotide substitutions are the same on both strands. These strand-symmetric regions show an exponential decay of local GC content at a pace determined by local substitution rates. DNA segments subjected to higher rates experience disproportionately accelerated decay and are AT rich, whereas segments subjected to lower rates decay more slowly and are GC rich. Although we are unable to draw any conclusions about causal factors, the results support the hypothesis proposed by Khelifi A, Meunier J, Duret L, and Mouchiroud D (2006. GC content evolution of the human and mouse genomes: insights from the study of processed pseudogenes in regions of different recombination rates. J Mol Evol. 62:745-752.) that the isochore structure has been reshaped over time. If rate variation were a determining factor, then the current isochore structure of mammalian genomes could result from the local differences in substitution rates. We predict that under current conditions strand-symmetric portions of the human genome will stabilize at an average GC content of 30% (considerably less than the current 42%), thus confirming that the human genome has not yet reached equilibrium.

The role of spin–rotation coupling in the non-exponential decay of hydrogen-like heavy ions

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

Lambiase, Gaetano, E-mail: lambiase@sa.infn.it; INFN, Sezione di Napoli; International Institute for Advanced Scientific Studies, 89019 Vietri sul Mare

2013-05-15

Recent experiments carried out at the storage ring of GSI in Darmstadt reveal an unexpected oscillation in the orbital electron capture and subsequent decay of hydrogen-like {sup 140}Pr{sup 58+}, {sup 142}Pm{sup 60+} and {sup 122}I{sup 52+}. The modulations have periods of 7.069(8) s, 7.10(22) s and 6.1 s respectively in the laboratory frame and are superimposed on the expected exponential decays. In this paper we propose a semiclassical model in which the observed modulations arise from the coupling of rotation to the spins of electron and nucleus. We show that the modulations are connected to quantum beats and to themore » effect of the Thomas precession on the spins of bound electron and nucleus, the magnetic moment precessions of electron and nucleus and their cyclotron frequencies. We also show that the spin–spin coupling of electron and nucleus, though dominant relative to the magnetic moment coupling of electron and nucleus with the storage ring magnetic field, does not contribute to the modulation because these terms average out during the time of flight of the ions, or cancel out. The model also predicts that the anomaly cannot be observed if the motion of the ions is rectilinear, or if the ions are stopped in a target (decay of neutral atoms in solid environments). It also supports the notion that no modulation occurs for the β{sup +}-decay branch. -- Highlights: ► Spin precession of the spin of nucleus and electron in storage ring. ► Coupling of rotation to the spin of electron and nucleus. ► Modulation in the decay probability of the heavy ions induced by quantum beats. ► Comparison with experimental data.« less

Alteration of the fast excitatory postsynaptic current by barium in voltage-clamped amphibian sympathetic ganglion cells.

PubMed Central

Connor, E. A.; Parsons, R. L.

1984-01-01

Barium-induced alterations in fast excitatory postsynaptic currents (e.p.s.cs) have been studied in voltage-clamped bullfrog sympathetic ganglion B cells. In the presence of 2-8 mM barium, e.p.s.c. decay was prolonged and in many cells the e.p.s.c. decay phase deviated from a single exponential function. The decay phase in these cases was more accurately described as the sum of two exponential functions. The frequency of occurrence of a complex decay increased both with increasing barium concentration and with hyperpolarization. Miniature e.p.s.c. decay also was prolonged in barium-treated cells. E.p.s.c. amplitude was not markedly affected by barium (2-8 mM) in cells voltage-clamped to -50 mV whereas at -90 mV there was a progressive increase in peak size with increasing barium concentration. In control cells the e.p.s.c.-voltage relationship was linear between -20 and -100 mV; however, this relationship became progressively non-linear with membrane hyperpolarization in barium-treated cells. The e.p.s.c. reversal potential was shifted to a more negative value in the presence of barium. There was a voltage-dependent increase in charge movement during the e.p.s.c. in barium-treated cells which was not present in control cells. We conclude that the voltage-dependent alteration in e.p.s.c. decay time course, peak amplitude and charge movement in barium-treated cells is due to a direct postsynaptic action of barium on the kinetics of receptor-channel gating in postganglionic sympathetic neurones. PMID:6333261

An accurate and efficient method for evaluating the kernel of the integral equation relating pressure to normalwash in unsteady potential flow

NASA Technical Reports Server (NTRS)

Desmarais, R. N.

1982-01-01

This paper describes an accurate economical method for generating approximations to the kernel of the integral equation relating unsteady pressure to normalwash in nonplanar flow. The method is capable of generating approximations of arbitrary accuracy. It is based on approximating the algebraic part of the non elementary integrals in the kernel by exponential approximations and then integrating termwise. The exponent spacing in the approximation is a geometric sequence. The coefficients and exponent multiplier of the exponential approximation are computed by least squares so the method is completely automated. Exponential approximates generated in this manner are two orders of magnitude more accurate than the exponential approximation that is currently most often used for this purpose. Coefficients for 8, 12, 24, and 72 term approximations are tabulated in the report. Also, since the method is automated, it can be used to generate approximations to attain any desired trade-off between accuracy and computing cost.

R-Function Relationships for Application in the Fractional Calculus

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.; Hartley, Tom T.

2000-01-01

The F-function, and its generalization the R-function, are of fundamental importance in the fractional calculus. It has been shown that the solution of the fundamental linear fractional differential equation may be expressed in terms of these functions. These functions serve as generalizations of the exponential function in the solution of fractional differential equations. Because of this central role in the fractional calculus, this paper explores various intrarelationships of the R-function, which will be useful in further analysis. Relationships of the R-function to the common exponential function, e(t), and its fractional derivatives are shown. From the relationships developed, some important approximations are observed. Further, the inverse relationships of the exponential function, el, in terms of the R-function are developed. Also, some approximations for the R-function are developed.

R-function relationships for application in the fractional calculus.

PubMed

Lorenzo, Carl F; Hartley, Tom T

2008-01-01

The F-function, and its generalization the R-function, are of fundamental importance in the fractional calculus. It has been shown that the solution of the fundamental linear fractional differential equation may be expressed in terms of these functions. These functions serve as generalizations of the exponential function in the solution of fractional differential equations. Because of this central role in the fractional calculus, this paper explores various intrarelationships of the R-function, which will be useful in further analysis. Relationships of the R-function to the common exponential function, et, and its fractional derivatives are shown. From the relationships developed, some important approximations are observed. Further, the inverse relationships of the exponential function, et, in terms of the R-function are developed. Also, some approximations for the R-function are developed.

FLIMX: A Software Package to Determine and Analyze the Fluorescence Lifetime in Time-Resolved Fluorescence Data from the Human Eye.

PubMed

Klemm, Matthias; Schweitzer, Dietrich; Peters, Sven; Sauer, Lydia; Hammer, Martin; Haueisen, Jens

2015-01-01

Fluorescence lifetime imaging ophthalmoscopy (FLIO) is a new technique for measuring the in vivo autofluorescence intensity decays generated by endogenous fluorophores in the ocular fundus. Here, we present a software package called FLIM eXplorer (FLIMX) for analyzing FLIO data. Specifically, we introduce a new adaptive binning approach as an optimal tradeoff between the spatial resolution and the number of photons required per pixel. We also expand existing decay models (multi-exponential, stretched exponential, spectral global analysis, incomplete decay) to account for the layered structure of the eye and present a method to correct for the influence of the crystalline lens fluorescence on the retina fluorescence. Subsequently, the Holm-Bonferroni method is applied to FLIO measurements to allow for group comparisons between patients and controls on the basis of fluorescence lifetime parameters. The performance of the new approaches was evaluated in five experiments. Specifically, we evaluated static and adaptive binning in a diabetes mellitus patient, we compared the different decay models in a healthy volunteer and performed a group comparison between diabetes patients and controls. An overview of the visualization capabilities and a comparison of static and adaptive binning is shown for a patient with macular hole. FLIMX's applicability to fluorescence lifetime imaging microscopy is shown in the ganglion cell layer of a porcine retina sample, obtained by a laser scanning microscope using two-photon excitation.

Applications of an exponential finite difference technique

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

Handschuh, R.F.; Keith, T.G. Jr.

1988-07-01

An exponential finite difference scheme first presented by Bhattacharya for one dimensional unsteady heat conduction problems in Cartesian coordinates was extended. The finite difference algorithm developed was used to solve the unsteady diffusion equation in one dimensional cylindrical coordinates and was applied to two and three dimensional conduction problems in Cartesian coordinates. Heat conduction involving variable thermal conductivity was also investigated. The method was used to solve nonlinear partial differential equations in one and two dimensional Cartesian coordinates. Predicted results are compared to exact solutions where available or to results obtained by other numerical methods.

Interaction phenomenon to dimensionally reduced p-gBKP equation

NASA Astrophysics Data System (ADS)

Zhang, Runfa; Bilige, Sudao; Bai, Yuexing; Lü, Jianqing; Gao, Xiaoqing

2018-02-01

Based on searching the combining of quadratic function and exponential (or hyperbolic cosine) function from the Hirota bilinear form of the dimensionally reduced p-gBKP equation, eight class of interaction solutions are derived via symbolic computation with Mathematica. The submergence phenomenon, presented to illustrate the dynamical features concerning these obtained solutions, is observed by three-dimensional plots and density plots with particular choices of the involved parameters between the exponential (or hyperbolic cosine) function and the quadratic function. It is proved that the interference between the two solitary waves is inelastic.

Leaf litter decomposition in Torna stream before and after a red mud disaster.

PubMed

Kucserka, T; Karádi-Kovács, Kata; Vass, M; Selmeczy, G B; Hubai, Katalin Eszter; Üveges, Viktória; Kacsala, I; Törő, N; Padisák, Judit

2014-03-01

The aim of the study was to estimate the breakdown of the allochthonous litter in an artificial stream running in an agricultural area and compare it with the same values following a toxic mud spill into the same stream. Litter bags were filled with three types of leaves (Quercus robur, Populus tremula and Salix alba) and placed to the bottom of the river. Ergosterol was used to detect fungal biomass. We supposed the absence of fungi and the retardation of leaf litter decomposition. Only pH and conductivity increased significantly. Leaf mass loss after the catastrophe was much slower than in 2009 and the decay curves did not follow the exponential decay model. Prior to the catastrophe, leaf mass loss was fast in Torna, compared to other streams in the area. The reason is that the stream is modified, the bed is trapezoid and covered with concrete stones. Fungal biomass was lower, than in the pre-disaster experiment, because fungi did not have enough leaves to sporulate. Leaf mass loss followed the exponential decay curve before the disaster, but after that it was possible only after a non-change period.

Airspace Dimension Assessment with nanoparticles reflects lung density as quantified by MRI

PubMed Central

Jakobsson, Jonas K; Löndahl, Jakob; Olsson, Lars E; Diaz, Sandra; Zackrisson, Sophia; Wollmer, Per

2018-01-01

Background Airspace Dimension Assessment with inhaled nanoparticles is a novel method to determine distal airway morphology. This is the first empirical study using Airspace Dimension Assessment with nanoparticles (AiDA) to estimate distal airspace radius. The technology is relatively simple and potentially accessible in clinical outpatient settings. Method Nineteen never-smoking volunteers performed nanoparticle inhalation tests at multiple breath-hold times, and the difference in nanoparticle concentration of inhaled and exhaled gas was measured. An exponential decay curve was fitted to the concentration of recovered nanoparticles, and airspace dimensions were assessed from the half-life of the decay. Pulmonary tissue density was measured using magnetic resonance imaging (MRI). Results The distal airspace radius measured by AiDA correlated with lung tissue density as measured by MRI (ρ = −0.584; p = 0.0086). The linear intercept of the logarithm of the exponential decay curve correlated with forced expiratory volume in one second (FEV1) (ρ = 0.549; p = 0.0149). Conclusion The AiDA method shows potential to be developed into a tool to assess conditions involving changes in distal airways, eg, emphysema. The intercept may reflect airway properties; this finding should be further investigated.

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

Proctor, Timothy; Rudinger, Kenneth; Young, Kevin

Randomized benchmarking (RB) is widely used to measure an error rate of a set of quantum gates, by performing random circuits that would do nothing if the gates were perfect. In the limit of no finite-sampling error, the exponential decay rate of the observable survival probabilities, versus circuit length, yields a single error metric r. For Clifford gates with arbitrary small errors described by process matrices, r was believed to reliably correspond to the mean, over all Clifford gates, of the average gate infidelity between the imperfect gates and their ideal counterparts. We show that this quantity is not amore » well-defined property of a physical gate set. It depends on the representations used for the imperfect and ideal gates, and the variant typically computed in the literature can differ from r by orders of magnitude. We present new theories of the RB decay that are accurate for all small errors describable by process matrices, and show that the RB decay curve is a simple exponential for all such errors. Here, these theories allow explicit computation of the error rate that RB measures (r), but as far as we can tell it does not correspond to the infidelity of a physically allowed (completely positive) representation of the imperfect gates.« less

Systematic approach to thermal leptogenesis

NASA Astrophysics Data System (ADS)

Frossard, T.; Garny, M.; Hohenegger, A.; Kartavtsev, A.; Mitrouskas, D.

2013-04-01

In this work we study thermal leptogenesis using nonequilibrium quantum field theory. Starting from fundamental equations for correlators of the quantum fields we describe the steps necessary to obtain quantum-kinetic equations for quasiparticles. These can easily be compared to conventional results and overcome conceptional problems inherent in the canonical approach. Beyond CP-violating decays we include also those scattering processes which are tightly related to the decays in a consistent approximation of fourth order in the Yukawa couplings. It is demonstrated explicitly how the S-matrix elements for the scattering processes in the conventional approach are related to two- and three-loop contributions to the effective action. We derive effective decay and scattering amplitudes taking medium corrections and thermal masses into account. In this context we also investigate CP-violating Higgs decay within the same formalism. From the kinetic equations we derive rate equations for the lepton asymmetry improved in that they include quantum-statistical effects and medium corrections to the quasiparticle properties.

Non-London electrodynamics in a multiband London model: Anisotropy-induced nonlocalities and multiple magnetic field penetration lengths

NASA Astrophysics Data System (ADS)

Silaev, Mihail; Winyard, Thomas; Babaev, Egor

2018-05-01

The London model describes strongly type-2 superconductors as massive vector field theories, where the magnetic field decays exponentially at the length scale of the London penetration length. This also holds for isotropic multiband extensions, where the presence of multiple bands merely renormalizes the London penetration length. We show that, by contrast, the magnetic properties of anisotropic multiband London models are not this simple, and the anisotropy leads to the interband phase differences becoming coupled to the magnetic field. This results in the magnetic field in such systems having N +1 penetration lengths, where N is the number of field components or bands. That is, in a given direction, the magnetic field decay is described by N +1 modes with different amplitudes and different decay length scales. For certain anisotropies we obtain magnetic modes with complex masses. That means that magnetic field decay is not described by a monotonic exponential increment set by a real penetration length but instead is oscillating. Some of the penetration lengths are shown to diverge away from the superconducting phase transition when the mass of the phase-difference mode vanishes. Finally the anisotropy-driven hybridization of the London mode with the Leggett modes can provide an effectively nonlocal magnetic response in the nominally local London model. Focusing on the two-component model, we discuss the magnetic field inversion that results from the effective nonlocality, both near the surface of the superconductor and around vortices. In the regime where the magnetic field decay becomes nonmonotonic, the multiband London superconductor is shown to form weakly-bound states of vortices.

Sensitivity of nonuniform sampling NMR.

PubMed

Palmer, Melissa R; Suiter, Christopher L; Henry, Geneive E; Rovnyak, James; Hoch, Jeffrey C; Polenova, Tatyana; Rovnyak, David

2015-06-04

Many information-rich multidimensional experiments in nuclear magnetic resonance spectroscopy can benefit from a signal-to-noise ratio (SNR) enhancement of up to about 2-fold if a decaying signal in an indirect dimension is sampled with nonconsecutive increments, termed nonuniform sampling (NUS). This work provides formal theoretical results and applications to resolve major questions about the scope of the NUS enhancement. First, we introduce the NUS Sensitivity Theorem in which any decreasing sampling density applied to any exponentially decaying signal always results in higher sensitivity (SNR per square root of measurement time) than uniform sampling (US). Several cases will illustrate this theorem and show that even conservative applications of NUS improve sensitivity by useful amounts. Next, we turn to a serious limitation of uniform sampling: the SNR by US decreases for extending evolution times, and thus total experimental times, beyond 1.26T2 (T2 = signal decay constant). Thus, SNR and resolution cannot be simultaneously improved by extending US beyond 1.26T2. We find that NUS can eliminate this constraint, and we introduce the matched NUS SNR Theorem: an exponential sampling density matched to the signal decay always improves the SNR with additional evolution time. Though proved for a specific case, broader classes of NUS densities also improve SNR with evolution time. Applications of these theoretical results are given for a soluble plant natural product and a solid tripeptide (u-(13)C,(15)N-MLF). These formal results clearly demonstrate the inadequacies of applying US to decaying signals in indirect nD-NMR dimensions, supporting a broader adoption of NUS.

Effective pathway of charge transfer in DNA duplex

NASA Astrophysics Data System (ADS)

Kim, Seongjin; Yi, Juyeon; Hwang, Sun-Yong

2009-03-01

We examine the most efficient route for charge propagation in DNA duplex. We find a direct path along one strand and a detour using the complementary strand compete with each other. Charge tends to take the path along the strand whose energy levels are close to its energy, and yet there exists a crossover length Nc so that for a transfer over a distance shorter than Nc the direct path is always advantageous. We obtain the analytic results for the behavior together with various decay types such as a constant decay, an exponential decay, and a crossover between them, whose validity is confirmed by the numerical calculation.

Codecaying Dark Matter.

PubMed

Dror, Jeff Asaf; Kuflik, Eric; Ng, Wee Hao

2016-11-18

We propose a new mechanism for thermal dark matter freeze-out, called codecaying dark matter. Multicomponent dark sectors with degenerate particles and out-of-equilibrium decays can codecay to obtain the observed relic density. The dark matter density is exponentially depleted through the decay of nearly degenerate particles rather than from Boltzmann suppression. The relic abundance is set by the dark matter annihilation cross section, which is predicted to be boosted, and the decay rate of the dark sector particles. The mechanism is viable in a broad range of dark matter parameter space, with a robust prediction of an enhanced indirect detection signal. Finally, we present a simple model that realizes codecaying dark matter.

On the Singularity Structure of WKB Solution of the Boosted Whittaker Equation: its Relevance to Resurgent Functions with Essential Singularities

NASA Astrophysics Data System (ADS)

Kamimoto, Shingo; Kawai, Takahiro; Koike, Tatsuya

2016-12-01

Inspired by the symbol calculus of linear differential operators of infinite order applied to the Borel transformed WKB solutions of simple-pole type equation [Kamimoto et al. (RIMS Kôkyûroku Bessatsu B 52:127-146, 2014)], which is summarized in Section 1, we introduce in Section 2 the space of simple resurgent functions depending on a parameter with an infra-exponential type growth order, and then we define the assigning operator A which acts on the space and produces resurgent functions with essential singularities. In Section 3, we apply the operator A to the Borel transforms of the Voros coefficient and its exponentiation for the Whittaker equation with a large parameter so that we may find the Borel transforms of the Voros coefficient and its exponentiation for the boosted Whittaker equation with a large parameter. In Section 4, we use these results to find the explicit form of the alien derivatives of the Borel transformed WKB solutions of the boosted Whittaker equation with a large parameter. The results in this paper manifest the importance of resurgent functions with essential singularities in developing the exact WKB analysis, the WKB analysis based on the resurgent function theory. It is also worth emphasizing that the concrete form of essential singularities we encounter is expressed by the linear differential operators of infinite order.

Modeling of Transmittance Degradation Caused by Optical Surface Contamination by Atomic Oxygen Reaction with Adsorbed Silicones

NASA Technical Reports Server (NTRS)

Snyder, Aaron; Banks, Bruce; Miller, Sharon; Stueber, Thomas; Sechkar, Edward

2001-01-01

A numerical procedure is presented to calculate transmittance degradation caused by contaminant films on spacecraft surfaces produced through the interaction of orbital atomic oxygen (AO) with volatile silicones and hydrocarbons from spacecraft components. In the model, contaminant accretion is dependent on the adsorption of species, depletion reactions due to gas-surface collisions, desorption, and surface reactions between AO and silicone producing SiO(x), (where x is near 2). A detailed description of the procedure used to calculate the constituents of the contaminant layer is presented, including the equations that govern the evolution of fractional coverage by specie type. As an illustrative example of film growth, calculation results using a prototype code that calculates the evolution of surface coverage by specie type is presented and discussed. An example of the transmittance degradation caused by surface interaction of AO with deposited contaminant is presented for the case of exponentially decaying contaminant flux. These examples are performed using hypothetical values for the process parameters.

Distribution of lifetimes for coronal soft X-ray bright points

NASA Technical Reports Server (NTRS)

Golub, L.; Krieger, A. S.; Vaiana, G. S.

1976-01-01

The lifetime 'spectrum' of X-ray bright points (XBPs) is measured for a sample of 300 such features using soft X-ray images obtained with the S-054 X-ray spectrographic telescope aboard Skylab. 'Spectrum' here is defined as a function which gives the relative number of XBPs having a specific lifetime as a function of lifetime. The results indicate that a two-lifetime exponential can be fit to the decay curves of XBPs, that the spectrum is heavily weighted toward short lifetimes, and that the number of features lasting 20 to 30 hr or more is greater than expected. A short-lived component with an average lifetime of about 8 hr and a long-lived 1.5-day component are consistently found along with a few features lasting 50 hr or more. An examination of differences among the components shows that features lasting 2 days or less have a broad heliocentric-latitude distribution while nearly all the longer-lived features are observed within 30 deg of the solar equator.

Using absolute gravimeter data to determine vertical gravity gradients

USGS Publications Warehouse

Robertson, D.S.

2001-01-01

The position versus time data from a free-fall absolute gravimeter can be used to estimate the vertical gravity gradient in addition to the gravity value itself. Hipkin has reported success in estimating the vertical gradient value using a data set of unusually good quality. This paper explores techniques that may be applicable to a broader class of data that may be contaminated with "system response" errors of larger magnitude than were evident in the data used by Hipkin. This system response function is usually modelled as a sum of exponentially decaying sinusoidal components. The technique employed here involves combining the x0, v0 and g parameters from all the drops made during a site occupation into a single least-squares solution, and including the value of the vertical gradient and the coefficients of system response function in the same solution. The resulting non-linear equations must be solved iteratively and convergence presents some difficulties. Sparse matrix techniques are used to make the least-squares problem computationally tractable.

Attenuation of the NMR signal in a field gradient due to stochastic dynamics with memory

NASA Astrophysics Data System (ADS)

Lisý, Vladimír; Tóthová, Jana

2017-03-01

The attenuation function S(t) for an ensemble of spins in a magnetic-field gradient is calculated by accumulation of the phase shifts in the rotating frame resulting from the displacements of spin-bearing particles. The found S(t), expressed through the particle mean square displacement, is applicable for any kind of stationary stochastic motion of spins, including their non-markovian dynamics with memory. The known expressions valid for normal and anomalous diffusion are obtained as special cases in the long time approximation. The method is also applicable to the NMR pulse sequences based on the refocusing principle. This is demonstrated by describing the Hahn spin echo experiment. The attenuation of the NMR signal is also evaluated providing that the random motion of particle is modeled by the generalized Langevin equation with the memory kernel exponentially decaying in time. The models considered in our paper assume massive particles driven by much smaller particles.

Propagation phenomena in monostable integro-differential equations: Acceleration or not?

NASA Astrophysics Data System (ADS)

Alfaro, Matthieu; Coville, Jérôme

2017-11-01

We consider the homogeneous integro-differential equation ∂t u = J * u - u + f (u) with a monostable nonlinearity f. Our interest is twofold: we investigate the existence/nonexistence of travelling waves, and the propagation properties of the Cauchy problem. When the dispersion kernel J is exponentially bounded, travelling waves are known to exist and solutions of the Cauchy problem typically propagate at a constant speed [7,10,11,22,26,27]. On the other hand, when the dispersion kernel J has heavy tails and the nonlinearity f is nondegenerate, i.e. f‧ (0) > 0, travelling waves do not exist and solutions of the Cauchy problem propagate by accelerating [14,20,27]. For a general monostable nonlinearity, a dichotomy between these two types of propagation behaviour is still not known. The originality of our work is to provide such dichotomy by studying the interplay between the tails of the dispersion kernel and the Allee effect induced by the degeneracy of f, i.e. f‧ (0) = 0. First, for algebraic decaying kernels, we prove the exact separation between existence and nonexistence of travelling waves. This in turn provides the exact separation between nonacceleration and acceleration in the Cauchy problem. In the latter case, we provide a first estimate of the position of the level sets of the solution.

Long-time dynamics of Rouse-Zimm polymers in dilute solutions with hydrodynamic memory.

PubMed

Lisy, V; Tothova, J; Zatovsky, A V

2004-12-01

The dynamics of flexible polymers in dilute solutions is studied taking into account the hydrodynamic memory, as a consequence of fluid inertia. As distinct from the Rouse-Zimm (RZ) theory, the Boussinesq friction force acts on the monomers (beads) instead of the Stokes force, and the motion of the solvent is governed by the nonstationary Navier-Stokes equations. The obtained generalized RZ equation is solved approximately using the preaveraging of the Oseen tensor. It is shown that the time correlation functions describing the polymer motion essentially differ from those in the RZ model. The mean-square displacement (MSD) of the polymer coil is at short times approximately t(2) (instead of approximately t). At long times the MSD contains additional (to the Einstein term) contributions, the leading of which is approximately t. The relaxation of the internal normal modes of the polymer differs from the traditional exponential decay. It is displayed in the long-time tails of their correlation functions, the longest lived being approximately t(-3/2) in the Rouse limit and t(-5/2) in the Zimm case, when the hydrodynamic interaction is strong. It is discussed that the found peculiarities, in particular, an effectively slower diffusion of the polymer coil, should be observable in dynamic scattering experiments. (c) 2004 American Institute of Physics

Climatology of the Arctic Sea Ice Thickness Distribution as a Stochastic Process

NASA Astrophysics Data System (ADS)

Toppaladoddi, S.; Wettlaufer, J. S.

2016-12-01

We study the seasonal changes in the thickness distribution of Arctic sea ice, g(h), under climate forcing. Our analytical and numerical approach is based on a Fokker-Planck equation for g(h) (Toppaladoddi & Wettlaufer Phys. Rev. Lett. 115, 148501, 2015), in which the thermodynamic growth rates are determined using observed climatology. In particular, the Fokker-Planck equation is coupled to the observationally consistent thermodynamic model of Eisenman & Wettlaufer (Proc. Natl. Acad. Sci. USA 106, pp. 28-32, 2009). We find that due to the combined effects of thermodynamics and mechanics, g(h) spreads during winter and contracts during summer. This behavior is in agreement with recent satellite observations from CryoSat-2 (Kwok & Cunningham, Phil. Trans. R. Soc. A 373, 20140157, 2015). Because g(h) is a probability density function, we quantify all of the key moments (e.g., mean thickness, fraction of thin/thick ice, mean albedo, relaxation time scales) as greenhouse-gas radiative forcing, ΔF0, increases. The mean ice thickness decays exponentially with ΔF0, but much slower than do solely thermodynamic models. This exhibits the crucial role that ice mechanics plays in maintaining the ice cover, by redistributing thin ice to thick ice-far more rapidly than can thermal growth alone.

Statistical Mechanics and the Climatology of the Arctic Sea Ice Thickness Distribution

NASA Astrophysics Data System (ADS)

Toppaladoddi, Srikanth; Wettlaufer, J. S.

2017-05-01

We study the seasonal changes in the thickness distribution of Arctic sea ice, g( h), under climate forcing. Our analytical and numerical approach is based on a Fokker-Planck equation for g( h) (Toppaladoddi and Wettlaufer in Phys Rev Lett 115(14):148501, 2015), in which the thermodynamic growth rates are determined using observed climatology. In particular, the Fokker-Planck equation is coupled to the observationally consistent thermodynamic model of Eisenman and Wettlaufer (Proc Natl Acad Sci USA 106:28-32, 2009). We find that due to the combined effects of thermodynamics and mechanics, g( h) spreads during winter and contracts during summer. This behavior is in agreement with recent satellite observations from CryoSat-2 (Kwok and Cunningham in Philos Trans R Soc A 373(2045):20140157, 2015). Because g( h) is a probability density function, we quantify all of the key moments (e.g., mean thickness, fraction of thin/thick ice, mean albedo, relaxation time scales) as greenhouse-gas radiative forcing, Δ F_0, increases. The mean ice thickness decays exponentially with Δ F_0, but much slower than do solely thermodynamic models. This exhibits the crucial role that ice mechanics plays in maintaining the ice cover, by redistributing thin ice to thick ice-far more rapidly than can thermal growth alone.

Modeling of ultrashort pulsed laser irradiation in the cornea based on parabolic and hyperbolic heat equations using electrical analogy

NASA Astrophysics Data System (ADS)

Gheitaghy, A. M.; Takabi, B.; Alizadeh, M.

2014-03-01

Hyperbolic and parabolic heat equations are formulated to study a nonperfused homogeneous transparent cornea irradiated by high power and ultrashort pulsed laser in the Laser Thermo Keratoplasty (LTK) surgery. Energy absorption inside the cornea is modeled using the Beer-Lambert law that is incorporated as an exponentially decaying heat source. The hyperbolic and parabolic bioheat models of the tissue were solved by exploiting the mathematical analogy between thermal and electrical systems, by using robust circuit simulation program called Hspice to get the solutions of simultaneous RLC and RC transmission line networks. This method can be used to rapidly calculate the temperature in laser-irradiated tissue at time and space domain. It is found that internal energy gained from the irradiated field results in a rapid rise of temperature in the cornea surface during the early heating period, while the hyperbolic wave model predicts a higher temperature rise than the classical heat diffusion model. In addition, this paper investigates and examines the effect of some critical parameters such as relaxation time, convection coefficient, radiation, tear evaporation and variable thermal conductivity of cornea. Accordingly, it is found that a better accordance between hyperbolic and parabolic models will be achieved by time.

Effect of soil parameters on the kinetics of the displacement of Fe from FeEDDHA chelates by Cu.

PubMed

Schenkeveld, Walter D C; Reichwein, Arjen M; Temminghoff, Erwin J M; van Riemsdijk, Willem H

2012-06-28

In soil application, o,o-FeEDDHA (iron (3+) ethylene diamine-N,N'-bis(2-hydroxy phenyl acetic acid) complex) is the active ingredient of FeEDDHA chelate-based Fe fertilizers. The effectiveness of o,o-FeEDDHA is potentially compromised by the displacement of Fe from FeEDDHA by Cu. The actual impact of Cu competition is codetermined by the kinetics of the displacement reaction. In this study, the influence of soil parameters on the displacement kinetics has been examined in goethite suspensions. The displacement reaction predominantly takes place on the reactive surface rather than in solution. The rate at which the o,o-FeEDDHA concentration declined depended on the available reactive surface area, the Cu loading, and the FeEDDHA loading. Soil factors reducing FeEDDHA adsorption (high ionic strength, humic acid adsorption onto the goethite surface, and monovalent instead of divalent cations in the electrolyte) decreased the displacement rate. For meso o,o-FeEDDHA, the displacement rate equation was derived, which is first order in FeEDDHA loading and half order in Cu loading. For soil conditions, the equation can be simplified to an exponential decay function in meso o,o-FeEDDHA solution concentration.

Spatial patterns of dengue cases in Brazil

PubMed Central

Antonio, Fernando Jose; de Picoli, Sergio; Teixeira, Jorge Juarez Vieira; Mendes, Renio dos Santos

2017-01-01

Dengue infection plays a central role in our society, since it is the most prevalent vector-borne viral disease affecting humans. We statistically investigated patterns concerning the spatial spreading of dengue epidemics in Brazil, as well as their temporal evolution in all Brazilian municipalities for a period of 12 years. We showed that the distributions of cases in municipalities follow power laws persistent in time and that the infection scales linearly with the population of the municipalities. We also found that the average number of dengue cases does not have a clear dependence on the longitudinal position of municipalities. On the other hand, we found that the average distribution of cases varies with the latitudinal position of municipalities, displaying an almost constant growth from high latitudes until reaching the Tropic of Capricorn leveling to a plateau closer to the Equator. We also characterized the spatial correlation of the number of dengue cases between pairs of municipalities, where our results showed that the spatial correlation function decays with the increase of distance between municipalities, following a power-law with an exponential cut-off. This regime leads to a typical dengue traveling distance. Finally, we considered modeling this last behaviour within the framework of a Edwards-Wilkinson equation with a fractional derivative on space. PMID:28715435

Dynamic screening in a two-species asymmetric exclusion process

NASA Astrophysics Data System (ADS)

Kim, Kyung Hyuk; den Nijs, Marcel

2007-08-01

The dynamic scaling properties of the one-dimensional Burgers equation are expected to change with the inclusion of additional conserved degrees of freedom. We study this by means of one-dimensional (1D) driven lattice gas models that conserve both mass and momentum. The most elementary version of this is the Arndt-Heinzel-Rittenberg (AHR) process, which is usually presented as a two-species diffusion process, with particles of opposite charge hopping in opposite directions and with a variable passing probability. From the hydrodynamics perspective this can be viewed as two coupled Burgers equations, with the number of positive and negative momentum quanta individually conserved. We determine the dynamic scaling dimension of the AHR process from the time evolution of the two-point correlation functions, and find numerically that the dynamic critical exponent is consistent with simple Kardar-Parisi-Zhang- (KPZ) type scaling. We establish that this is the result of perfect screening of fluctuations in the stationary state. The two-point correlations decay exponentially in our simulations and in such a manner that in terms of quasiparticles, fluctuations fully screen each other at coarse grained length scales. We prove this screening rigorously using the analytic matrix product structure of the stationary state. The proof suggests the existence of a topological invariant. The process remains in the KPZ universality class but only in the sense of a factorization, as (KPZ)2 . The two Burgers equations decouple at large length scales due to the perfect screening.

Variables and potential models for the bleaching of luminescence signals in fluvial environments

USGS Publications Warehouse

Gray, Harrison J.; Mahan, Shannon

2015-01-01

Luminescence dating of fluvial sediments rests on the assumption that sufficient sunlight is available to remove a previously obtained signal in a process deemed bleaching. However, luminescence signals obtained from sediment in the active channels of rivers often contain residual signals. This paper explores and attempts to build theoretical models for the bleaching of luminescence signals in fluvial settings. We present two models, one for sediment transported in an episodic manner, such as flood-driven washes in arid environments, and one for sediment transported in a continuous manner, such as in large continental scale rivers. The episodic flow model assumes that the majority of sediment is bleached while exposed to sunlight at the near surface between flood events and predicts a power-law decay in luminescence signal with downstream transport distance. The continuous flow model is developed by combining the Beer–Lambert law for the attenuation of light through a water column with a general-order kinetics equation to produce an equation with the form of a double negative exponential. The inflection point of this equation is compared with the sediment concentration from a Rouse profile to derive a non-dimensional number capable of assessing the likely extent of bleaching for a given set of luminescence and fluvial parameters. Although these models are theoretically based and not yet necessarily applicable to real-world fluvial systems, we introduce these ideas to stimulate discussion and encourage the development of comprehensive bleaching models with predictive power.

Evolution equation in the field theory of strings

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

Marui, M.; Sugamoto, A.; Oda, I.

This paper reports on a stringy version of the Altarelli-Parisi equation given within the field theory of bosonic strings formulated in the light-cone gauge. Using this equation, the authors study the behavior of the decay function of strings under the change of reference scale, especially imposing an assumption of large transverse momentum. In some cases the n-th moment of the decay function behaves very differently from QCD.

Bending Boundary Layers in Laminated-Composite Circular Cylindrical Shells

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.; Smeltzer, Stanley S., III

2000-01-01

A study of the attenuation of bending boundary layers in balanced and unbalanced, symmetrically and unsymmetrically laminated cylindrical shells is presented for nine contemporary material systems. The analysis is based on the linear Sanders-Koiter shell equations and specializations to the Love-Kirchhoff shell equations and Donnell's equations are included. Two nondimensional parameters are identified that characterize the effects of laminate orthotropy and anisotropy on the bending boundary-layer decay length in a very general manner. A substantial number of structural design technology results are presented for a wide range of laminated-composite cylinders. For all laminates considered, the results show that the differences between results obtained with the Sanders-Koiter shell equations, the Love-Kirchhoff shell equations, and Donnell's equations are negligible. The results also show that the effect of anisotropy in the form of coupling between pure bending and twisting has a negligible effect on the size of the bending boundary-layer decay length of the balanced, symmetrically laminated cylinders considered. Moreover, the results show that coupling between the various types of shell anisotropies has a negligible effect on the calculation of the bending boundary-layer decay length in most cases. The results also show that, in some cases, neglecting the shell anisotropy results in underestimating the bending boundary-layer decay length and, in other cases, results in an overestimation.

Kinetics analysis and quantitative calculations for the successive radioactive decay process

NASA Astrophysics Data System (ADS)

Zhou, Zhiping; Yan, Deyue; Zhao, Yuliang; Chai, Zhifang

2015-01-01

The general radioactive decay kinetics equations with branching were developed and the analytical solutions were derived by Laplace transform method. The time dependence of all the nuclide concentrations can be easily obtained by applying the equations to any known radioactive decay series. Taking the example of thorium radioactive decay series, the concentration evolution over time of various nuclide members in the family has been given by the quantitative numerical calculations with a computer. The method can be applied to the quantitative prediction and analysis for the daughter nuclides in the successive decay with branching of the complicated radioactive processes, such as the natural radioactive decay series, nuclear reactor, nuclear waste disposal, nuclear spallation, synthesis and identification of superheavy nuclides, radioactive ion beam physics and chemistry, etc.

Concept of the Exponential Law Prior to 1900

ERIC Educational Resources Information Center

Curtis, Lorenzo J.

1978-01-01

Presents the historical development of perceptions and applications of the exponential law, tracing it from its ancient origins until the year 1900. Shows that many concepts such as mean life and half life and their relationships to differential equations were known long before their application to nuclear radioactivity. (GA)

Nonlinear observers with linearizable error dynamics

NASA Technical Reports Server (NTRS)

Krener, A. J.; Respondek, W.

1985-01-01

A new method for designing asymptotic observers for a class of nonlinear systems is presented. The error between the state of the systems and the state of the observer in appropriate coordinates evolves linearly and can be made to decay aribtrarily exponentially fast.

Physics Notes.

ERIC Educational Resources Information Center

School Science Review, 1982

1982-01-01

Discusses dice model of exponential radionuclide decay; glancing and collinear perfectly elastic collisions; digital capacitance meter; use of top pan balance in physics; microcomputer calculation of gradient of straight line (includes complete Commodore PET computer program); Fresnel lenses; low-voltage radiant heater; Wheatssone's bridge used as…

Persistence of opinion in the Sznajd consensus model: computer simulation

NASA Astrophysics Data System (ADS)

Stauffer, D.; de Oliveira, P. M. C.

2002-12-01

The density of never changed opinions during the Sznajd consensus-finding process decays with time t as 1/t^θ. We find θ simeq 3/8 for a chain, compatible with the exact Ising result of Derrida et al. In higher dimensions, however, the exponent differs from the Ising θ. With simultaneous updating of sublattices instead of the usual random sequential updating, the number of persistent opinions decays roughly exponentially. Some of the simulations used multi-spin coding.

Ising model simulation in directed lattices and networks

NASA Astrophysics Data System (ADS)

Lima, F. W. S.; Stauffer, D.

2006-01-01

On directed lattices, with half as many neighbours as in the usual undirected lattices, the Ising model does not seem to show a spontaneous magnetisation, at least for lower dimensions. Instead, the decay time for flipping of the magnetisation follows an Arrhenius law on the square and simple cubic lattice. On directed Barabási-Albert networks with two and seven neighbours selected by each added site, Metropolis and Glauber algorithms give similar results, while for Wolff cluster flipping the magnetisation decays exponentially with time.

Continuous-Tone Electrostatic Electrography

DTIC Science & Technology

1948-12-15

TRANSLATOR <»>: Schaf fort, R.M. Williams, D.I. WfOiwp, L*E, = TYRS. SERIES . NUMBER AND PERIOD OF R*RO«T COVERED: Quarterly Progress ropt fjT...a passing wire (a ohöft distance abo’ve tho plato) or a series qf point a or othor oourpoo of aom<^> ^mat similar geometry hold at high voltage In... temporale of tho plat©» If tho dark decay i„s not of thermal : origin, an exponential typo of decay would still ho anticipated. Ih such caoe

Fractional order analysis of Sephadex gel structures: NMR measurements reflecting anomalous diffusion

NASA Astrophysics Data System (ADS)

Magin, Richard L.; Akpa, Belinda S.; Neuberger, Thomas; Webb, Andrew G.

2011-12-01

We report the appearance of anomalous water diffusion in hydrophilic Sephadex gels observed using pulse field gradient (PFG) nuclear magnetic resonance (NMR). The NMR diffusion data was collected using a Varian 14.1 Tesla imaging system with a home-built RF saddle coil. A fractional order analysis of the data was used to characterize heterogeneity in the gels for the dynamics of water diffusion in this restricted environment. Several recent studies of anomalous diffusion have used the stretched exponential function to model the decay of the NMR signal, i.e., exp[-( bD) α], where D is the apparent diffusion constant, b is determined the experimental conditions (gradient pulse separation, durations and strength), and α is a measure of structural complexity. In this work, we consider a different case where the spatial Laplacian in the Bloch-Torrey equation is generalized to a fractional order model of diffusivity via a complexity parameter, β, a space constant, μ, and a diffusion coefficient, D. This treatment reverts to the classical result for the integer order case. The fractional order decay model was fit to the diffusion-weighted signal attenuation for a range of b-values (0 < b < 4000 s mm -2). Throughout this range of b values, the parameters β, μ and D, were found to correlate with the porosity and tortuosity of the gel structure.

A numerical analysis of the performance of unpumped SBE 41 sensors at low flushing rates

NASA Astrophysics Data System (ADS)

Alvarez, A.

2018-05-01

The thermal and hydrodynamic response of a Sea-Bird unpumped CTD SBE 41, is numerically modeled to assess the biases occurring at the slow flushing rates typical of glider operations. Based on symmetry considerations, the sensor response is approximated by coupling the incompressible Navier-Stokes and the thermal advection-diffusion equations in two dimensions. Numerical results illustrate three regimes in the thermal response of the SBE 41 sensor, when crossing water layers with different thermal signatures. A linear decay in time of the bulk temperature of the conductivity cell is initially found. This is induced by the transit of the inflow through the conductivity cell in the form of a relatively narrow jet. Water masses with new thermal signatures do not immediately fill the sensor chambers, where the cross-section widens. Thermal equilibrium of these water masses is then achieved, in a second regime, via a cross-flow thermal diffusion between the boundary of the jet and the walls. Consequently, the evolution of the bulk temperature scales with the square root of time. In a third regime, the evolution of the bulk temperature depends on the thermal gradient between the fluid and the coating material. This results on an exponential decay of the bulk temperature with time. A comprehensive analytical model of the time evolution of the bulk temperature inside a cell is proposed based on these results.

Time-reversal symmetric resolution of unity without background integrals in open quantum systems

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

Hatano, Naomichi, E-mail: hatano@iis.u-tokyo.ac.jp; Ordonez, Gonzalo, E-mail: gordonez@butler.edu

2014-12-15

We present a new complete set of states for a class of open quantum systems, to be used in expansion of the Green’s function and the time-evolution operator. A remarkable feature of the complete set is that it observes time-reversal symmetry in the sense that it contains decaying states (resonant states) and growing states (anti-resonant states) parallelly. We can thereby pinpoint the occurrence of the breaking of time-reversal symmetry at the choice of whether we solve Schrödinger equation as an initial-condition problem or a terminal-condition problem. Another feature of the complete set is that in the subspace of the centralmore » scattering area of the system, it consists of contributions of all states with point spectra but does not contain any background integrals. In computing the time evolution, we can clearly see contribution of which point spectrum produces which time dependence. In the whole infinite state space, the complete set does contain an integral but it is over unperturbed eigenstates of the environmental area of the system and hence can be calculated analytically. We demonstrate the usefulness of the complete set by computing explicitly the survival probability and the escaping probability as well as the dynamics of wave packets. The origin of each term of matrix elements is clear in our formulation, particularly, the exponential decays due to the resonance poles.« less

Similarity of Turbulent Energy Scale Budget Equation of a Round Turbulent Jet

NASA Astrophysics Data System (ADS)

Sadeghi, Hamed; Lavoie, Philippe; Pollard, Andrew

2014-11-01

A novel extension to the similarity-based form of the transport equation for the second-order velocity structure function of <(δq) 2 > along the jet centreline (see Danaila et al., 2004) has been obtained. This new self-similar equation has the desirable benefit of requiring less extensive measurements to calculate the inhomogeneous (decay and production) terms of the transport equation. According to this equation, the normalized third-order structure function can be uniquely determined when the normalized second-order structure function, the power-law exponent of and the decay rate constants of and are available. In addition, on the basis of the current similarity analysis, the similarity assumptions in combination with power-law decay of mean velocity (U ~(x -x0) - 1) are strong enough to imply power-law decay of fluctuations ( ~(x -x0) m). The similarity solutions are then tested against new experimental data, which were taken along the centreline of a round jet at ReD = 50 , 000 . For the present set of initial conditions, exhibits a power-law behaviour with m = - 1 . 83 . This work was supported by grants from NSERC (Canada).

Locality of the Thomas-Fermi-von Weizsäcker Equations

NASA Astrophysics Data System (ADS)

Nazar, F. Q.; Ortner, C.

2017-06-01

We establish a pointwise stability estimate for the Thomas-Fermi-von Weiz-säcker (TFW) model, which demonstrates that a local perturbation of a nuclear arrangement results also in a local response in the electron density and electrostatic potential. The proof adapts the arguments for existence and uniqueness of solutions to the TFW equations in the thermodynamic limit by Catto et al. (The mathematical theory of thermodynamic limits: Thomas-Fermi type models. Oxford mathematical monographs. The Clarendon Press, Oxford University Press, New York, 1998). To demonstrate the utility of this combined locality and stability result we derive several consequences, including an exponential convergence rate for the thermodynamic limit, partition of total energy into exponentially localised site energies (and consequently, exponential locality of forces), and generalised and strengthened results on the charge neutrality of local defects.

Exponential Boundary Observers for Pressurized Water Pipe

NASA Astrophysics Data System (ADS)

Hermine Som, Idellette Judith; Cocquempot, Vincent; Aitouche, Abdel

2015-11-01

This paper deals with state estimation on a pressurized water pipe modeled by nonlinear coupled distributed hyperbolic equations for non-conservative laws with three known boundary measures. Our objective is to estimate the fourth boundary variable, which will be useful for leakage detection. Two approaches are studied. Firstly, the distributed hyperbolic equations are discretized through a finite-difference scheme. By using the Lipschitz property of the nonlinear term and a Lyapunov function, the exponential stability of the estimation error is proven by solving Linear Matrix Inequalities (LMIs). Secondly, the distributed hyperbolic system is preserved for state estimation. After state transformations, a Luenberger-like PDE boundary observer based on backstepping mathematical tools is proposed. An exponential Lyapunov function is used to prove the stability of the resulted estimation error. The performance of the two observers are shown on a water pipe prototype simulated example.

Propagators for the Time-Dependent Kohn-Sham Equations: Multistep, Runge-Kutta, Exponential Runge-Kutta, and Commutator Free Magnus Methods.

PubMed

Gómez Pueyo, Adrián; Marques, Miguel A L; Rubio, Angel; Castro, Alberto

2018-05-09

We examine various integration schemes for the time-dependent Kohn-Sham equations. Contrary to the time-dependent Schrödinger's equation, this set of equations is nonlinear, due to the dependence of the Hamiltonian on the electronic density. We discuss some of their exact properties, and in particular their symplectic structure. Four different families of propagators are considered, specifically the linear multistep, Runge-Kutta, exponential Runge-Kutta, and the commutator-free Magnus schemes. These have been chosen because they have been largely ignored in the past for time-dependent electronic structure calculations. The performance is analyzed in terms of cost-versus-accuracy. The clear winner, in terms of robustness, simplicity, and efficiency is a simplified version of a fourth-order commutator-free Magnus integrator. However, in some specific cases, other propagators, such as some implicit versions of the multistep methods, may be useful.

Mid-Infrared Lifetime Imaging for Viability Evaluation of Lettuce Seeds Based on Time-Dependent Thermal Decay Characterization

PubMed Central

Kim, Ghiseok; Kim, Geon Hee; Ahn, Chi-Kook; Yoo, Yoonkyu; Cho, Byoung-Kwan

2013-01-01

An infrared lifetime thermal imaging technique for the measurement of lettuce seed viability was evaluated. Thermal emission signals from mid-infrared images of healthy seeds and seeds aged for 24, 48, and 72 h were obtained and reconstructed using regression analysis. The emission signals were fitted with a two-term exponential model that had two amplitudes and two time variables as lifetime parameters. The lifetime thermal decay parameters were significantly different for seeds with different aging times. Single-seed viability was visualized using thermal lifetime images constructed from the calculated lifetime parameter values. The time-dependent thermal signal decay characteristics, along with the decay amplitude and delay time images, can be used to distinguish aged lettuce seeds from normal seeds. PMID:23529120

Imaging the He2 quantum halo state using a free electron laser

PubMed Central

Zeller, Stefan; Kunitski, Maksim; Voigtsberger, Jörg; Kalinin, Anton; Schottelius, Alexander; Schober, Carl; Waitz, Markus; Sann, Hendrik; Hartung, Alexander; Bauer, Tobias; Pitzer, Martin; Trinter, Florian; Goihl, Christoph; Janke, Christian; Richter, Martin; Kastirke, Gregor; Weller, Miriam; Czasch, Achim; Kitzler, Markus; Braune, Markus; Grisenti, Robert E.; Schmidt, Lothar Ph. H.; Schöffler, Markus S.; Williams, Joshua B.; Jahnke, Till; Dörner, Reinhard

2016-01-01

Quantum tunneling is a ubiquitous phenomenon in nature and crucial for many technological applications. It allows quantum particles to reach regions in space which are energetically not accessible according to classical mechanics. In this “tunneling region,” the particle density is known to decay exponentially. This behavior is universal across all energy scales from nuclear physics to chemistry and solid state systems. Although typically only a small fraction of a particle wavefunction extends into the tunneling region, we present here an extreme quantum system: a gigantic molecule consisting of two helium atoms, with an 80% probability that its two nuclei will be found in this classical forbidden region. This circumstance allows us to directly image the exponentially decaying density of a tunneling particle, which we achieved for over two orders of magnitude. Imaging a tunneling particle shows one of the few features of our world that is truly universal: the probability to find one of the constituents of bound matter far away is never zero but decreases exponentially. The results were obtained by Coulomb explosion imaging using a free electron laser and furthermore yielded He2’s binding energy of 151.9±13.3 neV, which is in agreement with most recent calculations. PMID:27930299

The Impact of Accelerating Faster than Exponential Population Growth on Genetic Variation

PubMed Central

Reppell, Mark; Boehnke, Michael; Zöllner, Sebastian

2014-01-01

Current human sequencing projects observe an abundance of extremely rare genetic variation, suggesting recent acceleration of population growth. To better understand the impact of such accelerating growth on the quantity and nature of genetic variation, we present a new class of models capable of incorporating faster than exponential growth in a coalescent framework. Our work shows that such accelerated growth affects only the population size in the recent past and thus large samples are required to detect the models’ effects on patterns of variation. When we compare models with fixed initial growth rate, models with accelerating growth achieve very large current population sizes and large samples from these populations contain more variation than samples from populations with constant growth. This increase is driven almost entirely by an increase in singleton variation. Moreover, linkage disequilibrium decays faster in populations with accelerating growth. When we instead condition on current population size, models with accelerating growth result in less overall variation and slower linkage disequilibrium decay compared to models with exponential growth. We also find that pairwise linkage disequilibrium of very rare variants contains information about growth rates in the recent past. Finally, we demonstrate that models of accelerating growth may substantially change estimates of present-day effective population sizes and growth times. PMID:24381333

The impact of accelerating faster than exponential population growth on genetic variation.

PubMed

Reppell, Mark; Boehnke, Michael; Zöllner, Sebastian

2014-03-01

Current human sequencing projects observe an abundance of extremely rare genetic variation, suggesting recent acceleration of population growth. To better understand the impact of such accelerating growth on the quantity and nature of genetic variation, we present a new class of models capable of incorporating faster than exponential growth in a coalescent framework. Our work shows that such accelerated growth affects only the population size in the recent past and thus large samples are required to detect the models' effects on patterns of variation. When we compare models with fixed initial growth rate, models with accelerating growth achieve very large current population sizes and large samples from these populations contain more variation than samples from populations with constant growth. This increase is driven almost entirely by an increase in singleton variation. Moreover, linkage disequilibrium decays faster in populations with accelerating growth. When we instead condition on current population size, models with accelerating growth result in less overall variation and slower linkage disequilibrium decay compared to models with exponential growth. We also find that pairwise linkage disequilibrium of very rare variants contains information about growth rates in the recent past. Finally, we demonstrate that models of accelerating growth may substantially change estimates of present-day effective population sizes and growth times.

Infinite-disorder critical points of models with stretched exponential interactions

NASA Astrophysics Data System (ADS)

Juhász, Róbert

2014-09-01

We show that an interaction decaying as a stretched exponential function of distance, J(l)˜ e-cl^a , is able to alter the universality class of short-range systems having an infinite-disorder critical point. To do so, we study the low-energy properties of the random transverse-field Ising chain with the above form of interaction by a strong-disorder renormalization group (SDRG) approach. We find that the critical behavior of the model is controlled by infinite-disorder fixed points different from those of the short-range model if 0 < a < 1/2. In this range, the critical exponents calculated analytically by a simplified SDRG scheme are found to vary with a, while, for a > 1/2, the model belongs to the same universality class as its short-range variant. The entanglement entropy of a block of size L increases logarithmically with L at the critical point but, unlike the short-range model, the prefactor is dependent on disorder in the range 0 < a < 1/2. Numerical results obtained by an improved SDRG scheme are found to be in agreement with the analytical predictions. The same fixed points are expected to describe the critical behavior of, among others, the random contact process with stretched exponentially decaying activation rates.

Electron transfer from nucleophilic species to N,N,N prime ,N prime -tetramethylbenzidine cation in micellar media: Effect of interfacial electrical potential on cation decay

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

Grand, D.; Hautecloque, S.

1990-01-25

Electron-transfer reaction between N,N,N{prime},N{prime}-tetramethylbenzidine cation (TMB{sup +}) and neutral nucleophiles, pyridine (Py) and triethylamine (Et{sub 3}N), is studied in NaLS micellar media. A biphasic decay of TMB{sup +} follows the laser-induced TMB photoionization. The very fast decay is attributed to an electron transfer between reactants located in the core of the micelle. The slow decay would correspond to an electron transfer from the nucleophile solubilized in the aqueous phase to TMB{sup +} embedded in the lipidic phase. The role of the electrical interfacial potential {Delta}{psi} is evidenced. The rate constant of the TMB{sup +} slow decay displays an exponential functionmore » of {Delta}{psi}. The effect of the localization and distance of the reactants is emphasized.« less

Decay characterization of solutions to the viscous Camassa-Holm equations

NASA Astrophysics Data System (ADS)

Anh, Cung The; Trang, Pham Thi

2018-02-01

In this paper we study the decay characterization in the space H^Kσ({R}^n) of solutions to the viscous Camassa-Holm equations (VCHE) in the whole space {R}n (n=2, 3, 4 ), namely, where m+2p≤slant K , r^*=r^*(v_0) is the decay character of the initial datum v_0\\in H^Kσ({R}^n) . We also get the optimal lower bounds for decay rates of solutions to VCHE when -{n}/{2}. In particular, when v_0\\in H^Kσ({R}^n) \\cap L^1({R}^n) has decay character r^*(v_0)=0 , then we recover the previous results of Bjorland and Schonbek (2008 Ann. Inst. Henri Poincaré Anal. Non Linéaire 25 907-36).

Current pulse amplifier transmits detector signals with minimum distortion and attenuation

NASA Technical Reports Server (NTRS)

Bush, N. E.

1967-01-01

Amplifier translates the square pulses generated by a boron-trifluoride neutron sensitive detector located adjacent to a nuclear reactor to slower, long exponential decay pulses. These pulses are transmitted over long coaxial cables with minimum distortion and loss of frequency.

Slip Effects On MHD Three Dimensional Flow Of Casson Fluid Over An Exponentially Stretching Surface

NASA Astrophysics Data System (ADS)

Madhusudhana Rao, B.; Krishna Murthy, M.; Sivakumar, N.; Rushi Kumar, B.; Raju, C. S. K.

2018-04-01

Heat and mass transfer effects on MHD three dimensional flow of Casson fluid over an exponentially stretching surface with slip conditions is examined. The similarity transformations are used to convert the governing equations into a set of nonlinear ordinary differential equations and are solved numerically using fourth order Runge-Kutta method along with shooting technique. The effects of Casson parameter, Hartmann number, heat source/sink,chemical reaction and slip factors on velocity, temperature and concentration are shown graphically. The skin friction coefficient and the Nusselt number are examined numerically.

Hypersurface Homogeneous Cosmological Model in Modified Theory of Gravitation

NASA Astrophysics Data System (ADS)

Katore, S. D.; Hatkar, S. P.; Baxi, R. J.

2016-12-01

We study a hypersurface homogeneous space-time in the framework of the f (R, T) theory of gravitation in the presence of a perfect fluid. Exact solutions of field equations are obtained for exponential and power law volumetric expansions. We also solve the field equations by assuming the proportionality relation between the shear scalar (σ ) and the expansion scalar (θ ). It is observed that in the exponential model, the universe approaches isotropy at large time (late universe). The investigated model is notably accelerating and expanding. The physical and geometrical properties of the investigated model are also discussed.

Time-splitting combined with exponential wave integrator fourier pseudospectral method for Schrödinger-Boussinesq system

NASA Astrophysics Data System (ADS)

Liao, Feng; Zhang, Luming; Wang, Shanshan

2018-02-01

In this article, we formulate an efficient and accurate numerical method for approximations of the coupled Schrödinger-Boussinesq (SBq) system. The main features of our method are based on: (i) the applications of a time-splitting Fourier spectral method for Schrödinger-like equation in SBq system, (ii) the utilizations of exponential wave integrator Fourier pseudospectral for spatial derivatives in the Boussinesq-like equation. The scheme is fully explicit and efficient due to fast Fourier transform. The numerical examples are presented to show the efficiency and accuracy of our method.

A method for exponential propagation of large systems of stiff nonlinear differential equations

NASA Technical Reports Server (NTRS)

Friesner, Richard A.; Tuckerman, Laurette S.; Dornblaser, Bright C.; Russo, Thomas V.

1989-01-01

A new time integrator for large, stiff systems of linear and nonlinear coupled differential equations is described. For linear systems, the method consists of forming a small (5-15-term) Krylov space using the Jacobian of the system and carrying out exact exponential propagation within this space. Nonlinear corrections are incorporated via a convolution integral formalism; the integral is evaluated via approximate Krylov methods as well. Gains in efficiency ranging from factors of 2 to 30 are demonstrated for several test problems as compared to a forward Euler scheme and to the integration package LSODE.

Relationship between population dynamics and the self-energy in driven non-equilibrium systems

DOE PAGES

Kemper, Alexander F.; Freericks, James K.

2016-05-13

We compare the decay rates of excited populations directly calculated within a Keldysh formalism to the equation of motion of the population itself for a Hubbard-Holstein model in two dimensions. While it is true that these two approaches must give the same answer, it is common to make a number of simplifying assumptions, within the differential equation for the populations, that allows one to interpret the decay in terms of hot electrons interacting with a phonon bath. Furthermore, we show how care must be taken to ensure an accurate treatment of the equation of motion for the populations due tomore » the fact that there are identities that require cancellations of terms that naively look like they contribute to the decay rates. In particular, the average time dependence of the Green's functions and self-energies plays a pivotal role in determining these decay rates.« less

Structural and optical properties of Dy3+ doped Aluminofluoroborophosphate glasses for white light applications

NASA Astrophysics Data System (ADS)

Vijayakumar, M.; Mahesvaran, K.; Patel, Dinesh K.; Arunkumar, S.; Marimuthu, K.

2014-11-01

Dy3+ doped Aluminofluoroborophosphate glasses (BPAxD) have been prepared following conventional melt quenching technique and their structural and optical properties were explored through XRD, FTIR, optical absorption, excitation, emission and decay measurements. The coexistence of BO3 groups in borate rich domain and BO4 groups in phosphate rich domain have been confirmed through vibrational energy analysis. Negative bonding parameter (δ) values indicate that, the metal-ligand environment in the prepared glasses is of ionic in nature. The oscillator strength and the luminescent intensity Ωλ (λ = 2, 4 and 6) parameters are calculated using Judd-Ofelt theory. The radiative properties such as transition probability (A), stimulated emission cross-section (σpE) and branching ratios (β) have been calculated using JO intensity parameters and compared with the reported Dy3+ doped glasses. Concentration effect on Y/B intensity ratios and the CIE chromaticity coordinates were calculated for the generation of white light from the luminescence spectra. The color purity and the correlated color temperature were also calculated and the results are discussed in the present work. The decay of the 4F9/2 excited level is found to be single exponential for lower concentration and become non-exponential for higher concentration. The non-exponential behavior arises due to the efficient energy transfer between the Dy3+ ions through various non-radiative relaxation channels and the decay of the 4F9/2 excited level have been analyzed with IH model. Among the prepared glasses, BPA0.5D glass exhibits higher σpE, βR, σpE×σpE, σpE×Δλeff and η values for the 6H13/2 emission band which in turn specifies its suitability for white LEDs, laser applications and optical amplifiers.

White light generation in Dy3+-doped fluorosilicate glasses for W-LED applications

NASA Astrophysics Data System (ADS)

Krishnaiah, K. Venkata; Jayasankar, C. K.

2011-05-01

Dysprosium doped fluorosilicate (SNbKZLF:SiO2-Nb2O5-K2O-ZnF2-LiF) glasses have been prepared and studied through excitation, emission and decay rate analysis. Sharp emission peaks were observed at 485 nm (blue) and 577 nm (yellow) under 387 nm excitation, which are attributed to 4F9/2 --> 6H15/2 and 4F9/2 --> 6H13/2 transitions, respectively, of Dy3+ ions. The yellow-to-blue intensity ratio increases (0.85 to 1.19) with increase in Dy3+ ion concentration. The decay rates exhibit single exponential for lower concentrations and turns into non-exponential for higher concentrations. The non-exponential nature of the decay rates are well-fitted to the Inokuti-Hirayama model for S = 6, which indicates that the nature of the energy transfer between donor and acceptor ions is of dipole-dipole type. The lifetime for the 4F9/2 level of Dy3+ ion decreases (0.42 to 0.14 ms), whereas energy transfer parameter increases (0.11 to 0.99) with increase of Dy3+ ion concentration (0.05 to 4.0 mol %). The chromaticity coordinates have been calculated from the emission spectra and analyzed with Commission International de I'Eclairage diagram. The chromaticity coordinates appeared in the white light region for all concentrations of Dy3+ ions in the present glasses. The correlated color temperature value decreases from 5597 K (closer to the day light value of 5500 K) to 4524 K with increase of Dy2O3 ion concentration from 0.01 to 4.0 mol %. These results indicate that Dy3+:SNbKZLF glasses can be considered as a potential host material for the development of white light emitting diodes.

Lumley decomposition of turbulent boundary layer at high Reynolds numbers

NASA Astrophysics Data System (ADS)

Tutkun, Murat; George, William K.

2017-02-01

The decomposition proposed by Lumley in 1966 is applied to a high Reynolds number turbulent boundary layer. The experimental database was created by a hot-wire rake of 143 probes in the Laboratoire de Mécanique de Lille wind tunnel. The Reynolds numbers based on momentum thickness (Reθ) are 9800 and 19 100. Three-dimensional decomposition is performed, namely, proper orthogonal decomposition (POD) in the inhomogeneous and bounded wall-normal direction, Fourier decomposition in the homogeneous spanwise direction, and Fourier decomposition in time. The first POD modes in both cases carry nearly 50% of turbulence kinetic energy when the energy is integrated over Fourier dimensions. The eigenspectra always peak near zero frequency and most of the large scale, energy carrying features are found at the low end of the spectra. The spanwise Fourier mode which has the largest amount of energy is the first spanwise mode and its symmetrical pair. Pre-multiplied eigenspectra have only one distinct peak and it matches the secondary peak observed in the log-layer of pre-multiplied velocity spectra. Energy carrying modes obtained from the POD scale with outer scaling parameters. Full or partial reconstruction of turbulent velocity signal based only on energetic modes or non-energetic modes revealed the behaviour of urms in distinct regions across the boundary layer. When urms is based on energetic reconstruction, there exists (a) an exponential decay from near wall to log-layer, (b) a constant layer through the log-layer, and (c) another exponential decay in the outer region. The non-energetic reconstruction reveals that urms has (a) an exponential decay from the near-wall to the end of log-layer and (b) a constant layer in the outer region. Scaling of urms using the outer parameters is best when both energetic and non-energetic profiles are combined.

Sensitivity of coronal loop sausage mode frequencies and decay rates to radial and longitudinal density inhomogeneities: a spectral approach

NASA Astrophysics Data System (ADS)

Cally, Paul S.; Xiong, Ming

2018-01-01

Fast sausage modes in solar magnetic coronal loops are only fully contained in unrealistically short dense loops. Otherwise they are leaky, losing energy to their surrounds as outgoing waves. This causes any oscillation to decay exponentially in time. Simultaneous observations of both period and decay rate therefore reveal the eigenfrequency of the observed mode, and potentially insight into the tubes’ nonuniform internal structure. In this article, a global spectral description of the oscillations is presented that results in an implicit matrix eigenvalue equation where the eigenvalues are associated predominantly with the diagonal terms of the matrix. The off-diagonal terms vanish identically if the tube is uniform. A linearized perturbation approach, applied with respect to a uniform reference model, is developed that makes the eigenvalues explicit. The implicit eigenvalue problem is easily solved numerically though, and it is shown that knowledge of the real and imaginary parts of the eigenfrequency is sufficient to determine the width and density contrast of a boundary layer over which the tubes’ enhanced internal densities drop to ambient values. Linearized density kernels are developed that show sensitivity only to the extreme outside of the loops for radial fundamental modes, especially for small density enhancements, with no sensitivity to the core. Higher radial harmonics do show some internal sensitivity, but these will be more difficult to observe. Only kink modes are sensitive to the tube centres. Variation in internal and external Alfvén speed along the loop is shown to have little effect on the fundamental dimensionless eigenfrequency, though the associated eigenfunction becomes more compact at the loop apex as stratification increases, or may even displace from the apex.

FLIMX: A Software Package to Determine and Analyze the Fluorescence Lifetime in Time-Resolved Fluorescence Data from the Human Eye

PubMed Central

Klemm, Matthias; Schweitzer, Dietrich; Peters, Sven; Sauer, Lydia; Hammer, Martin; Haueisen, Jens

2015-01-01

Fluorescence lifetime imaging ophthalmoscopy (FLIO) is a new technique for measuring the in vivo autofluorescence intensity decays generated by endogenous fluorophores in the ocular fundus. Here, we present a software package called FLIM eXplorer (FLIMX) for analyzing FLIO data. Specifically, we introduce a new adaptive binning approach as an optimal tradeoff between the spatial resolution and the number of photons required per pixel. We also expand existing decay models (multi-exponential, stretched exponential, spectral global analysis, incomplete decay) to account for the layered structure of the eye and present a method to correct for the influence of the crystalline lens fluorescence on the retina fluorescence. Subsequently, the Holm-Bonferroni method is applied to FLIO measurements to allow for group comparisons between patients and controls on the basis of fluorescence lifetime parameters. The performance of the new approaches was evaluated in five experiments. Specifically, we evaluated static and adaptive binning in a diabetes mellitus patient, we compared the different decay models in a healthy volunteer and performed a group comparison between diabetes patients and controls. An overview of the visualization capabilities and a comparison of static and adaptive binning is shown for a patient with macular hole. FLIMX’s applicability to fluorescence lifetime imaging microscopy is shown in the ganglion cell layer of a porcine retina sample, obtained by a laser scanning microscope using two-photon excitation. PMID:26192624

Thermal decay of Coulomb blockade oscillations

NASA Astrophysics Data System (ADS)

Idrisov, Edvin G.; Levkivskyi, Ivan P.; Sukhorukov, Eugene V.

2017-10-01

We study transport properties and the charge quantization phenomenon in a small metallic island connected to the leads through two quantum point contacts (QPCs). The linear conductance is calculated perturbatively with respect to weak tunneling and weak backscattering at QPCs as a function of the temperature T and gate voltage. The conductance shows Coulomb blockade (CB) oscillations as a function of the gate voltage that decay with the temperature as a result of thermally activated fluctuations of the charge in the island. The regimes of quantum T ≪EC and thermal T ≫EC fluctuations are considered, where EC is the charging energy of an isolated island. Our predictions for CB oscillations in the quantum regime coincide with previous findings by Furusaki and Matveev [Phys. Rev. B 52, 16676 (1995), 10.1103/PhysRevB.52.16676]. In the thermal regime the visibility of Coulomb blockade oscillations decays with the temperature as √{T /EC }exp(-π2T /EC) , where the exponential dependence originates from the thermal averaging over the instant charge fluctuations, while the prefactor has a quantum origin. This dependence does not depend on the strength of couplings to the leads. The differential capacitance, calculated in the case of a single tunnel junction, shows the same exponential decay, however the prefactor is linear in the temperature. This difference can be attributed to the nonlocality of the quantum effects. Our results agree with the recent experiment [Nature (London) 536, 58 (2016), 10.1038/nature19072] in the whole range of the parameter T /EC .

Bending Boundary Layers in Laminated-Composite Circular Cylindrical Shells

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.; Smeltzer, Stanley S., III

2000-01-01

An analytical, parametric study of the attenuation of bending boundary layers or edge effects in balanced and unbalanced, symmetrically and unsymmetrically laminated thin cylindrical shells is presented for nine contemporary material systems. The analysis is based on the linear Sanders-Koiter shell equations and specializations to the Love-Kirchhoff shell equations and Donnell's equations are included. Two nondimensional parameters are identified that characterize and quantify the effects of laminate orthotropy and laminate anisotropy on the bending boundary-layer decay length in a very general and encompassing manner. A substantial number of structural design technology results are presented for a wide range of laminated-composite cylinders. For all the laminate constructions considered, the results show that the differences between results that were obtained with the Sanders-Koiter shell equations, the Love-Kirchhoff shell equations, and Donnell's equations are negligible. The results also show that the effect of anisotropy in the form of coupling between pure bending and twisting has a negligible effect on the size of the bending boundary-layer decay length of the balanced, symmetrically laminated cylinders considered. Moreover, the results show that coupling between the various types of shell anisotropies has a negligible effect on the calculation of the bending boundary-layer decay length in most cases. The results also show that in some cases neglecting the shell anisotropy results in underestimating the bending boundary-layer decay length and in other cases it results in an overestimation.

Semiclassical analysis of spectral singularities and their applications in optics

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

Mostafazadeh, Ali

2011-08-15

Motivated by possible applications of spectral singularities in optics, we develop a semiclassical method of computing spectral singularities. We use this method to examine the spectral singularities of a planar slab gain medium whose gain coefficient varies due to the exponential decay of the intensity of the pumping beam inside the medium. For both singly and doublypumped samples, we obtain universal upper bounds on the decay constant beyond which no lasing occurs. Furthermore, we show that the dependence of the wavelength of the spectral singularities on the value of the decay constant is extremely mild. This is an indication ofmore » the stability of optical spectral singularities.« less

Modified spontaneous emission of silicon nanocrystals embedded in artificial opals

NASA Astrophysics Data System (ADS)

Janda, Petr; Valenta, Jan; Rehspringer, Jean-Luc; Mafouana, Rodrigue R.; Linnros, Jan; Elliman, Robert G.

2007-10-01

Si nanocrystals (NCs) were embedded in synthetic silica opals by means of Si-ion implantation or opal impregnation with porous-Si suspensions. In both types of sample photoluminescence (PL) is strongly Bragg-reflection attenuated (up to 75%) at the frequency of the opal stop-band in a direction perpendicular to the (1 1 1) face of the perfect hcp opal structure. Time-resolved PL shows a rich distribution of decay rates, which contains both shorter and longer decay components compared with the ordinary stretched exponential decay of Si NCs. This effect reflects changes in the spontaneous emission rate of Si NCs due to variations in the local density of states of real opal containing defects.

Exponential integrators in time-dependent density-functional calculations

NASA Astrophysics Data System (ADS)

Kidd, Daniel; Covington, Cody; Varga, Kálmán

2017-12-01

The integrating factor and exponential time differencing methods are implemented and tested for solving the time-dependent Kohn-Sham equations. Popular time propagation methods used in physics, as well as other robust numerical approaches, are compared to these exponential integrator methods in order to judge the relative merit of the computational schemes. We determine an improvement in accuracy of multiple orders of magnitude when describing dynamics driven primarily by a nonlinear potential. For cases of dynamics driven by a time-dependent external potential, the accuracy of the exponential integrator methods are less enhanced but still match or outperform the best of the conventional methods tested.

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

Bourdon, J.C.; Peltier, B.; Cooper, G.A.

In this paper, field drill-off test results are compared with data from laboratory simulations. A simple theory for analyzing drill-off tests is developed. The weight-on bit (WOB) decay with time is close to exponential, but large threshold WOB's, resulting from poor weight transmission downhole, are sometimes observed in field tests.

Higgsplosion: Solving the hierarchy problem via rapid decays of heavy states into multiple Higgs bosons

NASA Astrophysics Data System (ADS)

Khoze, Valentin V.; Spannowsky, Michael

2018-01-01

We introduce and discuss two inter-related mechanisms operative in the electroweak sector of the Standard Model at high energies. Higgsplosion, the first mechanism, occurs at some critical energy in the 25 to 103 TeV range, and leads to an exponentially growing decay rate of highly energetic particles into multiple Higgs bosons. We argue that this is a well-controlled non-perturbative phenomenon in the Higgs-sector which involves the final state Higgs multiplicities n in the regime nλ ≫ 1 where λ is the Higgs self-coupling. If this mechanism is realised in nature, the cross-sections for producing ultra-high multiplicities of Higgs bosons are likely to become observable and even dominant in this energy range. At the same time, however, the apparent exponential growth of these cross-sections at even higher energies will be tamed and automatically cut-off by a related Higgspersion mechanism. As a result, and in contrast to previous studies, multi-Higgs production does not violate perturbative unitarity. Building on this approach, we then argue that the effects of Higgsplosion alter quantum corrections from very heavy states to the Higgs boson mass. Above a certain energy, which is much smaller than their masses, these states would rapidly decay into multiple Higgs bosons. The heavy states become unrealised as they decay much faster than they are formed. The loop integrals contributing to the Higgs mass will be cut off not by the masses of the heavy states, but by the characteristic loop momenta where their decay widths become comparable to their masses. Hence, the cut-off scale would be many orders of magnitude lower than the heavy mass scales themselves, thus suppressing their quantum corrections to the Higgs boson mass.

Freezing and melting water in lamellar structures.

PubMed Central

Gleeson, J T; Erramilli, S; Gruner, S M

1994-01-01

The manner in which ice forms in lamellar suspensions of dielaidoylphosphatidylethanolamine, dielaidoylphosphatidylcholine, and dioleoylphosphatidylcholine in water depends strongly on the water fraction. For weight fractions between 15 and 9%, the freezing and melting temperatures are significantly depressed below 0 degree C. The ice exhibits a continuous melting transition spanning as much as 20 degrees C. When the water weight fraction is below 9%, ice never forms at temperatures as low as -40 degrees C. We show that when water contained in a lamellar lipid suspension freezes, the ice is not found between the bilayers; it exists as pools of crystalline ice in equilibrium with the bound water associated with the polar lipid headgroups. We have used this effect, together with the known chemical potential of ice, to measure hydration forces between lipid bilayers. We find exponentially decaying hydration repulsion when the bilayers are less than about 7 A apart. For larger separations, we find significant deviations from single exponential decay. PMID:7948683

Taming the runaway problem of inflationary landscapes

NASA Astrophysics Data System (ADS)

Hall, Lawrence J.; Watari, Taizan; Yanagida, T. T.

2006-05-01

A wide variety of vacua, and their cosmological realization, may provide an explanation for the apparently anthropic choices of some parameters of particle physics and cosmology. If the probability on various parameters is weighted by volume, a flat potential for slow-roll inflation is also naturally understood, since the flatter the potential the larger the volume of the subuniverse. However, such inflationary landscapes have a serious problem, predicting an environment that makes it exponentially hard for observers to exist and giving an exponentially small probability for a moderate universe like ours. A general solution to this problem is proposed, and is illustrated in the context of inflaton decay and leptogenesis, leading to an upper bound on the reheating temperature in our subuniverse. In a particular scenario of chaotic inflation and nonthermal leptogenesis, predictions can be made for the size of CP violating phases, the rate of neutrinoless double beta decay and, in the case of theories with gauge-mediated weak-scale supersymmetry, for the fundamental scale of supersymmetry breaking.

Maximum nondiffracting propagation distance of aperture-truncated Airy beams

NASA Astrophysics Data System (ADS)

Chu, Xingchun; Zhao, Shanghong; Fang, Yingwu

2018-05-01

Airy beams have called attention of many researchers due to their non-diffracting, self-healing and transverse accelerating properties. A key issue in research of Airy beams and its applications is how to evaluate their nondiffracting propagation distance. In this paper, the critical transverse extent of physically realizable Airy beams is analyzed under the local spatial frequency methodology. The maximum nondiffracting propagation distance of aperture-truncated Airy beams is formulated and analyzed based on their local spatial frequency. The validity of the formula is verified by comparing the maximum nondiffracting propagation distance of an aperture-truncated ideal Airy beam, aperture-truncated exponentially decaying Airy beam and exponentially decaying Airy beam. Results show that the formula can be used to evaluate accurately the maximum nondiffracting propagation distance of an aperture-truncated ideal Airy beam. Therefore, it can guide us to select appropriate parameters to generate Airy beams with long nondiffracting propagation distance that have potential application in the fields of laser weapons or optical communications.

Wealth distribution, Pareto law, and stretched exponential decay of money: Computer simulations analysis of agent-based models

NASA Astrophysics Data System (ADS)

Aydiner, Ekrem; Cherstvy, Andrey G.; Metzler, Ralf

2018-01-01

We study by Monte Carlo simulations a kinetic exchange trading model for both fixed and distributed saving propensities of the agents and rationalize the person and wealth distributions. We show that the newly introduced wealth distribution - that may be more amenable in certain situations - features a different power-law exponent, particularly for distributed saving propensities of the agents. For open agent-based systems, we analyze the person and wealth distributions and find that the presence of trap agents alters their amplitude, leaving however the scaling exponents nearly unaffected. For an open system, we show that the total wealth - for different trap agent densities and saving propensities of the agents - decreases in time according to the classical Kohlrausch-Williams-Watts stretched exponential law. Interestingly, this decay does not depend on the trap agent density, but rather on saving propensities. The system relaxation for fixed and distributed saving schemes are found to be different.

Investigation of stickiness influence in the anomalous transport and diffusion for a non-dissipative Fermi-Ulam model

NASA Astrophysics Data System (ADS)

Livorati, André L. P.; Palmero, Matheus S.; Díaz-I, Gabriel; Dettmann, Carl P.; Caldas, Iberê L.; Leonel, Edson D.

2018-02-01

We study the dynamics of an ensemble of non interacting particles constrained by two infinitely heavy walls, where one of them is moving periodically in time, while the other is fixed. The system presents mixed dynamics, where the accessible region for the particle to diffuse chaotically is bordered by an invariant spanning curve. Statistical analysis for the root mean square velocity, considering high and low velocity ensembles, leads the dynamics to the same steady state plateau for long times. A transport investigation of the dynamics via escape basins reveals that depending of the initial velocity ensemble, the decay rates of the survival probability present different shapes and bumps, in a mix of exponential, power law and stretched exponential decays. After an analysis of step-size averages, we found that the stable manifolds play the role of a preferential path for faster escape, being responsible for the bumps and different shapes of the survival probability.

Photoluminescence study of MBE grown InGaN with intentional indium segregation

NASA Astrophysics Data System (ADS)

Cheung, Maurice C.; Namkoong, Gon; Chen, Fei; Furis, Madalina; Pudavar, Haridas E.; Cartwright, Alexander N.; Doolittle, W. Alan

2005-05-01

Proper control of MBE growth conditions has yielded an In0.13Ga0.87N thin film sample with emission consistent with In-segregation. The photoluminescence (PL) from this epilayer showed multiple emission components. Moreover, temperature and power dependent studies of the PL demonstrated that two of the components were excitonic in nature and consistent with indium phase separation. At 15 K, time resolved PL showed a non-exponential PL decay that was well fitted with the stretched exponential solution expected for disordered systems. Consistent with the assumed carrier hopping mechanism of this model, the effective lifetime, , and the stretched exponential parameter, , decrease with increasing emission energy. Finally, room temperature micro-PL using a confocal microscope showed spatial clustering of low energy emission.

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.

Dichotomies for generalized ordinary differential equations and applications

NASA Astrophysics Data System (ADS)

Bonotto, E. M.; Federson, M.; Santos, F. L.

2018-03-01

In this work we establish the theory of dichotomies for generalized ordinary differential equations, introducing the concepts of dichotomies for these equations, investigating their properties and proposing new results. We establish conditions for the existence of exponential dichotomies and bounded solutions. Using the correspondences between generalized ordinary differential equations and other equations, we translate our results to measure differential equations and impulsive differential equations. The fact that we work in the framework of generalized ordinary differential equations allows us to manage functions with many discontinuities and of unbounded variation.

Kinetic study on non-thermal volumetric plasma decay in the early afterglow of air discharge generated by a short pulse microwave or laser

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

Yang, Wei, E-mail: yangwei861212@126.com; Zhou, Qianhong; Dong, Zhiwei

This paper reports a kinetic study on non-thermal plasma decay in the early afterglow of air discharge generated by short pulse microwave or laser. A global self-consistent model is based on the particle balance of complex plasma chemistry, electron energy equation, and gas thermal balance equation. Electron-ion Coulomb collision is included in the steady state Boltzmann equation solver to accurately describe the electron mobility and other transport coefficients. The model is used to simulate the afterglow of microsecond to nanosecond pulse microwave discharge in N{sub 2}, O{sub 2}, and air, as well as femtosecond laser filament discharge in dry andmore » humid air. The simulated results for electron density decay are in quantitative agreement with the available measured ones. The evolution of plasma decay under an external electric field is also investigated, and the effect of gas heating is considered. The underlying mechanism of plasma density decay is unveiled through the above kinetic modeling.« less

What Randomized Benchmarking Actually Measures

DOE PAGES

Proctor, Timothy; Rudinger, Kenneth; Young, Kevin; ...

2017-09-28

Randomized benchmarking (RB) is widely used to measure an error rate of a set of quantum gates, by performing random circuits that would do nothing if the gates were perfect. In the limit of no finite-sampling error, the exponential decay rate of the observable survival probabilities, versus circuit length, yields a single error metric r. For Clifford gates with arbitrary small errors described by process matrices, r was believed to reliably correspond to the mean, over all Clifford gates, of the average gate infidelity between the imperfect gates and their ideal counterparts. We show that this quantity is not amore » well-defined property of a physical gate set. It depends on the representations used for the imperfect and ideal gates, and the variant typically computed in the literature can differ from r by orders of magnitude. We present new theories of the RB decay that are accurate for all small errors describable by process matrices, and show that the RB decay curve is a simple exponential for all such errors. Here, these theories allow explicit computation of the error rate that RB measures (r), but as far as we can tell it does not correspond to the infidelity of a physically allowed (completely positive) representation of the imperfect gates.« less

Normal mode analysis on the relaxation of an excited nitromethane molecule in argon bath

NASA Astrophysics Data System (ADS)

Rivera-Rivera, Luis; Wagner, Albert

In our previous work [J. Chem. Phys. 142, 014303 (2015)] classical molecular dynamics simulations followed in an Ar bath the relaxation of nitromethane (CH3NO2) instantaneously excited by statistically distributing 50 kcal/mol among all its internal degrees of freedom. The 300 K Ar bath was at pressures of 10 to 400 atm, a range spanning the breakdown of the isolated binary collision approximation. Both rotational and vibrational energies exhibit multi-exponential decay. This study explores mode-specific mechanisms at work in the decay process. With the separation of rotation and vibration developed by Rhee and Kim [J. Chem. Phys. 107, 1394 (1997)], one can show that the vibrational kinetic energy decomposes only into vibrational normal modes while the rotational and Coriolis energies decompose into both vibrational and rotational normal modes. Then the saved CH3NO2 positions and momenta can be converted into mode-specific energies whose decay over 1000 ps can be monitored. The results identify vibrational and rotational modes that promote/resist energy lost and drive multi-exponential behavior. Increasing pressure can be shown to increasingly interfere with post-collision IVR. The work was supported by the U.S. Department of Energy, Office of Science, Chemical Sciences, Geosciences, and Biosciences Division.

Short range shooting distance estimation using variable pressure SEM images of the surroundings of bullet holes in textiles.

PubMed

Hinrichs, Ruth; Frank, Paulo Ricardo Ost; Vasconcellos, M A Z

2017-03-01

Modifications of cotton and polyester textiles due to shots fired at short range were analyzed with a variable pressure scanning electron microscope (VP-SEM). Different mechanisms of fiber rupture as a function of fiber type and shooting distance were detected, namely fusing, melting, scorching, and mechanical breakage. To estimate the firing distance, the approximately exponential decay of GSR coverage as a function of radial distance from the entrance hole was determined from image analysis, instead of relying on chemical analysis with EDX, which is problematic in the VP-SEM. A set of backscattered electron images, with sufficient magnification to discriminate micrometer wide GSR particles, was acquired at different radial distances from the entrance hole. The atomic number contrast between the GSR particles and the organic fibers allowed to find a robust procedure to segment the micrographs into binary images, in which the white pixel count was attributed to GSR coverage. The decrease of the white pixel count followed an exponential decay, and it was found that the reciprocal of the decay constant, obtained from the least-square fitting of the coverage data, showed a linear dependence on the shooting distance. Copyright © 2017 Elsevier Ireland Ltd. All rights reserved.

Kinetics and components of the flash photocurrent of isolated retinal rods of the larval salamander, Ambystoma tigrinum.

PubMed Central

Cobbs, W H; Pugh, E N

1987-01-01

1. Membrane currents initiated by intense, 20 microseconds flashes (photocurrents) were recorded from isolated salamander rods by combined extracellular suction electrodes and intracellular tight-seal electrodes either in current or voltage clamp mode. The magnitudes (mean +/- 2 S.E.M.) of the maximal photoresponses recorded by the suction and by the intracellular electrode respectively were 40 +/- 5 pA (n = 18) and 35 +/- 7 mV (n = 8) for current clamp at zero current; 43 +/- 9 pA and 66 +/- 13 (n = 11) pA for voltage clamp at the zero-current holding potential, -24 +/- 3 mV. 2. Photocurrents initiated by flashes isomerizing 0.1% or more of the outer segment's rhodopsin achieved a saturated velocity and were 95% complete in less than 50 ms. The effect of incrementing flash intensity above 0.1% isomerization can be described as a translation of the photocurrent along the time axis towards the origin. Within the interval 0-50 ms the latter two-thirds of the velocity-saturated photocurrent is well described as a single-exponential decay. The decay was much faster in voltage clamp (2.8 +/- 1.2 ms, n = 11) than in current clamp mode (17 +/- 5 ms, n = 17). 3. The initial third of the velocity-saturated photocurrent, occurring over the interval from the flash to the onset of exponential decay, followed about the same time course in current and voltage clamp. The time interval occupied by this initial 'latent' phase decreased with increasing flash intensity and attained an apparent minimum of about 7 ms in response to flashes isomerizing 10% or more of the rhodopsin at ca. 22 degrees C. 4. The hypothesis that the decay of outer segment light-sensitive membrane current is the same in current and voltage clamp was supported by an analysis of the difference between outer segment currents measured successively in the two recording modes. First, the tail of the difference current decayed exponentially with a time constant approximately equal to R x C, where R and C are independently estimated slope resistance and capacitance of the rod. Secondly, the integral of the difference current, when divided by outer segment capacitance, closely approximated the hyperpolarizing light response measured under current clamp. Thus, displacement current accounted for the difference between photocurrents measured in current and voltage clamp.(ABSTRACT TRUNCATED AT 400 WORDS) PMID:2832596

Growth or decay of cosmological inhomogeneities as a function of their equation of state

NASA Astrophysics Data System (ADS)

Comer, G. L.; Deruelle, Nathalie; Langlois, David; Parry, Joe

1994-03-01

We expand Einstein's equations in the synchronous gauge in terms of a purely space-dependent, ``seed,'' metric. The (nonlinear) solution accurately describes a universe inhomogeneous at scales larger than the Hubble radius. We show that the inhomogeneities grow or decay, as time increases, depending on the equation of state for the matter (supposed to be a perfect fluid). We then consider the case when matter is a scalar field with an arbitrary potential. Finally we discuss the generality of the model and show that it is an attractor for a class of generic solutions of Einstein's equations.

An implicit semianalytic numerical method for the solution of nonequilibrium chemistry problems

NASA Technical Reports Server (NTRS)

Graves, R. A., Jr.; Gnoffo, P. A.; Boughner, R. E.

1974-01-01

The first order differential equation form systems of equations. They are solved by a simple and relatively accurate implicit semianalytic technique which is derived from a quadrature solution of the governing equation. This method is mathematically simpler than most implicit methods and has the exponential nature of the problem embedded in the solution.

Regional height-diameter equations for major tree species of southwest Oregon.

Treesearch

H. Temesgen; D.W. Hann; V.J. Monleon

2006-01-01

Selected tree height and diameter functions were evaluated for their predictive abilities for major tree species of southwest Oregon. The equations included tree diameter alone, or diameter plus alternative measures of stand density and relative position. Two of the base equations were asymptotic functions, and two were exponential functional forms. The inclusion of...

Well-posedness and decay for the dissipative system modeling electro-hydrodynamics in negative Besov spaces

NASA Astrophysics Data System (ADS)

Zhao, Jihong; Liu, Qiao

2017-07-01

In Guo and Wang (2012) [10], Y. Guo and Y. Wang developed a general new energy method for proving the optimal time decay rates of the solutions to dissipative equations. In this paper, we generalize this method in the framework of homogeneous Besov spaces. Moreover, we apply this method to a model arising from electro-hydrodynamics, which is a strongly coupled system of the Navier-Stokes equations and the Poisson-Nernst-Planck equations through charge transport and external forcing terms. We show that some weighted negative Besov norms of solutions are preserved along time evolution, and obtain the optimal time decay rates of the higher-order spatial derivatives of solutions by the Fourier splitting approach and the interpolation techniques.

Scattering transform for nonstationary Schroedinger equation with bidimensionally perturbed N-soliton potential

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

Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.

2006-12-15

In the framework of the extended resolvent approach the direct and inverse scattering problems for the nonstationary Schroedinger equation with a potential being a perturbation of the N-soliton potential by means of a generic bidimensional smooth function decaying at large spaces are introduced and investigated. The initial value problem of the Kadomtsev-Petviashvili I equation for a solution describing N wave solitons on a generic smooth decaying background is then linearized, giving the time evolution of the spectral data.

Eigenmode Analysis of Boundary Conditions for One-Dimensional Preconditioned Euler Equations

NASA Technical Reports Server (NTRS)

Darmofal, David L.

1998-01-01

An analysis of the effect of local preconditioning on boundary conditions for the subsonic, one-dimensional Euler equations is presented. Decay rates for the eigenmodes of the initial boundary value problem are determined for different boundary conditions. Riemann invariant boundary conditions based on the unpreconditioned Euler equations are shown to be reflective with preconditioning, and, at low Mach numbers, disturbances do not decay. Other boundary conditions are investigated which are non-reflective with preconditioning and numerical results are presented confirming the analysis.

Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities

PubMed Central

Vázquez, J. L.

2010-01-01

The goal of this paper is to state the optimal decay rate for solutions of the nonlinear fast diffusion equation and, in self-similar variables, the optimal convergence rates to Barenblatt self-similar profiles and their generalizations. It relies on the identification of the optimal constants in some related Hardy–Poincaré inequalities and concludes a long series of papers devoted to generalized entropies, functional inequalities, and rates for nonlinear diffusion equations. PMID:20823259

X-ray detection capability of a BaCl{sub 2} single crystal scintillator

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

Koshimizu, Masanori; CREST, Japan Science and Technology Agency, Sanbancho, Chiyoda-ku, Tokyo 102-0075; Onodera, Kazuya

2012-01-15

The x-ray detection capability of a scintillation detector equipped with a BaCl{sub 2} single crystal was evaluated. The scintillation decay kinetics can be expressed by a sum of two exponential decay components. The fast and slow components have lifetimes of 1.5 and 85 ns, respectively. The total light output is 5% that of YAP:Ce. A subnanosecond timing resolution was obtained. The detection efficiency of a 67.41 keV x-ray is 87% for a detector equipped with a BaCl{sub 2} crystal 6-mm thick. Thus, excellent timing resolution and high detection efficiency can be simultaneously achieved. Additionally, luminescence decay characteristics under vacuum ultravioletmore » excitation have been investigated. Radiative decay of self-trapped excitons is thought to be responsible for the fast scintillation component.« less

A demographic study of the exponential distribution applied to uneven-aged forests

Treesearch

Jeffrey H. Gove

2016-01-01

A demographic approach based on a size-structured version of the McKendrick-Von Foerster equation is used to demonstrate a theoretical link between the population size distribution and the underlying vital rates (recruitment, mortality and diameter growth) for the population of individuals whose diameter distribution is negative exponential. This model supports the...

Ground-state proton decay of 69Br and implications for the rp -process 68Se waiting-point

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

Rogers, Andrew M; Shapira, Dan; Lynch, William

2011-01-01

The first direct measurement of the proton separation energy, S p , for the proton-unbound nucleus 69Br is reported. Of interest is the exponential dependence of the 2 p-capture rate on S p which can bypass the 68Se waiting-point in the astrophysical rp process. An analysis of the observed proton decay spectrum is given in terms of the 69Se mirror nucleus and the influence of S p is explored within the context of a single-zone X-ray burst model.

Evolution and modulation of intracellular calcium release during long-lasting, depleting depolarization in mouse muscle

PubMed Central

Royer, Leandro; Pouvreau, Sandrine; Ríos, Eduardo

2008-01-01

Intracellular calcium signals regulate multiple cellular functions. They depend on release of Ca2+ from cellular stores into the cytosol, a process that in many types of cells appears to be tightly controlled by changes in [Ca2+] within the store. In contrast with cardiac muscle, where depletion of Ca2+ in the sarcoplasmic reticulum is a crucial determinant of termination of Ca2+ release, in skeletal muscle there is no agreement regarding the sign, or even the existence of an effect of SR Ca2+ level on Ca2+ release. To address this issue we measured Ca2+ transients in mouse flexor digitorum brevis (FDB) skeletal muscle fibres under voltage clamp, using confocal microscopy and the Ca2+ monitor rhod-2. The evolution of Ca2+ release flux was quantified during long-lasting depolarizations that reduced severely the Ca2+ content of the SR. As in all previous determinations in mammals and non-mammals, release flux consisted of an early peak, relaxing to a lower level from which it continued to decay more slowly. Decay of flux in this second stage, which has been attributed largely to depletion of SR Ca2+, was studied in detail. A simple depletion mechanism without change in release permeability predicts an exponential decay with time. In contrast, flux decreased non-exponentially, to a finite, measurable level that could be maintained for the longest pulses applied (1.8 s). An algorithm on the flux record allowed us to define a quantitative index, the normalized flux rate of change (NFRC), which was shown to be proportional to the ratio of release permeability P and inversely proportional to Ca2+ buffering power B of the SR, thus quantifying the ‘evacuability’ or ability of the SR to empty its content. When P and B were constant, flux then decayed exponentially, and NFRC was equal to the exponential rate constant. Instead, in most cases NFRC increased during the pulse, from a minimum reached immediately after the early peak in flux, to a time between 200 and 250 ms, when the index was no longer defined. NFRC increased by 111% on average (in 27 images from 18 cells), reaching 300% in some cases. The increase may reflect an increase in P, a decrease in B, or both. On experimental and theoretical grounds, both changes are to be expected upon SR depletion. A variable evacuability helps maintain a constant Ca2+ output under conditions of diminishing store Ca2+ load. PMID:18687715

Adiabatic decay of internal solitons due to Earth's rotation within the framework of the Gardner-Ostrovsky equation

NASA Astrophysics Data System (ADS)

Obregon, Maria; Raj, Nawin; Stepanyants, Yury

2018-03-01

The adiabatic decay of different types of internal wave solitons caused by the Earth's rotation is studied within the framework of the Gardner-Ostrovsky equation. The governing equation describing such processes includes quadratic and cubic nonlinear terms, as well as the Boussinesq and Coriolis dispersions: (ut + c ux + α u ux + α1 u2 ux + β uxxx)x = γ u. It is shown that at the early stage of evolution solitons gradually decay under the influence of weak Earth's rotation described by the parameter γ. The characteristic decay time is derived for different types of solitons for positive and negative coefficients of cubic nonlinearity α1 (both signs of that parameter may occur in the oceans). The coefficient of quadratic nonlinearity α determines only a polarity of solitary wave when α1 < 0 or the asymmetry of solitary waves of opposite polarity when α1 > 0. It is found that the adiabatic theory describes well the decay of solitons having bell-shaped profiles. In contrast to that, large amplitude table-top solitons, which can exist when α1 is negative, are structurally unstable. Under the influence of Earth's rotation, they transfer first to the bell-shaped solitons, which decay then adiabatically. Estimates of the characteristic decay time of internal solitons are presented for the real oceanographic conditions.

Lump solutions and interaction phenomenon to the third-order nonlinear evolution equation

NASA Astrophysics Data System (ADS)

Kofane, T. C.; Fokou, M.; Mohamadou, A.; Yomba, E.

2017-11-01

In this work, the lump solution and the kink solitary wave solution from the (2 + 1) -dimensional third-order evolution equation, using the Hirota bilinear method are obtained through symbolic computation with Maple. We have assumed that the lump solution is centered at the origin, when t = 0 . By considering a mixing positive quadratic function with exponential function, as well as a mixing positive quadratic function with hyperbolic cosine function, interaction solutions like lump-exponential and lump-hyperbolic cosine are presented. A completely non-elastic interaction between a lump and kink soliton is observed, showing that a lump solution can be swallowed by a kink soliton.

A nonperturbative light-front coupled-cluster method

NASA Astrophysics Data System (ADS)

Hiller, J. R.

2012-10-01

The nonperturbative Hamiltonian eigenvalue problem for bound states of a quantum field theory is formulated in terms of Dirac's light-front coordinates and then approximated by the exponential-operator technique of the many-body coupled-cluster method. This approximation eliminates any need for the usual approximation of Fock-space truncation. Instead, the exponentiated operator is truncated, and the terms retained are determined by a set of nonlinear integral equations. These equations are solved simultaneously with an effective eigenvalue problem in the valence sector, where the number of constituents is small. Matrix elements can be calculated, with extensions of techniques from standard coupled-cluster theory, to obtain form factors and other observables.

Exponential model normalization for electrical capacitance tomography with external electrodes under gap permittivity conditions

NASA Astrophysics Data System (ADS)

Baidillah, Marlin R.; Takei, Masahiro

2017-06-01

A nonlinear normalization model which is called exponential model for electrical capacitance tomography (ECT) with external electrodes under gap permittivity conditions has been developed. The exponential model normalization is proposed based on the inherently nonlinear relationship characteristic between the mixture permittivity and the measured capacitance due to the gap permittivity of inner wall. The parameters of exponential equation are derived by using an exponential fitting curve based on the simulation and a scaling function is added to adjust the experiment system condition. The exponential model normalization was applied to two dimensional low and high contrast dielectric distribution phantoms by using simulation and experimental studies. The proposed normalization model has been compared with other normalization models i.e. Parallel, Series, Maxwell and Böttcher models. Based on the comparison of image reconstruction results, the exponential model is reliable to predict the nonlinear normalization of measured capacitance in term of low and high contrast dielectric distribution.

Study of effect of magnetohydrodynamics and couple stress on steady and dynamic characteristics of porous exponential slider bearings

NASA Astrophysics Data System (ADS)

Hanumagowda, B. N.; Gonchigara, Thippeswamy; Santhosh Kumar, J.; MShiva Kumar, H.

2018-04-01

Exponential slider bearings with porous facing is analysed in this article. The modified Reynolds equation is derived for the Exponential porous slider bearing with MHD and couple stress fluid. Computed values of Steady film pressure, Steady load capacity, Dynamic stiffness and Damping coefficient are presented in graphical form. The Steady film pressure, Steady load capacity, Dynamic stiffness and Damping coefficient decreases with increasing values of permeability parameter and increases with increasing values of couplestress parameter and Hartmann number.

An iterative phase-space explicit discontinuous Galerkin method for stellar radiative transfer in extended atmospheres

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

de Almeida, Valmor F.

In this work, a phase-space discontinuous Galerkin (PSDG) method is presented for the solution of stellar radiative transfer problems. It allows for greater adaptivity than competing methods without sacrificing generality. The method is extensively tested on a spherically symmetric, static, inverse-power-law scattering atmosphere. Results for different sizes of atmospheres and intensities of scattering agreed with asymptotic values. The exponentially decaying behavior of the radiative field in the diffusive-transparent transition region, and the forward peaking behavior at the surface of extended atmospheres were accurately captured. The integrodifferential equation of radiation transfer is solved iteratively by alternating between the radiative pressure equationmore » and the original equation with the integral term treated as an energy density source term. In each iteration, the equations are solved via an explicit, flux-conserving, discontinuous Galerkin method. Finite elements are ordered in wave fronts perpendicular to the characteristic curves so that elemental linear algebraic systems are solved quickly by sweeping the phase space element by element. Two implementations of a diffusive boundary condition at the origin are demonstrated wherein the finite discontinuity in the radiation intensity is accurately captured by the proposed method. This allows for a consistent mechanism to preserve photon luminosity. The method was proved to be robust and fast, and a case is made for the adequacy of parallel processing. In addition to classical two-dimensional plots, results of normalized radiation intensity were mapped onto a log-polar surface exhibiting all distinguishing features of the problem studied.« less

An iterative phase-space explicit discontinuous Galerkin method for stellar radiative transfer in extended atmospheres

DOE PAGES

de Almeida, Valmor F.

2017-04-19

In this work, a phase-space discontinuous Galerkin (PSDG) method is presented for the solution of stellar radiative transfer problems. It allows for greater adaptivity than competing methods without sacrificing generality. The method is extensively tested on a spherically symmetric, static, inverse-power-law scattering atmosphere. Results for different sizes of atmospheres and intensities of scattering agreed with asymptotic values. The exponentially decaying behavior of the radiative field in the diffusive-transparent transition region, and the forward peaking behavior at the surface of extended atmospheres were accurately captured. The integrodifferential equation of radiation transfer is solved iteratively by alternating between the radiative pressure equationmore » and the original equation with the integral term treated as an energy density source term. In each iteration, the equations are solved via an explicit, flux-conserving, discontinuous Galerkin method. Finite elements are ordered in wave fronts perpendicular to the characteristic curves so that elemental linear algebraic systems are solved quickly by sweeping the phase space element by element. Two implementations of a diffusive boundary condition at the origin are demonstrated wherein the finite discontinuity in the radiation intensity is accurately captured by the proposed method. This allows for a consistent mechanism to preserve photon luminosity. The method was proved to be robust and fast, and a case is made for the adequacy of parallel processing. In addition to classical two-dimensional plots, results of normalized radiation intensity were mapped onto a log-polar surface exhibiting all distinguishing features of the problem studied.« less

An accurate method for evaluating the kernel of the integral equation relating lift to downwash in unsteady potential flow

NASA Technical Reports Server (NTRS)

Desmarais, R. N.

1982-01-01

The method is capable of generating approximations of arbitrary accuracy. It is based on approximating the algebraic part of the nonelementary integrals in the kernel by exponential functions and then integrating termwise. The exponent spacing in the approximation is a geometric sequence. The coefficients and exponent multiplier of the exponential approximation are computed by least squares so the method is completely automated. Exponential approximates generated in this manner are two orders of magnitude more accurate than the exponential approximation that is currently most often used for this purpose. The method can be used to generate approximations to attain any desired trade-off between accuracy and computing cost.

Imaging the He2 quantum halo state using a free electron laser

NASA Astrophysics Data System (ADS)

Zeller, Stefan; Kunitski, Maksim; Voigtsberger, Jörg; Kalinin, Anton; Schottelius, Alexander; Schober, Carl; Waitz, Markus; Sann, Hendrik; Hartung, Alexander; Bauer, Tobias; Pitzer, Martin; Trinter, Florian; Goihl, Christoph; Janke, Christian; Richter, Martin; Kastirke, Gregor; Weller, Miriam; Czasch, Achim; Kitzler, Markus; Braune, Markus; Grisenti, Robert E.; Schöllkopf, Wieland; Schmidt, Lothar Ph. H.; Schöffler, Markus S.; Williams, Joshua B.; Jahnke, Till; Dörner, Reinhard

2016-12-01

Quantum tunneling is a ubiquitous phenomenon in nature and crucial for many technological applications. It allows quantum particles to reach regions in space which are energetically not accessible according to classical mechanics. In this “tunneling region,” the particle density is known to decay exponentially. This behavior is universal across all energy scales from nuclear physics to chemistry and solid state systems. Although typically only a small fraction of a particle wavefunction extends into the tunneling region, we present here an extreme quantum system: a gigantic molecule consisting of two helium atoms, with an 80% probability that its two nuclei will be found in this classical forbidden region. This circumstance allows us to directly image the exponentially decaying density of a tunneling particle, which we achieved for over two orders of magnitude. Imaging a tunneling particle shows one of the few features of our world that is truly universal: the probability to find one of the constituents of bound matter far away is never zero but decreases exponentially. The results were obtained by Coulomb explosion imaging using a free electron laser and furthermore yielded He2’s binding energy of 151.9±13.3151.9±13.3 neV, which is in agreement with most recent calculations.

Anomalous T2 relaxation in normal and degraded cartilage.

PubMed

Reiter, David A; Magin, Richard L; Li, Weiguo; Trujillo, Juan J; Pilar Velasco, M; Spencer, Richard G

2016-09-01

To compare the ordinary monoexponential model with three anomalous relaxation models-the stretched Mittag-Leffler, stretched exponential, and biexponential functions-using both simulated and experimental cartilage relaxation data. Monte Carlo simulations were used to examine both the ability of identifying a given model under high signal-to-noise ratio (SNR) conditions and the accuracy and precision of parameter estimates under more modest SNR as would be encountered clinically. Experimental transverse relaxation data were analyzed from normal and enzymatically degraded cartilage samples under high SNR and rapid echo sampling to compare each model. Both simulation and experimental results showed improvement in signal representation with the anomalous relaxation models. The stretched exponential model consistently showed the lowest mean squared error in experimental data and closely represents the signal decay over multiple decades of the decay time (e.g., 1-10 ms, 10-100 ms, and >100 ms). The stretched exponential parameter αse showed an inverse correlation with biochemically derived cartilage proteoglycan content. Experimental results obtained at high field suggest potential application of αse as a measure of matrix integrity. Simulation reflecting more clinical imaging conditions, indicate the ability to robustly estimate αse and distinguish between normal and degraded tissue, highlighting its potential as a biomarker for human studies. Magn Reson Med 76:953-962, 2016. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.

Vibronic relaxation dynamics of o-dichlorobenzene in its lowest excited singlet state

NASA Astrophysics Data System (ADS)

Liu, Benkang; Zhao, Haiyan; Lin, Xiang; Li, Xinxin; Gao, Mengmeng; Wang, Li; Wang, Wei

2018-01-01

Vibronic dynamics of o-dichlorobenzene in its lowest excited singlet state, S1, is investigated in real time by using femtosecond pump-probe method, combined with time-of-flight mass spectroscopy and photoelectron velocity mapping technique. Relaxation processes for the excitation in the range of 276-252 nm can be fitted by single exponential decay model, while in the case of wavelength shorter than 252 nm two-exponential decay model must be adopted for simulating transient profiles. Lifetime constants of the vibrationally excited S1 states change from 651 ± 10 ps for 276 nm excitation to 61 ± 1 ps for 242 nm excitation. Both the internal conversion from the S1 to the highly vibrationally excited ground state S0 and the intersystem crossing from the S1 to the triplet state are supposed to play important roles in de-excitation processes. Exponential fitting of the de-excitation rates on the excitation energy implies such de-excitation process starts from the highly vibrationally excited S0 state, which is validated, by probing the relaxation following photoexcitation at 281 nm, below the S1 origin. Time-dependent photoelectron kinetic energy distributions have been obtained experimentally. As the excitation wavelength changes from 276 nm to 242 nm, different cationic vibronic vibrations can be populated, determined by the Franck-Condon factors between the large geometry distorted excited singlet states and final cationic states.

The electrostatic interaction between interfacial colloidal particles

NASA Astrophysics Data System (ADS)

Hurd, A. J.

1985-11-01

The electrostatic interaction between charged, colloidal particles trapped at an air-water interface is considered using linearised Poisson-Boltzmann results for point particles. In addition to the expected screened-Coulomb contribution, which decays exponentially, an algebraic dipole-dipole interaction occurs that may account for long-range interactions in interfacial colloidal systems.

Forgetting Curves: Implications for Connectionist Models

ERIC Educational Resources Information Center

Sikstrom, Sverker

2002-01-01

Forgetting in long-term memory, as measured in a recall or a recognition test, is faster for items encoded more recently than for items encoded earlier. Data on forgetting curves fit a power function well. In contrast, many connectionist models predict either exponential decay or completely flat forgetting curves. This paper suggests a…

The Beer Lambert Law Measurement Made Easy

ERIC Educational Resources Information Center

Onorato, Pasquale; Gratton, Luigi M.; Polesell, Marta; Salmoiraghi, Alessandro; Oss, Stefano

2018-01-01

We propose the use of a smartphone based apparatus as a valuable tool for investigating the optical absorption of a material and to verify the exponential decay predicted by Beer's law. The very simple experimental activities presented here, suitable for undergraduate students, allows one to measure the material transmittance including its…

Measurement of the Convective Heat-Transfer Coefficient

ERIC Educational Resources Information Center

Conti, Rosaria; Gallitto, Aurelio Agliolo; Fiordilino, Emilio

2014-01-01

We propose an experiment for investigating how objects cool down toward the thermal equilibrium with their surroundings. We describe the time dependence of the temperature difference of the cooling objects and the environment with an exponential decay function. By measuring the thermal constant t, we determine the convective heat-transfer…

Antiferromagnetic exchange and magnetoresistance enhancement in Co-Re superlattices

NASA Astrophysics Data System (ADS)

Freitas, P. P.; Melo, L. V.; Trindade, I.; From, M.; Ferreira, J.; Monteiro, P.

1992-02-01

Co-Re superlattices were prepared that show either antiferromagnetic or ferromagnetic coupling between the Co layers depending on the Re spacer thickness. Enhanced saturation magnetoresistance occurs for antiferromagnetically coupled layers. The saturation magnetoresistance decays exponentially with Re thickness but does not depend critically on the Co thickness.

Well-posedness of the Prandtl equation with monotonicity in Sobolev spaces

NASA Astrophysics Data System (ADS)

Chen, Dongxiang; Wang, Yuxi; Zhang, Zhifei

2018-05-01

By using the paralinearization technique, we prove the well-posedness of the Prandtl equation for monotonic data in anisotropic Sobolev space with exponential weight and low regularity. The proof is very elementary, thus is expected to provide a new possible way for the zero-viscosity limit problem of the Navier-Stokes equations with the non-slip boundary condition.

Current of interacting particles inside a channel of exponential cavities: Application of a modified Fick-Jacobs equation.

PubMed

Suárez, G; Hoyuelos, M; Mártin, H

2016-06-01

Recently a nonlinear Fick-Jacobs equation has been proposed for the description of transport and diffusion of particles interacting through a hard-core potential in tubes or channels of varying cross section [Suárez et al., Phys. Rev. E 91, 012135 (2015)]PLEEE81539-375510.1103/PhysRevE.91.012135. Here we focus on the analysis of the current and mobility when the channel is composed by a chain of asymmetric cavities and a force is applied in one or the opposite direction, for both interacting and noninteracting particles, and compare analytical and Monte Carlo simulation results. We consider a cavity with a shape given by exponential functions; the linear Fick-Jacobs equation for noninteracting particles can be exactly solved in this case. The results of the current difference (when a force is applied in opposite directions) are more accurate for the modified Fick-Jacobs equation for particles with hard-core interaction than for noninteracting ones.

A new modification in the exponential rational function method for nonlinear fractional differential equations

NASA Astrophysics Data System (ADS)

Ahmed, Naveed; Bibi, Sadaf; Khan, Umar; Mohyud-Din, Syed Tauseef

2018-02-01

We have modified the traditional exponential rational function method (ERFM) and have used it to find the exact solutions of two different fractional partial differential equations, one is the time fractional Boussinesq equation and the other is the (2+1)-dimensional time fractional Zoomeron equation. In both the cases it is observed that the modified scheme provides more types of solutions than the traditional one. Moreover, a comparison of the recent solutions is made with some already existing solutions. We can confidently conclude that the modified scheme works better and provides more types of solutions with almost similar computational cost. Our generalized solutions include periodic, soliton-like, singular soliton and kink solutions. A graphical simulation of all types of solutions is provided and the correctness of the solution is verified by direct substitution. The extended version of the solutions is expected to provide more flexibility to scientists working in the relevant field to test their simulation data.

Bifurcation Analysis and Nonlinear Decay of a Tumor in the Presence of an Immune Response

NASA Astrophysics Data System (ADS)

López, Álvaro G.; Seoane, Jesús M.; Sanjuán, Miguel A. F.

2017-12-01

The decay of a planar compact surface that is reduced through its boundary is considered. The interest of this problem lies in the fact that it can represent the destruction of a solid tumor by a population of immune cells. The theory of curves is utilized to derive the rate at which the area of the set decreases. Firstly, the process is represented as a discrete dynamical system. A recurrence equation describing the shrinkage of the area at any step is deduced. Then, a continuum limit is attained to derive an ordinary differential equation that governs the decay of the set. The solutions to the differential equation and its implications are discussed, and numerical simulations are carried out to test the accuracy of the decay law. Finally, the dynamics of a tumor-immune aggregate is inspected using this law and the theory of bifurcations. As the ratio of immune destruction to tumor growth increases, a saddle-node bifurcation stabilizes the tumor-free fixed point.

Error analysis for fast scintillator-based inertial confinement fusion burn history measurements

NASA Astrophysics Data System (ADS)

Lerche, R. A.; Ognibene, T. J.

1999-01-01

Plastic scintillator material acts as a neutron-to-light converter in instruments that make inertial confinement fusion burn history measurements. Light output for a detected neutron in current instruments has a fast rise time (<20 ps) and a relatively long decay constant (1.2 ns). For a burst of neutrons whose duration is much shorter than the decay constant, instantaneous light output is approximately proportional to the integral of the neutron interaction rate with the scintillator material. Burn history is obtained by deconvolving the exponential decay from the recorded signal. The error in estimating signal amplitude for these integral measurements is calculated and compared with a direct measurement in which light output is linearly proportional to the interaction rate.

Near-field excitation exchange between motionless point atoms located near the conductive surface

NASA Astrophysics Data System (ADS)

Kuraptsev, Aleksei S.; Sokolov, Igor M.

2018-04-01

On the basis of quantum microscopic approach we study the excitation dynamics of two motionless point atoms located near the perfectly conducting mirror. We have analyzed the spontaneous decay rate of individual atoms near the mirror as well as the strength of dipole-dipole interaction between different atoms. It is shown that the spontaneous decay rate of an excited atom significantly depends on the distance from this atom to the mirror. In the case when the interatomic separation is less or comparable with the wavelength of resonant radiation, the spontaneous decay dynamics of an excited atom is described by multi-exponential law. It depends both the interatomic separation and the spatial orientation of diatomic quasimolecule.

Energy-Transfer Kinetics for Xe (6p[1/2]0) Atoms in Kr, Ar, Ne, and He.

PubMed

He, Shan; Liu, Dong; Li, Xueyang; Chu, Junzhi; Guo, Jingwei; Liu, Jinbo; Hu, Shu; Sang, Fengting; Jin, Yuqi

2018-06-11

The kinetic processes for the Xe (6p[1/2] 0 ) atoms in Kr, Ar, Ne, and He buffer gases were studied. We found that Kr, Ar, and Ne atoms can be used to switch the amplified spontaneous emission (ASE) channel from 3408 nm (6p[1/2] 0 -6s'[1/2] 1 ) to 3680 nm (5d[1/2] 1 -6p[1/2] 1 ), while Xe and He atoms do not show such a phenomenon. This ASE channel switch is mainly ascribed to the fast transfer of 6p[1/2] 0 → 5d[1/2] 1 . On the basis of the rate equations for two-state coupling (energy-transfer processes between the two states are very rapid), the reason why the ASE channel switch effect normally coincides with a double exponential decay of the spontaneous emission at 828 nm (6p[1/2] 0 -6s[3/2] 1 ) is explained. The actual situations in Xe, Ar, Ne, and He follow this rule. However, the strictly single exponential decay of the spontaneous emission at 828 nm and strong ASE channel switch effect simultaneously emerge in Kr. This indicates that the transfer of 6p[1/2] 0 → 5d[1/2] 1 in Kr does not occur via two-state coupling, but via two steps of near-resonance collision through the 5s[3/2] 2 (Kr) state as the intermediate state (6p[1/2] 0 → 5s[3/2] 2 (Kr) → 5d[1/2] 1 ). In addition, we found Xe (6p[1/2] 0 ) atoms strongly tend to reach the 6p[3/2] 2 , 6p[3/2] 1 , and 6p[5/2] 2 states through the 5s[3/2] 2 (Kr) state as the intermediate state in Kr. The 5s[3/2] 2 (Kr) state plays a very important role in the energy-transfer kinetics for the Xe (6p[1/2] 0 ) atoms. Kr is probably an excellent buffer gas for laser systems based on Xe.

Relationship between the Decomposition Process of Coarse Woody Debris and Fungal Community Structure as Detected by High-Throughput Sequencing in a Deciduous Broad-Leaved Forest in Japan

PubMed Central

Yamashita, Satoshi; Masuya, Hayato; Abe, Shin; Masaki, Takashi; Okabe, Kimiko

2015-01-01

We examined the relationship between the community structure of wood-decaying fungi, detected by high-throughput sequencing, and the decomposition rate using 13 years of data from a forest dynamics plot. For molecular analysis and wood density measurements, drill dust samples were collected from logs and stumps of Fagus and Quercus in the plot. Regression using a negative exponential model between wood density and time since death revealed that the decomposition rate of Fagus was greater than that of Quercus. The residual between the expected value obtained from the regression curve and the observed wood density was used as a decomposition rate index. Principal component analysis showed that the fungal community compositions of both Fagus and Quercus changed with time since death. Principal component analysis axis scores were used as an index of fungal community composition. A structural equation model for each wood genus was used to assess the effect of fungal community structure traits on the decomposition rate and how the fungal community structure was determined by the traits of coarse woody debris. Results of the structural equation model suggested that the decomposition rate of Fagus was affected by two fungal community composition components: one that was affected by time since death and another that was not affected by the traits of coarse woody debris. In contrast, the decomposition rate of Quercus was not affected by coarse woody debris traits or fungal community structure. These findings suggest that, in the case of Fagus coarse woody debris, the fungal community structure is related to the decomposition process of its host substrate. Because fungal community structure is affected partly by the decay stage and wood density of its substrate, these factors influence each other. Further research on interactive effects is needed to improve our understanding of the relationship between fungal community structure and the woody debris decomposition process. PMID:26110605

Atomic theory of viscoelastic response and memory effects in metallic glasses

NASA Astrophysics Data System (ADS)

Cui, Bingyu; Yang, Jie; Qiao, Jichao; Jiang, Minqiang; Dai, Lanhong; Wang, Yun-Jiang; Zaccone, Alessio

2017-09-01

An atomic-scale theory of the viscoelastic response of metallic glasses is derived from first principles, using a Zwanzig-Caldeira-Leggett system-bath Hamiltonian as a starting point within the framework of nonaffine linear response to mechanical deformation. This approach provides a generalized Langevin equation (GLE) as the average equation of motion for an atom or ion in the material, from which non-Markovian nonaffine viscoelastic moduli are extracted. These can be evaluated using the vibrational density of states (DOS) as input, where the boson peak plays a prominent role in the mechanics. To compare with experimental data for binary ZrCu alloys, a numerical DOS was obtained from simulations of this system, which also take electronic degrees of freedom into account via the embedded-atom method for the interatomic potential. It is shown that the viscoelastic α -relaxation, including the α -wing asymmetry in the loss modulus, can be very well described by the theory if the memory kernel (the non-Markovian friction) in the GLE is taken to be a stretched-exponential decaying function of time. This finding directly implies strong memory effects in the atomic-scale dynamics and suggests that the α -relaxation time is related to the characteristic time scale over which atoms retain memory of their previous collision history. This memory time grows dramatically below the glass transition.

Modeling the turbulent kinetic energy equation for compressible, homogeneous turbulence

NASA Technical Reports Server (NTRS)

Aupoix, B.; Blaisdell, G. A.; Reynolds, William C.; Zeman, Otto

1990-01-01

The turbulent kinetic energy transport equation, which is the basis of turbulence models, is investigated for homogeneous, compressible turbulence using direct numerical simulations performed at CTR. It is shown that the partition between dilatational and solenoidal modes is very sensitive to initial conditions for isotropic decaying turbulence but not for sheared flows. The importance of the dilatational dissipation and of the pressure-dilatation term is evidenced from simulations and a transport equation is proposed to evaluate the pressure-dilatation term evolution. This transport equation seems to work well for sheared flows but does not account for initial condition sensitivity in isotropic decay. An improved model is proposed.

Oblate-Earth Effects on the Calculation of Ec During Spacecraft Reentry

NASA Technical Reports Server (NTRS)

Bacon, John B.; Matney, Mark J.

2017-01-01

The bulge in the Earth at its equator has been shown to lead to a clustering of natural decays biased to occur towards the equator and away from the orbit's extreme latitudes. Such clustering must be considered when predicting the Expectation of Casualty (Ec) during a natural decay because of the clustering of the human population in the same lower latitudes. This study expands upon prior work, and formalizes the correction that must be made to the calculation of the average exposed population density as a result of this effect. Although a generic equation can be derived from this work to approximate the effects of gravitational and atmospheric perturbations on a final decay, such an equation averages certain important subtleties in achieving a best fit over all conditions. The authors recommend that direct simulation be used to calculate the true Ec for any specific entry as a more accurate method. A generic equation is provided, represented as a function of ballistic number and inclination of the entering spacecraft over the credible range of ballistic numbers.

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

Brown, Samuel L.; Krishnan, Retheesh; Elbaradei, Ahmed

A detailed understanding of the photoluminescence (PL) from silicon nanocrystals (SiNCs) is convoluted by the complexity of the decay mechanism, including a stretched-exponential relaxation and the presence of both nanosecond and microsecond time scales. In this publication, we analyze the microsecond PL decay of size-resolved SiNC fractions in both full-spectrum (FS) and spectrally resolved (SR) configurations, where the stretching exponent and lifetime are used to deduce a probability distribution function (PDF) of decay rates. For the PL decay measured at peak emission, we find a systematic shift and narrowing of the PDF in comparison to the FS measurements. In amore » similar fashion, we resolve the PL lifetime of the ‘blue’, ‘peak’, and ‘red’ regions of the spectrum and map PL decays of different photon energy onto their corresponding location in the PDF. Furthermore, a general trend is observed where higher and lower photon energies are correlated with shorter and longer lifetimes, respectively, which we relate to the PL line width and electron-phonon coupling.« less

Decoherence in yeast cell populations and its implications for genome-wide expression noise.

PubMed

Briones, M R S; Bosco, F

2009-01-20

Gene expression "noise" is commonly defined as the stochastic variation of gene expression levels in different cells of the same population under identical growth conditions. Here, we tested whether this "noise" is amplified with time, as a consequence of decoherence in global gene expression profiles (genome-wide microarrays) of synchronized cells. The stochastic component of transcription causes fluctuations that tend to be amplified as time progresses, leading to a decay of correlations of expression profiles, in perfect analogy with elementary relaxation processes. Measuring decoherence, defined here as a decay in the auto-correlation function of yeast genome-wide expression profiles, we found a slowdown in the decay of correlations, opposite to what would be expected if, as in mixing systems, correlations decay exponentially as the equilibrium state is reached. Our results indicate that the populational variation in gene expression (noise) is a consequence of temporal decoherence, in which the slow decay of correlations is a signature of strong interdependence of the transcription dynamics of different genes.

Stochastic Mixing Model with Power Law Decay of Variance

NASA Technical Reports Server (NTRS)

Fedotov, S.; Ihme, M.; Pitsch, H.

2003-01-01

Here we present a simple stochastic mixing model based on the law of large numbers (LLN). The reason why the LLN is involved in our formulation of the mixing problem is that the random conserved scalar c = c(t,x(t)) appears to behave as a sample mean. It converges to the mean value mu, while the variance sigma(sup 2)(sub c) (t) decays approximately as t(exp -1). Since the variance of the scalar decays faster than a sample mean (typically is greater than unity), we will introduce some non-linear modifications into the corresponding pdf-equation. The main idea is to develop a robust model which is independent from restrictive assumptions about the shape of the pdf. The remainder of this paper is organized as follows. In Section 2 we derive the integral equation from a stochastic difference equation describing the evolution of the pdf of a passive scalar in time. The stochastic difference equation introduces an exchange rate gamma(sub n) which we model in a first step as a deterministic function. In a second step, we generalize gamma(sub n) as a stochastic variable taking fluctuations in the inhomogeneous environment into account. In Section 3 we solve the non-linear integral equation numerically and analyze the influence of the different parameters on the decay rate. The paper finishes with a conclusion.

A multi-timescale map of radiative and nonradiative decay pathways for excitons in CdSe quantum dots.

PubMed

Knowles, Kathryn E; McArthur, Eric A; Weiss, Emily A

2011-03-22

A combination of transient absorption (TA) and time-resolved photoluminescence (TRPL) spectroscopies performed on solution-phase samples of colloidal CdSe quantum dots (QDs) allows the construction of a time-resolved, charge carrier-resolved map of decay from the first excitonic state of the QD. Data from TA and TRPL yield the same six exponential components, with time constants ranging from ∼1 ps to 50 ns, for excitonic decay. Comparison of TA signals in the visible and near-infrared (NIR) spectral regions enables determination of the relative contributions of electron and hole dynamics to each decay component, and comparison of TA and TRPL reveals that each component represents a competition between radiative and nonradiative decay pathways. In total, these data suggest that the QD sample comprises at least three distinct populations that differ in both the radiative and nonradiative decay pathways available to the excitonic charge carriers, and provide evidence for multiple emissive excitonic states in which the hole is not in the valence band, but rather a relaxed or trapped state.

Interaction quantum quenches in the one-dimensional Fermi-Hubbard model

NASA Astrophysics Data System (ADS)

Heidrich-Meisner, Fabian; Bauer, Andreas; Dorfner, Florian; Riegger, Luis; Orso, Giuliano

2016-05-01

We discuss the nonequilibrium dynamics in two interaction quantum quenches in the one-dimensional Fermi-Hubbard model. First, we study the decay of the Néel state as a function of interaction strength. We observe a fast charge dynamics over which double occupancies are built up, while the long-time decay of the staggered moment is controlled by spin excitations, corroborated by the analysis of the entanglement dynamics. Second, we investigate the formation of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) correlations in a spin-imbalanced system in quenches from the noninteracting case to attractive interactions. Even though the quench puts the system at a finite energy density, peaks at the characteristic FFLO quasimomenta are visible in the quasi-momentum distribution function, albeit with an exponential decay of s-wave pairing correlations. We also discuss the imprinting of FFLO correlations onto repulsively bound pairs and their rapid decay in ramps. Supported by the DFG (Deutsche Forschungsgemeinschaft) via FOR 1807.

Transitionless driving on adiabatic search algorithm

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

Oh, Sangchul, E-mail: soh@qf.org.qa; Kais, Sabre, E-mail: kais@purdue.edu; Department of Chemistry, Department of Physics and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907

We study quantum dynamics of the adiabatic search algorithm with the equivalent two-level system. Its adiabatic and non-adiabatic evolution is studied and visualized as trajectories of Bloch vectors on a Bloch sphere. We find the change in the non-adiabatic transition probability from exponential decay for the short running time to inverse-square decay in asymptotic running time. The scaling of the critical running time is expressed in terms of the Lambert W function. We derive the transitionless driving Hamiltonian for the adiabatic search algorithm, which makes a quantum state follow the adiabatic path. We demonstrate that a uniform transitionless driving Hamiltonian,more » approximate to the exact time-dependent driving Hamiltonian, can alter the non-adiabatic transition probability from the inverse square decay to the inverse fourth power decay with the running time. This may open up a new but simple way of speeding up adiabatic quantum dynamics.« less

Problems Relating Mathematics and Science in the High School.

ERIC Educational Resources Information Center

Morrow, Richard; Beard, Earl

This document contains various science problems which require a mathematical solution. The problems are arranged under two general areas. The first (algebra I) contains biology, chemistry, and physics problems which require solutions related to linear equations, exponentials, and nonlinear equations. The second (algebra II) contains physics…

A general decay result of a viscoelastic equation with past history and boundary feedback

NASA Astrophysics Data System (ADS)

Messaoudi, Salim A.; Al-Gharabli, Mohammad M.

2015-08-01

In this paper, we consider a viscoelastic equation with a nonlinear feedback localized on a part of the boundary and in the presence of infinite memory term. In the domain as well as on a part of the boundary, we use the multiplier method and some properties of the convex functions to prove an explicit and general decay result.

Approach to calculation of mass spectra and two-photon decays of c c¯ mesons in the framework of Bethe-Salpeter equation

NASA Astrophysics Data System (ADS)

Bhatnagar, Shashank; Alemu, Lmenew

2018-02-01

In this work we calculate the mass spectra of charmonium for 1 P ,…,4 P states of 0++ and 1++, for 1 S ,…,5 S states of 0-+, and for 1 S ,…,4 D states of 1- along with the two-photon decay widths of the ground and first excited states of 0++ quarkonia for the process O++→γ γ in the framework of a QCD-motivated Bethe-Salpeter equation (BSE). In this 4 ×4 BSE framework, the coupled Salpeter equations are first shown to decouple for the confining part of the interaction (under the heavy-quark approximation) and are analytically solved, and later the one-gluon-exchange interaction is perturbatively incorporated, leading to mass spectral equations for various quarkonia. The analytic forms of wave functions obtained are used for the calculation of the two-photon decay widths of χc 0. Our results are in reasonable agreement with data (where available) and other models.

Fine structure of α decay from the variational principle

NASA Astrophysics Data System (ADS)

Mirea, M.

2017-12-01

Starting from the variational principle, the time-dependent pairing equations are generalized by including the Landau-Zener effect and the Coriolis coupling. A system of microscopic equations of motion for configuration mixing is deduced, allowing the determination of quantities that have the same meaning as the preformation factors of the α particle. These equations are solved in order to reproduce the hindrance factors of the α decay of an odd-A mass nucleus. The α decay of 211Po is treated as a superasymmetric fission process, by following the rearrangement of the nuclear orbitals from the parent ground state up to the scission configuration. The probabilities of finding the excited states of the daughter at scission are obtained from the microscopic equations of motion. The intensities of the transitions to the excited states of the daughter were evaluated theoretically. The experimental data were compared with the theoretical findings. A very good agreement was obtained. A mean value of the tunneling velocity of about 2 ×104 fm/fs was extracted.

Correlation between elastic energy density and deep earthquakes distribution

NASA Astrophysics Data System (ADS)

Gunawardana, P. M.; Morra, G.

2017-05-01

The mechanism at the origin of the earthquakes below 30 km remains elusive as these events cannot be explained by brittle frictional processes. In this work we focus on the global total distribution of earthquakes frequency vs. depth from ∼50 km to 670 km depth. We develop a numerical model of self-driven subduction by solving the non-homogeneous Stokes equation using the ;Particle in cell method; in combination with a conservative finite difference scheme, here solved for the first time using Python and NumPy only. We show that most of the elastic energy is stored in the slab core and that it is strongly correlated with the earthquake frequency-depth distribution for a wide range of lithosphere and lithosphere-core viscosities. According to our results, we suggest that 1) slab bending at the bottom of the upper mantle causes the peak of the earthquake frequency-depth distribution that is observed at mantle transition depth; 2) the presence of a high viscous stiff core inside the lithosphere generates an elastic energy distribution that fits better with the exponential decay that is observed at intermediate depth.

On computing special functions in marine engineering

NASA Astrophysics Data System (ADS)

Constantinescu, E.; Bogdan, M.

2015-11-01

Important modeling applications in marine engineering conduct us to a special class of solutions for difficult differential equations with variable coefficients. In order to be able to solve and implement such models (in wave theory, in acoustics, in hydrodynamics, in electromagnetic waves, but also in many other engineering fields), it is necessary to compute so called special functions: Bessel functions, modified Bessel functions, spherical Bessel functions, Hankel functions. The aim of this paper is to develop numerical solutions in Matlab for the above mentioned special functions. Taking into account the main properties for Bessel and modified Bessel functions, we shortly present analytically solutions (where possible) in the form of series. Especially it is studied the behavior of these special functions using Matlab facilities: numerical solutions and plotting. Finally, it will be compared the behavior of the special functions and point out other directions for investigating properties of Bessel and spherical Bessel functions. The asymptotic forms of Bessel functions and modified Bessel functions allow determination of important properties of these functions. The modified Bessel functions tend to look more like decaying and growing exponentials.

Analytical prediction of the unsteady lift on a rotor caused by downstream struts

NASA Technical Reports Server (NTRS)

Taylor, A. C., III; Ng, W. F.

1987-01-01

A two-dimensional, inviscid, incompressible procedure is presented for predicting the unsteady lift on turbomachinery blades caused by the upstream potential disturbance of downstream flow obstructions. Using the Douglas-Neumann singularity superposition potential flow computer program to model the downstream flow obstructions, classical equations of thin airfoil theory are then employed, to compute the unsteady lift on the upstream rotor blades. The method is applied to a particular geometry which consists of a rotor, a downstream stator, and downstream struts which support the engine casing. Very good agreement between the Douglas-Neumann program and experimental measurements was obtained for the downstream stator-strut flow field. The calculations for the unsteady lift due to the struts were in good agreement with the experiments in showing that the unsteady lift due to the struts decays exponentially with increased axial separation of the rotor and the struts. An application of the method showed that for a given axial spacing between the rotor and the strut, strut-induced unsteady lift is a very weak function of the axial or circumferential position of the stator.

Continuity properties of the semi-group and its integral kernel in non-relativistic QED

NASA Astrophysics Data System (ADS)

Matte, Oliver

2016-07-01

Employing recent results on stochastic differential equations associated with the standard model of non-relativistic quantum electrodynamics by B. Güneysu, J. S. Møller, and the present author, we study the continuity of the corresponding semi-group between weighted vector-valued Lp-spaces, continuity properties of elements in the range of the semi-group, and the pointwise continuity of an operator-valued semi-group kernel. We further discuss the continuous dependence of the semi-group and its integral kernel on model parameters. All these results are obtained for Kato decomposable electrostatic potentials and the actual assumptions on the model are general enough to cover the Nelson model as well. As a corollary, we obtain some new pointwise exponential decay and continuity results on elements of low-energetic spectral subspaces of atoms or molecules that also take spin into account. In a simpler situation where spin is neglected, we explain how to verify the joint continuity of positive ground state eigenvectors with respect to spatial coordinates and model parameters. There are no smallness assumptions imposed on any model parameter.

High temperature dielectric relaxation anomaly of Y³⁺ and Mn²⁺ doped barium strontium titanate ceramics

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

Yan, Shiguang; Mao, Chaoliang, E-mail: maochaoliang@mail.sic.ac.cn, E-mail: xldong@mail.sic.ac.cn; Wang, Genshui

2014-10-14

Relaxation like dielectric anomaly is observed in Y³⁺ and Mn²⁺ doped barium strontium titanate ceramics when the temperature is over 450 K. Apart from the conventional dielectric relaxation analysis method with Debye or modified Debye equations, which is hard to give exact temperature dependence of the relaxation process, dielectric response in the form of complex impedance, assisted with Cole-Cole impedance model corrected equivalent circuits, is adopted to solve this problem and chase the polarization mechanism in this paper. Through this method, an excellent description to temperature dependence of the dielectric relaxation anomaly and its dominated factors are achieved. Further analysismore » reveals that the exponential decay of the Cole distribution parameter n with temperature is confirmed to be induced by the microscopic lattice distortion due to ions doping and the interaction between the defects. At last, a clear sight to polarization mechanism containing both the intrinsic dipolar polarization and extrinsic distributed oxygen vacancies hopping response under different temperature is obtained.« less

Temporal complexity in emission from Anderson localized lasers

NASA Astrophysics Data System (ADS)

Kumar, Randhir; Balasubrahmaniyam, M.; Alee, K. Shadak; Mujumdar, Sushil

2017-12-01

Anderson localization lasers exploit resonant cavities formed due to structural disorder. The inherent randomness in the structure of these cavities realizes a probability distribution in all cavity parameters such as quality factors, mode volumes, mode structures, and so on, implying resultant statistical fluctuations in the temporal behavior. Here we provide direct experimental measurements of temporal width distributions of Anderson localization lasing pulses in intrinsically and extrinsically disordered coupled-microresonator arrays. We first illustrate signature exponential decays in the spatial intensity distributions of the lasing modes that quantify their localized character, and then measure the temporal width distributions of the pulsed emission over several configurations. We observe a dependence of temporal widths on the disorder strength, wherein the widths show a single-peaked, left-skewed distribution in extrinsic disorder and a dual-peaked distribution in intrinsic disorder. We propose a model based on coupled rate equations for an emitter and an Anderson cavity with a random mode structure, which gives excellent quantitative and qualitative agreement with the experimental observations. The experimental and theoretical analyses bring to the fore the temporal complexity in Anderson-localization-based lasing systems.