Analytical formulation of cellular automata rules using data models

NASA Astrophysics Data System (ADS)

Jaenisch, Holger M.; Handley, James W.

2009-05-01

We present a unique method for converting traditional cellular automata (CA) rules into analytical function form. CA rules have been successfully used for morphological image processing and volumetric shape recognition and classification. Further, the use of CA rules as analog models to the physical and biological sciences can be significantly extended if analytical (as opposed to discrete) models could be formulated. We show that such transformations are possible. We use as our example John Horton Conway's famous "Game of Life" rule set. We show that using Data Modeling, we are able to derive both polynomial and bi-spectrum models of the IF-THEN rules that yield equivalent results. Further, we demonstrate that the "Game of Life" rule set can be modeled using the multi-fluxion, yielding a closed form nth order derivative and integral. All of the demonstrated analytical forms of the CA rule are general and applicable to real-time use.

A New Twist on the Marcum Q-Function and its Application

NASA Technical Reports Server (NTRS)

Simon, Marvin K.

1997-01-01

A new form of the Marcum Q-Function is presented that has both computational and analytical advantages. The new form is particularly useful in simplifying and rendering more accurate the analysis of the error probability performance of uncoded and coded partially coherent, differentially coherent, and noncoherent communication systems in the presence of fading.

Morse oscillator propagator in the high temperature limit II: Quantum dynamics and spectroscopy

NASA Astrophysics Data System (ADS)

Toutounji, Mohamad

2018-04-01

This paper is a continuation of Paper I (Toutounji, 2017) of which motivation was testing the applicability of Morse oscillator propagator whose analytical form was derived by Duru (1983). This is because the Morse oscillator propagator was reported (Duru, 1983) in a triple-integral form of a functional of modified Bessel function of the first kind, which considerably limits its applicability. For this reason, I was prompted to find a regime under which Morse oscillator propagator may be simplified and hence be expressed in a closed-form. This was well accomplished in Paper I. Because Morse oscillator is of central importance and widely used in modelling vibrations, its propagator applicability will be extended to applications in quantum dynamics and spectroscopy as will be reported in this paper using the off-diagonal propagator of Morse oscillator whose analytical form is derived.

Roy-Steiner equations for pion-nucleon scattering

NASA Astrophysics Data System (ADS)

Ditsche, C.; Hoferichter, M.; Kubis, B.; Meißner, U.-G.

2012-06-01

Starting from hyperbolic dispersion relations, we derive a closed system of Roy-Steiner equations for pion-nucleon scattering that respects analyticity, unitarity, and crossing symmetry. We work out analytically all kernel functions and unitarity relations required for the lowest partial waves. In order to suppress the dependence on the high energy regime we also consider once- and twice-subtracted versions of the equations, where we identify the subtraction constants with subthreshold parameters. Assuming Mandelstam analyticity we determine the maximal range of validity of these equations. As a first step towards the solution of the full system we cast the equations for the π π to overline N N partial waves into the form of a Muskhelishvili-Omnès problem with finite matching point, which we solve numerically in the single-channel approximation. We investigate in detail the role of individual contributions to our solutions and discuss some consequences for the spectral functions of the nucleon electromagnetic form factors.

Quantitative detection of pathogens in centrifugal microfluidic disks

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

Koh, Chung-Yan; Schaff, Ulrich Y.; Sommer, Gregory Jon

A system and methods for detection of a nucleic acid including forming a plurality of nucleic acid detection complexes are described, each of the complexes including a nucleic acid analyte, a detection agent and a functionalized probe. The method further including binding the nucleic acid detection complexes to a plurality of functionalized particles in a fluid sample and separating the functionalized particles having the nucleic acid detection complexes bound thereto from the fluid sample using a density media. The nucleic acid analyte is detected by detecting the detection agent.

New Ways of Treating Data for Diatomic Molecule 'shelf' and Double-Minimum States

NASA Astrophysics Data System (ADS)

Le Roy, Robert J.; Tao, Jason; Khanna, Shirin; Pashov, Asen; Tellinghuisen, Joel

2017-06-01

Electronic states whose potential energy functions have 'shelf' or double-minimum shapes have always presented special challenges because, as functions of vibrational quantum number, the vibrational energies/spacings and inertial rotational constants either have an abrupt change of character with discontinuous slope, or past a given point, become completely chaotic. The present work shows that a `traditional' methodology developed for deep `regular' single-well potentials can also provide accurate `parameter-fit' descriptions of the v-dependence of the vibrational energies and rotational constants of shelf-state potentials that allow a conventional RKR calculation of their Potential energy functions. It is also shown that a merging of Pashov's uniquely flexible 'spline point-wise' potential function representation with Le Roy's `Morse/Long-Range' (MLR) analytic functional form which automatically incorporates the correct theoretically known long-range form, yields an analytic function that incorporates most of the advantages of both approaches. An illustrative application of this method to data to a double-minimum state of Na_2 will be described.

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

NASA Technical Reports Server (NTRS)

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

1993-01-01

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

Analytical Model for Thermal Elastoplastic Stresses of Functionally Graded Materials

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

Zhai, P. C.; Chen, G.; Liu, L. S.

2008-02-15

A modification analytical model is presented for the thermal elastoplastic stresses of functionally graded materials subjected to thermal loading. The presented model follows the analytical scheme presented by Y. L. Shen and S. Suresh [6]. In the present model, the functionally graded materials are considered as multilayered materials. Each layer consists of metal and ceramic with different volume fraction. The ceramic layer and the FGM interlayers are considered as elastic brittle materials. The metal layer is considered as elastic-perfectly plastic ductile materials. Closed-form solutions for different characteristic temperature for thermal loading are presented as a function of the structure geometriesmore » and the thermomechanical properties of the materials. A main advance of the present model is that the possibility of the initial and spread of plasticity from the two sides of the ductile layers taken into account. Comparing the analytical results with the results from the finite element analysis, the thermal stresses and deformation from the present model are in good agreement with the numerical ones.« less

Approximate analytical solutions in the analysis of elastic structures of complex geometry

NASA Astrophysics Data System (ADS)

Goloskokov, Dmitriy P.; Matrosov, Alexander V.

2018-05-01

A method of analytical decomposition for analysis plane structures of a complex configuration is presented. For each part of the structure in the form of a rectangle all the components of the stress-strain state are constructed by the superposition method. The method is based on two solutions derived in the form of trigonometric series with unknown coefficients using the method of initial functions. The coefficients are determined from the system of linear algebraic equations obtained while satisfying the boundary conditions and the conditions for joining the structure parts. The components of the stress-strain state of a bent plate with holes are calculated using the analytical decomposition method.

Completeness of the Coulomb Wave Functions in Quantum Mechanics

ERIC Educational Resources Information Center

Mukunda, N.

1978-01-01

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

The Partition Function in the Four-Dimensional Schwarz-Type Topological Half-Flat Two-Form Gravity

NASA Astrophysics Data System (ADS)

Abe, Mitsuko

We derive the partition functions of the Schwarz-type four-dimensional topological half-flat two-form gravity model on K3-surface or T4 up to on-shell one-loop corrections. In this model the bosonic moduli spaces describe an equivalent class of a trio of the Einstein-Kähler forms (the hyper-Kähler forms). The integrand of the partition function is represented by the product of some bar ∂ -torsions. bar ∂ -torsion is the extension of R-torsion for the de Rham complex to that for the bar ∂ -complex of a complex analytic manifold.

Group specific internal standard technology (GSIST) for simultaneous identification and quantification of small molecules

DOEpatents

Adamec, Jiri; Yang, Wen-Chu; Regnier, Fred E

2014-01-14

Reagents and methods are provided that permit simultaneous analysis of multiple diverse small molecule analytes present in a complex mixture. Samples are labeled with chemically identical but isotopically distince forms of the labeling reagent, and analyzed using mass spectrometry. A single reagent simultaneously derivatizes multiple small molecule analytes having different reactive functional groups.

Numerical implementation of complex orthogonalization, parallel transport on Stiefel bundles, and analyticity

NASA Astrophysics Data System (ADS)

Avitabile, Daniele; Bridges, Thomas J.

2010-06-01

Numerical integration of complex linear systems of ODEs depending analytically on an eigenvalue parameter are considered. Complex orthogonalization, which is required to stabilize the numerical integration, results in non-analytic systems. It is shown that properties of eigenvalues are still efficiently recoverable by extracting information from a non-analytic characteristic function. The orthonormal systems are constructed using the geometry of Stiefel bundles. Different forms of continuous orthogonalization in the literature are shown to correspond to different choices of connection one-form on the Stiefel bundle. For the numerical integration, Gauss-Legendre Runge-Kutta algorithms are the principal choice for preserving orthogonality, and performance results are shown for a range of GLRK methods. The theory and methods are tested by application to example boundary value problems including the Orr-Sommerfeld equation in hydrodynamic stability.

Interacting steps with finite-range interactions: Analytical approximation and numerical results

NASA Astrophysics Data System (ADS)

Jaramillo, Diego Felipe; Téllez, Gabriel; González, Diego Luis; Einstein, T. L.

2013-05-01

We calculate an analytical expression for the terrace-width distribution P(s) for an interacting step system with nearest- and next-nearest-neighbor interactions. Our model is derived by mapping the step system onto a statistically equivalent one-dimensional system of classical particles. The validity of the model is tested with several numerical simulations and experimental results. We explore the effect of the range of interactions q on the functional form of the terrace-width distribution and pair correlation functions. For physically plausible interactions, we find modest changes when next-nearest neighbor interactions are included and generally negligible changes when more distant interactions are allowed. We discuss methods for extracting from simulated experimental data the characteristic scale-setting terms in assumed potential forms.

Continuous Optimization on Constraint Manifolds

NASA Technical Reports Server (NTRS)

Dean, Edwin B.

1988-01-01

This paper demonstrates continuous optimization on the differentiable manifold formed by continuous constraint functions. The first order tensor geodesic differential equation is solved on the manifold in both numerical and closed analytic form for simple nonlinear programs. Advantages and disadvantages with respect to conventional optimization techniques are discussed.

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

NASA Astrophysics Data System (ADS)

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

2014-12-01

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

An analytical method for the inverse Cauchy problem of Lame equation in a rectangle

NASA Astrophysics Data System (ADS)

Grigor’ev, Yu

2018-04-01

In this paper, we present an analytical computational method for the inverse Cauchy problem of Lame equation in the elasticity theory. A rectangular domain is frequently used in engineering structures and we only consider the analytical solution in a two-dimensional rectangle, wherein a missing boundary condition is recovered from the full measurement of stresses and displacements on an accessible boundary. The essence of the method consists in solving three independent Cauchy problems for the Laplace and Poisson equations. For each of them, the Fourier series is used to formulate a first-kind Fredholm integral equation for the unknown function of data. Then, we use a Lavrentiev regularization method, and the termwise separable property of kernel function allows us to obtain a closed-form regularized solution. As a result, for the displacement components, we obtain solutions in the form of a sum of series with three regularization parameters. The uniform convergence and error estimation of the regularized solutions are proved.

Limits in the evolution of biological form: a theoretical morphologic perspective.

PubMed

McGhee, George R

2015-12-06

Limits in the evolution of biological form can be empirically demonstrated by using theoretical morphospace analyses, and actual analytic examples are given for univalved ammonoid shell form, bivalved brachiopod shell form and helical bryozoan colony form. Limits in the evolution of form in these animal groups can be shown to be due to functional and developmental constraints on possible evolutionary trajectories in morphospace. Future evolutionary-limit research is needed to analyse the possible existence of temporal constraint in the evolution of biological form on Earth, and in the search for the possible existence of functional alien life forms on Titan and Triton that are developmentally impossible for Earth life.

A theoretical study on pure bending of hexagonal close-packed metal sheet

NASA Astrophysics Data System (ADS)

Mehrabi, Hamed; Yang, Chunhui

2018-05-01

Hexagonal close-packed (HCP) metals have quite different mechanical behaviours in comparison to conventional cubic metals such as steels and aluminum alloys [1, 2]. They exhibit a significant tension-compression asymmetry in initial yielding and subsequent plastic hardening. The reason for this unique behaviour can be attributed to their limited symmetric crystal structure, which leads to twining deformation [3-5]. This unique behaviour strongly influences sheet metal forming of such metals, especially for roll forming, in which the bending is dominant. Hence, it is crucial to represent constitutive relations of HCP metals for accurate estimation of bending moment-curvature behaviours. In this paper, an analytical model for asymmetric elastoplastic pure bending with an application of Cazacu-Barlat asymmetric yield function [6] is presented. This yield function considers the asymmetrical tension-compression behaviour of HCP metals by using second and third invariants of the stress deviator tensor and a specified constant, which can be expressed in terms of uniaxial yield stresses in tension and compression. As a case study, the analytical model is applied to predict the moment-curvature behaviours of AZ31B magnesium alloy sheets under uniaxial loading condition. Furthermore, the analytical model is implemented as a user-defined material through the UMAT interface in Abaqus [7, 8] for conducting pure bending simulations. The results show that the analytical model can reasonably capture the asymmetric tension-compression behaviour of the magnesium alloy. The predicted moment-curvature behaviour has good agreement with the experimental results. Furthermore, numerical results show a better accuracy by the application of the Cazacu-Barlat yield function than those using the von-Mises yield function, which are more conservative than analytical results.

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

PubMed

Cammi, R

2009-10-28

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

The Analytical Pragmatic Structure of Procedural Due Process: A Framework for Inquiry in Administrative Decision Making.

ERIC Educational Resources Information Center

Fisher, James E.; Sealey, Ronald W.

The study describes the analytical pragmatic structure of concepts and applies this structure to the legal concept of procedural due process. This structure consists of form, purpose, content, and function. The study conclusions indicate that the structure of the concept of procedural due process, or any legal concept, is not the same as the…

Search for and investigation of extraterrestrial forms of life

NASA Technical Reports Server (NTRS)

Rubin, A. B.

1975-01-01

Correct combinations of remote, analytic, and functional methods and measuring devices for detecting extraterrestrial life are elaborated. Considered are techniques and instruments available both on earth and aboard spacecraft and artificial planetary satellites. Emphasis is placed on the abiogenetic synthesis of organic compounds formed in photosynthesis on Mars.

Theoretical study of production of unique glasses in space

NASA Technical Reports Server (NTRS)

Larsen, D. C.

1974-01-01

Analytical functional relationships describing homogeneous nucleation and crystallization in various supercooled liquids were developed. The time and temperature dependent relationships of nucleation and crystallization (intrinsic properties) are being used to relate glass forming tendency to extrinsic parameters such as cooling rate through computer simulation. Single oxide systems are being studied initially to aid in developing workable kinetic models and to indicate the primary materials parameters affecting glass formation. The theory and analytical expressions developed for simple systems is then extended to complex oxide systems. A thorough understanding of nucleation and crystallization kinetics of glass forming systems provides a priori knowledge of the ability of a given system to form a glass.

Sensor Functionality of Conducting Polyaniline-Metal Oxide (TiO2/SnO2) Hybrid Materials Films toward Benzene and Toluene Vapors at Room Temperature

NASA Astrophysics Data System (ADS)

Subramanian, E.; Santhanamari, P.; Murugan, C.

2018-05-01

Polyaniline-metal oxide (TiO2/SnO2) organic-inorganic hybrid materials films were fabricated in situ on a printed circuit board (PCB) via drop coating technique. The mixture of aniline and metal oxide (TiO2/SnO2) dispersed in ethanol was applied along with an oxidant for the coating process. The formed material films were characterized by Fourier transform infra-red spectroscopy, x-ray diffraction and scanning electron microscopy techniques. The sensor functionality of the prepared films on PCB was investigated individually for the detection of benzene or toluene vapor at room temperature. The promptness of sensor response to analyte vapor and its recovery to air, as well as the concentration-dependent sensor functionality of the hybrid material films were investigated. The film form of hybrid materials has shown much improved sensor efficiency even at ambient air condition compared to the pellet form of the polyaniline-SnO2 hybrid material reported earlier, which sensed the same analytes only in nitrogen atmosphere.

Peculiar velocity effect on galaxy correlation functions in nonlinear clustering regime

NASA Astrophysics Data System (ADS)

Matsubara, Takahiko

1994-03-01

We studied the distortion of the apparent distribution of galaxies in redshift space contaminated by the peculiar velocity effect. Specifically we obtained the expressions for N-point correlation functions in redshift space with given functional form for velocity distribution f(v) and evaluated two- and three-point correlation functions quantitatively. The effect of velocity correlations is also discussed. When the two-point correlation function in real space has a power-law form, Xir(r) is proportional to r(-gamma), the redshift-space counterpart on small scales also has a power-law form but with an increased power-law index: Xis(s) is proportional to s(1-gamma). When the three-point correlation function has the hierarchical form and the two-point correlation function has the power-law form in real space, the hierarchical form of the three-point correlation function is almost preserved in redshift space. The above analytic results are compared with the direct analysis based on N-body simulation data for cold dark matter models. Implications on the hierarchical clustering ansatz are discussed in detail.

Constructing and Deriving Reciprocal Trigonometric Relations: A Functional Analytic Approach

ERIC Educational Resources Information Center

Ninness, Chris; Dixon, Mark; Barnes-Holmes, Dermot; Rehfeldt, Ruth Anne; Rumph, Robin; McCuller, Glen; Holland, James; Smith, Ronald; Ninness, Sharon K.; McGinty, Jennifer

2009-01-01

Participants were pretrained and tested on mutually entailed trigonometric relations and combinatorially entailed relations as they pertained to positive and negative forms of sine, cosine, secant, and cosecant. Experiment 1 focused on training and testing transformations of these mathematical functions in terms of amplitude and frequency followed…

Exact analytical approach for six-degree-of-freedom measurement using image-orientation-change method.

PubMed

Tsai, Chung-Yu

2012-04-01

An exact analytical approach is proposed for measuring the six-degree-of-freedom (6-DOF) motion of an object using the image-orientation-change (IOC) method. The proposed measurement system comprises two reflector systems, where each system consists of two reflectors and one position sensing detector (PSD). The IOCs of the object in the two reflector systems are described using merit functions determined from the respective PSD readings before and after motion occurs, respectively. The three rotation variables are then determined analytically from the eigenvectors of the corresponding merit functions. After determining the three rotation variables, the order of the translation equations is downgraded to a linear form. Consequently, the solution for the three translation variables can also be analytically determined. As a result, the motion transformation matrix describing the 6-DOF motion of the object is fully determined. The validity of the proposed approach is demonstrated by means of an illustrative example.

Semi-analytical solution for the generalized absorbing boundary condition in molecular dynamics simulations

NASA Astrophysics Data System (ADS)

Lee, Chung-Shuo; Chen, Yan-Yu; Yu, Chi-Hua; Hsu, Yu-Chuan; Chen, Chuin-Shan

2017-07-01

We present a semi-analytical solution of a time-history kernel for the generalized absorbing boundary condition in molecular dynamics (MD) simulations. To facilitate the kernel derivation, the concept of virtual atoms in real space that can conform with an arbitrary boundary in an arbitrary lattice is adopted. The generalized Langevin equation is regularized using eigenvalue decomposition and, consequently, an analytical expression of an inverse Laplace transform is obtained. With construction of dynamical matrices in the virtual domain, a semi-analytical form of the time-history kernel functions for an arbitrary boundary in an arbitrary lattice can be found. The time-history kernel functions for different crystal lattices are derived to show the generality of the proposed method. Non-equilibrium MD simulations in a triangular lattice with and without the absorbing boundary condition are conducted to demonstrate the validity of the solution.

Free iterative-complement-interaction calculations of the hydrogen molecule

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

Kurokawa, Yusaku; Nakashima, Hiroyuki; Nakatsuji, Hiroshi

2005-12-15

The free iterative-complement-interaction (ICI) method based on the scaled Schroedinger equation proposed previously has been applied to the calculations of very accurate wave functions of the hydrogen molecule in an analytical expansion form. All the variables were determined with the variational principle by calculating the necessary integrals analytically. The initial wave function and the scaling function were changes to see the effects on the convergence speed of the ICI calculations. The free ICI wave functions that were generated automatically were different from the existing wave functions, and this difference was shown to be physically important. The best wave function reportedmore » in this paper seems to be the best worldwide in the literature from the variational point of view. The quality of the wave function was examined by calculating the nuclear and electron cusps.« less

Statistical correlation analysis for comparing vibration data from test and analysis

NASA Technical Reports Server (NTRS)

Butler, T. G.; Strang, R. F.; Purves, L. R.; Hershfeld, D. J.

1986-01-01

A theory was developed to compare vibration modes obtained by NASTRAN analysis with those obtained experimentally. Because many more analytical modes can be obtained than experimental modes, the analytical set was treated as expansion functions for putting both sources in comparative form. The dimensional symmetry was developed for three general cases: nonsymmetric whole model compared with a nonsymmetric whole structural test, symmetric analytical portion compared with a symmetric experimental portion, and analytical symmetric portion with a whole experimental test. The theory was coded and a statistical correlation program was installed as a utility. The theory is established with small classical structures.

Semantic False Memories in the Form of Derived Relational Intrusions Following Training

ERIC Educational Resources Information Center

Guinther, Paul M.; Dougher, Michael J.

2010-01-01

Contemporary behavior analytic research is making headway in characterizing memory phenomena that typically have been characterized by cognitive models, and the current study extends this development by producing "false memories" in the form of functional equivalence responding. A match-to-sample training procedure was administered in order to…

Matrix Theory of Small Oscillations

ERIC Educational Resources Information Center

Chavda, L. K.

1978-01-01

A complete matrix formulation of the theory of small oscillations is presented. Simple analytic solutions involving matrix functions are found which clearly exhibit the transients, the damping factors, the Breit-Wigner form for resonances, etc. (BB)

POTENTIOLOGY (noun): study focusing on the development of new interatomic pair potential forms; sometimes pursued in an obsessive compulsive manner [The New Yorel Dictionary (2002, unpublished)].} IN SPECTROSCOPY: IT MATTERS

NASA Astrophysics Data System (ADS)

Le Roy, Robert J.

2009-06-01

Spectroscopists have long attempted to summarize what they know about small molecules in terms of a knowledge of potential energy curves or surfaces. For most of the past century, this involved deducing polynomial-expansion force-field coefficients from energy level expressions fitted to experimental data, or for diatomic molecules, by generating tables of many-digit RKR turning points from such expressions. In recent years, however, it has become increasingly common either to use high-level ab initio calculations to compute the desired potentials, or to determine parametrized global analytic potential functions from direct fits to spectroscopic data. In the former case, this invoked a need for robust, flexible, compact, and `portable' analytic potentials for summarizing the information contained in the (sometimes very large numbers of) ab initio points, and making them `user friendly'. In the latter case, the same properties are required for potentials used in the least-squares fitting procedure. In both cases, there is also a cardinal need for potential function forms that extrapolate sensibly, beyond the range of the experimental data or ab initio points. This talk will describe some recent developments in this area, and make a case for what is arguably the `best' general-purpose analytic potential function form now available. Applications to both diatomic molecules and simple polyatomic molecules will be discussed. footnote

Constraints on the [Formula: see text] form factor from analyticity and unitarity.

PubMed

Ananthanarayan, B; Caprini, I; Kubis, B

Motivated by the discrepancies noted recently between the theoretical calculations of the electromagnetic [Formula: see text] form factor and certain experimental data, we investigate this form factor using analyticity and unitarity in a framework known as the method of unitarity bounds. We use a QCD correlator computed on the spacelike axis by operator product expansion and perturbative QCD as input, and exploit unitarity and the positivity of its spectral function, including the two-pion contribution that can be reliably calculated using high-precision data on the pion form factor. From this information, we derive upper and lower bounds on the modulus of the [Formula: see text] form factor in the elastic region. The results provide a significant check on those obtained with standard dispersion relations, confirming the existence of a disagreement with experimental data in the region around [Formula: see text].

KAM Tori for 1D Nonlinear Wave Equationswith Periodic Boundary Conditions

NASA Astrophysics Data System (ADS)

Chierchia, Luigi; You, Jiangong

In this paper, one-dimensional (1D) nonlinear wave equations with periodic boundary conditions are considered; V is a periodic smooth or analytic function and the nonlinearity f is an analytic function vanishing together with its derivative at u≡0. It is proved that for ``most'' potentials V(x), the above equation admits small-amplitude periodic or quasi-periodic solutions corresponding to finite dimensional invariant tori for an associated infinite dimensional dynamical system. The proof is based on an infinite dimensional KAM theorem which allows for multiple normal frequencies.

Analytical fitting model for rough-surface BRDF.

PubMed

Renhorn, Ingmar G E; Boreman, Glenn D

2008-08-18

A physics-based model is developed for rough surface BRDF, taking into account angles of incidence and scattering, effective index, surface autocovariance, and correlation length. Shadowing is introduced on surface correlation length and reflectance. Separate terms are included for surface scatter, bulk scatter and retroreflection. Using the FindFit function in Mathematica, the functional form is fitted to BRDF measurements over a wide range of incident angles. The model has fourteen fitting parameters; once these are fixed, the model accurately describes scattering data over two orders of magnitude in BRDF without further adjustment. The resulting analytical model is convenient for numerical computations.

Generalised quasiprobability distribution for Hermite polynomial squeezed states

NASA Astrophysics Data System (ADS)

Datta, Sunil; D'Souza, Richard

1996-02-01

Generalized quasiprobability distributions (QPD) for Hermite polynomial states are presented. These states are solutions of an eigenvalue equation which is quadratic in creation and annihilation operators. Analytical expressions for the QPD are presented for some special cases of the eigenvalues. For large squeezing these analytical expressions for the QPD take the form of a finite series in even Hermite functions. These expressions very transparently exhibit the transition between, P, Q and W functions corresponding to the change of the s-parameter of the QPD. Further, they clearly show the two-photon nature of the processes involved in the generation of these states.

Compressive Detection of Highly Overlapped Spectra Using Walsh-Hadamard-Based Filter Functions.

PubMed

Corcoran, Timothy C

2018-03-01

In the chemometric context in which spectral loadings of the analytes are already known, spectral filter functions may be constructed which allow the scores of mixtures of analytes to be determined in on-the-fly fashion directly, by applying a compressive detection strategy. Rather than collecting the entire spectrum over the relevant region for the mixture, a filter function may be applied within the spectrometer itself so that only the scores are recorded. Consequently, compressive detection shrinks data sets tremendously. The Walsh functions, the binary basis used in Walsh-Hadamard transform spectroscopy, form a complete orthonormal set well suited to compressive detection. A method for constructing filter functions using binary fourfold linear combinations of Walsh functions is detailed using mathematics borrowed from genetic algorithm work, as a means of optimizing said functions for a specific set of analytes. These filter functions can be constructed to automatically strip the baseline from analysis. Monte Carlo simulations were performed with a mixture of four highly overlapped Raman loadings and with ten excitation-emission matrix loadings; both sets showed a very high degree of spectral overlap. Reasonable estimates of the true scores were obtained in both simulations using noisy data sets, proving the linearity of the method.

On the analytic lunar and solar perturbations of a near earth satellite

NASA Technical Reports Server (NTRS)

Estes, R. H.

1972-01-01

The disturbing function of the moon (sun) is expanded as a sum of products of two harmonic functions, one depending on the position of the satellite and the other on the position of the moon (sun). The harmonic functions depending on the position of the perturbing body are developed into trigonometric series with the ecliptic elements l, l', F, D, and Gamma of the lunar theory which are nearly linear with respect to time. Perturbation of elements are in the form of trigonometric series with the ecliptic lunar elements and the equatorial elements omega and Omega of the satellite so that analytic integration is simple and the results accurate over a long period of time.

Applying the method of fundamental solutions to harmonic problems with singular boundary conditions

NASA Astrophysics Data System (ADS)

Valtchev, Svilen S.; Alves, Carlos J. S.

2017-07-01

The method of fundamental solutions (MFS) is known to produce highly accurate numerical results for elliptic boundary value problems (BVP) with smooth boundary conditions, posed in analytic domains. However, due to the analyticity of the shape functions in its approximation basis, the MFS is usually disregarded when the boundary functions possess singularities. In this work we present a modification of the classical MFS which can be applied for the numerical solution of the Laplace BVP with Dirichlet boundary conditions exhibiting jump discontinuities. In particular, a set of harmonic functions with discontinuous boundary traces is added to the MFS basis. The accuracy of the proposed method is compared with the results form the classical MFS.

Semi-analytical Karhunen-Loeve representation of irregular waves based on the prolate spheroidal wave functions

NASA Astrophysics Data System (ADS)

Lee, Gibbeum; Cho, Yeunwoo

2018-01-01

A new semi-analytical approach is presented to solving the matrix eigenvalue problem or the integral equation in Karhunen-Loeve (K-L) representation of random data such as irregular ocean waves. Instead of direct numerical approach to this matrix eigenvalue problem, which may suffer from the computational inaccuracy for big data, a pair of integral and differential equations are considered, which are related to the so-called prolate spheroidal wave functions (PSWF). First, the PSWF is expressed as a summation of a small number of the analytical Legendre functions. After substituting them into the PSWF differential equation, a much smaller size matrix eigenvalue problem is obtained than the direct numerical K-L matrix eigenvalue problem. By solving this with a minimal numerical effort, the PSWF and the associated eigenvalue of the PSWF differential equation are obtained. Then, the eigenvalue of the PSWF integral equation is analytically expressed by the functional values of the PSWF and the eigenvalues obtained in the PSWF differential equation. Finally, the analytically expressed PSWFs and the eigenvalues in the PWSF integral equation are used to form the kernel matrix in the K-L integral equation for the representation of exemplary wave data such as ordinary irregular waves. It is found that, with the same accuracy, the required memory size of the present method is smaller than that of the direct numerical K-L representation and the computation time of the present method is shorter than that of the semi-analytical method based on the sinusoidal functions.

PROPOSED SIAM PROBLEM

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

BAILEY, DAVID H.; BORWEIN, JONATHAN M.

A recent paper by the present authors, together with mathematical physicists David Broadhurst and M. Larry Glasser, explored Bessel moment integrals, namely definite integrals of the general form {integral}{sub 0}{sup {infinity}} t{sup m}f{sup n}(t) dt, where the function f(t) is one of the classical Bessel functions. In that paper, numerous previously unknown analytic evaluations were obtained, using a combination of analytic methods together with some fairly high-powered numerical computations, often performed on highly parallel computers. In several instances, while we were able to numerically discover what appears to be a solid analytic identity, based on extremely high-precision numerical computations, wemore » were unable to find a rigorous proof. Thus we present here a brief list of some of these unproven but numerically confirmed identities.« less

Quantifying wall turbulence via a symmetry approach: A Lie group theory

NASA Astrophysics Data System (ADS)

She, Zhen-Su; Chen, Xi; Hussain, Fazle

2017-11-01

We present a symmetry-based approach which yields analytic expressions for the mean velocity and kinetic energy profiles from a Lie-group analysis. After verifying the dilation-group invariance of the Reynolds averaged Navier-Stokes equation in the presence of a wall, we select a stress and energy length function as similarity variables which are assumed to have a simple dilation-invariant form. Three kinds of (local) invariant forms of the length functions are postulated, a combination of which yields a multi-layer formula giving its distribution in the entire flow region normal to the wall. The mean velocity profile is then predicted using the mean momentum equation, which yields, in particular, analytic expressions for the (universal) wall function and separate wake functions for pipe and channel - which are validated by data from direct numerical simulations (DNS). Future applications to a variety of wall flows such as flows around flat plate or airfoil, in a Rayleigh-Benard cell or Taylor-Couette system, etc., are discussed, for which the dilation group invariance is valid in the wall-normal direction.

QCD triple Pomeron coupling from string amplitudes

NASA Astrophysics Data System (ADS)

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

1998-06-01

Using the recent solution of the triple Pomeron coupling in the QCD dipole picture as a closed string amplitude with six legs, its analytical form in terms of hypergeometric functions and numerical value are derived.

Tables for determining lead, uranium, and thorium isotope ages

NASA Technical Reports Server (NTRS)

Schonfeld, E.

1974-01-01

Tables for determining lead, uranium, and thorium isotope ages are presented in the form of computer printouts. Decay constants, analytical expressions for the functions evaluated, and the precision of the calculations are briefly discussed.

An analytical model for scanning electron microscope Type I magnetic contrast with energy filtering

NASA Astrophysics Data System (ADS)

Chim, W. K.

1994-02-01

In this article, a theoretical model for type I magnetic contrast calculations in the scanning electron microscope with energy filtering is presented. This model uses an approximate form of the secondary electron (SE) energy distribution by Chung and Everhart [M. S. Chung and T. E. Everhart, J. Appl. Phys. 45, 707 (1974). Closed form analytical expressions for the contrast and quality factors, which take into consideration the work function and field-distance integral of the material being studied, are obtained. This analytical model is compared with that of a more accurate numerical model. Results showed that the contrast and quality factors for the analytical model differed by not more than 20% from the numerical model, with the actual difference depending on the range of filtered SE energies considered. This model has also been extended to the situation of a two-detector (i.e., detector A and B) configuration, in which enhanced magnetic contrast and quality factor can be obtained by operating in the ``A-B'' mode.

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

NASA Technical Reports Server (NTRS)

Cao, Y.; Faghri, A.

1992-01-01

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

Analytic approximations to the modon dispersion relation. [in oceanography

NASA Technical Reports Server (NTRS)

Boyd, J. P.

1981-01-01

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

Controllable parabolic-cylinder optical rogue wave.

PubMed

Zhong, Wei-Ping; Chen, Lang; Belić, Milivoj; Petrović, Nikola

2014-10-01

We demonstrate controllable parabolic-cylinder optical rogue waves in certain inhomogeneous media. An analytical rogue wave solution of the generalized nonlinear Schrödinger equation with spatially modulated coefficients and an external potential in the form of modulated quadratic potential is obtained by the similarity transformation. Numerical simulations are performed for comparison with the analytical solutions and to confirm the stability of the rogue wave solution obtained. These optical rogue waves are built by the products of parabolic-cylinder functions and the basic rogue wave solution of the standard nonlinear Schrödinger equation. Such rogue waves may appear in different forms, as the hump and paw profiles.

Analytical and numerical solutions for heat transfer and effective thermal conductivity of cracked media

NASA Astrophysics Data System (ADS)

Tran, A. B.; Vu, M. N.; Nguyen, S. T.; Dong, T. Q.; Le-Nguyen, K.

2018-02-01

This paper presents analytical solutions to heat transfer problems around a crack and derive an adaptive model for effective thermal conductivity of cracked materials based on singular integral equation approach. Potential solution of heat diffusion through two-dimensional cracked media, where crack filled by air behaves as insulator to heat flow, is obtained in a singular integral equation form. It is demonstrated that the temperature field can be described as a function of temperature and rate of heat flow on the boundary and the temperature jump across the cracks. Numerical resolution of this boundary integral equation allows determining heat conduction and effective thermal conductivity of cracked media. Moreover, writing this boundary integral equation for an infinite medium embedding a single crack under a far-field condition allows deriving the closed-form solution of temperature discontinuity on the crack and particularly the closed-form solution of temperature field around the crack. These formulas are then used to establish analytical effective medium estimates. Finally, the comparison between the developed numerical and analytical solutions allows developing an adaptive model for effective thermal conductivity of cracked media. This model takes into account both the interaction between cracks and the percolation threshold.

On the Complexity of Item Response Theory Models.

PubMed

Bonifay, Wes; Cai, Li

2017-01-01

Complexity in item response theory (IRT) has traditionally been quantified by simply counting the number of freely estimated parameters in the model. However, complexity is also contingent upon the functional form of the model. We examined four popular IRT models-exploratory factor analytic, bifactor, DINA, and DINO-with different functional forms but the same number of free parameters. In comparison, a simpler (unidimensional 3PL) model was specified such that it had 1 more parameter than the previous models. All models were then evaluated according to the minimum description length principle. Specifically, each model was fit to 1,000 data sets that were randomly and uniformly sampled from the complete data space and then assessed using global and item-level fit and diagnostic measures. The findings revealed that the factor analytic and bifactor models possess a strong tendency to fit any possible data. The unidimensional 3PL model displayed minimal fitting propensity, despite the fact that it included an additional free parameter. The DINA and DINO models did not demonstrate a proclivity to fit any possible data, but they did fit well to distinct data patterns. Applied researchers and psychometricians should therefore consider functional form-and not goodness-of-fit alone-when selecting an IRT model.

Analysis of social optimum for staggered shifts in a single-entry traffic corridor with no late arrivals

NASA Astrophysics Data System (ADS)

Li, Chuan-Yao; Huang, Hai-Jun; Tang, Tie-Qiao

2017-03-01

This paper investigates the traffic flow dynamics under the social optimum (SO) principle in a single-entry traffic corridor with staggered shifts from the analytical and numerical perspectives. The LWR (Lighthill-Whitham and Richards) model and the Greenshield's velocity-density function are utilized to describe the dynamic properties of traffic flow. The closed-form SO solution is analytically derived and some numerical examples are used to further testify the analytical solution. The optimum proportion of the numbers of commuters with different desired arrival times is further discussed, where the analytical and numerical results both indicate that the cumulative outflow curve under the SO principle is piecewise smooth.

Reactant conversion in homogeneous turbulence: Mathematical modeling, computational validations and practical applications

NASA Technical Reports Server (NTRS)

Madnia, C. K.; Frankel, S. H.; Givi, P.

1992-01-01

Closed form analytical expressions are obtained for predicting the limited rate of reactant conversion in a binary reaction of the type F + rO yields (1 + r) Product in unpremixed homogeneous turbulence. These relations are obtained by means of a single point Probability Density Function (PDF) method based on the Amplitude Mapping Closure. It is demonstrated that with this model, the maximum rate of the reactants' decay can be conveniently expressed in terms of definite integrals of the Parabolic Cylinder Functions. For the cases with complete initial segregation, it is shown that the results agree very closely with those predicted by employing a Beta density of the first kind for an appropriately defined Shvab-Zeldovich scalar variable. With this assumption, the final results can also be expressed in terms of closed form analytical expressions which are based on the Incomplete Beta Functions. With both models, the dependence of the results on the stoichiometric coefficient and the equivalence ratio can be expressed in an explicit manner. For a stoichiometric mixture, the analytical results simplify significantly. In the mapping closure, these results are expressed in terms of simple trigonometric functions. For the Beta density model, they are in the form of Gamma Functions. In all the cases considered, the results are shown to agree well with data generated by Direct Numerical Simulations (DNS). Due to the simplicity of these expressions and because of nice mathematical features of the Parabolic Cylinder and the Incomplete Beta Functions, these models are recommended for estimating the limiting rate of reactant conversion in homogeneous reacting flows. These results also provide useful insights in assessing the extent of validity of turbulence closures in the modeling of unpremixed reacting flows. Some discussions are provided on the extension of the model for treating more complicated reacting systems including realistic kinetics schemes and multi-scalar mixing with finite rate chemical reactions in more complex configurations.

Almost analytical Karhunen-Loeve representation of irregular waves based on the prolate spheroidal wave functions

NASA Astrophysics Data System (ADS)

Lee, Gibbeum; Cho, Yeunwoo

2017-11-01

We present an almost analytical new approach to solving the matrix eigenvalue problem or the integral equation in Karhunen-Loeve (K-L) representation of random data such as irregular ocean waves. Instead of solving this matrix eigenvalue problem purely numerically, which may suffer from the computational inaccuracy for big data, first, we consider a pair of integral and differential equations, which are related to the so-called prolate spheroidal wave functions (PSWF). For the PSWF differential equation, the pair of the eigenvectors (PSWF) and eigenvalues can be obtained from a relatively small number of analytical Legendre functions. Then, the eigenvalues in the PSWF integral equation are expressed in terms of functional values of the PSWF and the eigenvalues of the PSWF differential equation. Finally, the analytically expressed PSWFs and the eigenvalues in the PWSF integral equation are used to form the kernel matrix in the K-L integral equation for the representation of exemplary wave data; ordinary irregular waves and rogue waves. We found that the present almost analytical method is better than the conventional data-independent Fourier representation and, also, the conventional direct numerical K-L representation in terms of both accuracy and computational cost. This work was supported by the National Research Foundation of Korea (NRF). (NRF-2017R1D1A1B03028299).

Spiral Form of the Human Cochlea Results from Spatial Constraints.

PubMed

Pietsch, M; Aguirre Dávila, L; Erfurt, P; Avci, E; Lenarz, T; Kral, A

2017-08-08

The human inner ear has an intricate spiral shape often compared to shells of mollusks, particularly to the nautilus shell. It has inspired many functional hearing theories. The reasons for this complex geometry remain unresolved. We digitized 138 human cochleae at microscopic resolution and observed an astonishing interindividual variability in the shape. A 3D analytical cochlear model was developed that fits the analyzed data with high precision. The cochlear geometry neither matched a proposed function, namely sound focusing similar to a whispering gallery, nor did it have the form of a nautilus. Instead, the innate cochlear blueprint and its actual ontogenetic variants were determined by spatial constraints and resulted from an efficient packing of the cochlear duct within the petrous bone. The analytical model predicts well the individual 3D cochlear geometry from few clinical measures and represents a clinical tool for an individualized approach to neurosensory restoration with cochlear implants.

Morse oscillator propagator in the high temperature limit I: Theory

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

Toutounji, Mohamad, E-mail: Mtoutounji@uaeu.ac.ae

2017-02-15

In an earlier work of the author the time evolution of Morse oscillator was studied analytically and exactly at low temperatures whereupon optical correlation functions were calculated using Morse oscillator coherent states were employed. Morse oscillator propagator in the high temperature limit is derived and a closed form of its corresponding canonical partition function is obtained. Both diagonal and off-diagonal forms of Morse oscillator propagator are derived in the high temperature limit. Partition functions of diatomic molecules are calculated. - Highlights: • Derives the quantum propagator of Morse oscillator in the high temperature limit. • Uses the resulting diagonal propagatormore » to derive a closed form of Morse oscillator partition function. • Provides a more sophisticated formula of the quantum propagator to test the accuracy of the herein results.« less

mrpy: Renormalized generalized gamma distribution for HMF and galaxy ensemble properties comparisons

NASA Astrophysics Data System (ADS)

Murray, Steven G.; Robotham, Aaron S. G.; Power, Chris

2018-02-01

mrpy calculates the MRP parameterization of the Halo Mass Function. It calculates basic statistics of the truncated generalized gamma distribution (TGGD) with the TGGD class, including mean, mode, variance, skewness, pdf, and cdf. It generates MRP quantities with the MRP class, such as differential number counts and cumulative number counts, and offers various methods for generating normalizations. It can generate the MRP-based halo mass function as a function of physical parameters via the mrp_b13 function, and fit MRP parameters to data in the form of arbitrary curves and in the form of a sample of variates with the SimFit class. mrpy also calculates analytic hessians and jacobians at any point, and allows the user to alternate parameterizations of the same form via the reparameterize module.

An Updated Typology of Causative Constructions: Form-Function Mappings in Hupa (California Athabaskan), Chungli Ao (Tibeto-Burman) and Beyond

ERIC Educational Resources Information Center

Escamilla, Ramon Matthew, Jr.

2012-01-01

Taking up analytical issues raised primarily in Dixon (2000) and Dixon & Aikhenvald (2000), this dissertation combines descriptive work with a medium-sized (50-language) typological study. Chapter 1 situates the dissertation against a concise survey of typological-functional work on causative constructions from the last few decades, and…

Error analysis in some Gauss-Turan-Radau and Gauss-Turan-Lobatto quadratures for analytic functions

NASA Astrophysics Data System (ADS)

Milovanovic, Gradimir V.; Spalevic, Miodrag M.

2004-03-01

We consider the generalized Gauss-Turan quadrature formulae of Radau and Lobatto type for approximating . The aim of this paper is to analyze the remainder term in the case when f is an analytic function in some region of the complex plane containing the interval [-1,1] in its interior. The remainder term is presented in the form of a contour integral over confocal ellipses (cf. SIAM J. Numer. Anal. 80 (1983) 1170). Sufficient conditions on the convergence for some of such quadratures, associated with the generalized Chebyshev weight functions, are found. Using some ideas from Hunter (BIT 35 (1995) 64) we obtain new estimates of the remainder term, which are very exact. Some numerical results and illustrations are shown.

On the Kernel function of the integral equation relating lift and downwash distributions of oscillating wings in supersonic flow

NASA Technical Reports Server (NTRS)

Watkins, Charles E; Berman, Julian H

1956-01-01

This report treats the Kernel function of the integral equation that relates a known or prescribed downwash distribution to an unknown lift distribution for harmonically oscillating wings in supersonic flow. The treatment is essentially an extension to supersonic flow of the treatment given in NACA report 1234 for subsonic flow. For the supersonic case the Kernel function is derived by use of a suitable form of acoustic doublet potential which employs a cutoff or Heaviside unit function. The Kernel functions are reduced to forms that can be accurately evaluated by considering the functions in two parts: a part in which the singularities are isolated and analytically expressed, and a nonsingular part which can be tabulated.

Analytic Results for e+e- --> tt-bar and gammagamma --> tt-bar Observables near the Threshold up to the Next-to-Next-to-Leading Order of NRQCD

NASA Astrophysics Data System (ADS)

Penin, A. A.; Pivovarov, A. A.

2001-02-01

We present an analytical description of top-antitop pair production near the threshold in $e^+e^-$ annihilation and $\\g\\g$ collisions. A set of basic observables considered includes the total cross sections, forward-backward asymmetry and top quark polarization. The threshold effects relevant for the basic observables are described by three universal functions related to S wave production, P wave production and S-P interference. These functions are computed analytically up to the next-to-next-to-leading order of NRQCD. The total $e^+e^-\\to t\\bar t$ cross section near the threshold is obtained in the next-to-next-to-leading order in the closed form including the contribution due to the axial coupling of top quark and mediated by the Z-boson. The effects of the running of the strong coupling constant and of the finite top quark width are taken into account analytically for the P wave production and S-P wave interference.

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

NASA Astrophysics Data System (ADS)

Chen, Wenting; Du, Meiyu; Xu, Xiang

2017-01-01

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

Analytical Description of the H/D Exchange Kinetic of Macromolecule.

PubMed

Kostyukevich, Yury; Kononikhin, Alexey; Popov, Igor; Nikolaev, Eugene

2018-04-17

We present the accurate analytical solution obtained for the system of rate equations describing the isotope exchange process for molecules containing an arbitrary number of equivalent labile atoms. The exact solution was obtained using Mathematica 7.0 software, and this solution has the form of the time-dependent Gaussian distribution. For the case when forward exchange considerably overlaps the back exchange, it is possible to estimate the activation energy of the reaction by obtaining a temperature dependence of the reaction degree. Using a previously developed approach for performing H/D exchange directly in the ESI source, we have estimated the activation energies for ions with different functional groups and they were found to be in a range 0.04-0.3 eV. Since the value of the activation energy depends on the type of functional group, the developed approach can have potential analytical applications for determining types of functional groups in complex mixtures, such as petroleum, humic substances, bio-oil, and so on.

A series solution for horizontal infiltration in an initially dry aquifer

NASA Astrophysics Data System (ADS)

Furtak-Cole, Eden; Telyakovskiy, Aleksey S.; Cooper, Clay A.

2018-06-01

The porous medium equation (PME) is a generalization of the traditional Boussinesq equation for hydraulic conductivity as a power law function of height. We analyze the horizontal recharge of an initially dry unconfined aquifer of semi-infinite extent, as would be found in an aquifer adjacent a rising river. If the water level can be modeled as a power law function of time, similarity variables can be introduced and the original problem can be reduced to a boundary value problem for a nonlinear ordinary differential equation. The position of the advancing front is not known ahead of time and must be found in the process of solution. We present an analytical solution in the form of a power series, with the coefficients of the series given by a recurrence relation. The analytical solution compares favorably with a highly accurate numerical solution, and only a small number of terms of the series are needed to achieve high accuracy in the scenarios considered here. We also conduct a series of physical experiments in an initially dry wedged Hele-Shaw cell, where flow is modeled by a special form of the PME. Our analytical solution closely matches the hydraulic head profiles in the Hele-Shaw cell experiment.

Analytic evaluation of the weighting functions for remote sensing of blackbody planetary atmospheres : the case of limb viewing geometry

NASA Technical Reports Server (NTRS)

Ustinov, Eugene A.

2006-01-01

In a recent publication (Ustinov, 2002), we proposed an analytic approach to evaluation of radiative and geophysical weighting functions for remote sensing of a blackbody planetary atmosphere, based on general linearization approach applied to the case of nadir viewing geometry. In this presentation, the general linearization approach is applied to the limb viewing geometry. The expressions, similar to those obtained in (Ustinov, 2002), are obtained for weighting functions with respect to the distance along the line of sight. Further on, these expressions are converted to the expressions for weighting functions with respect to the vertical coordinate in the atmosphere. Finally, the numerical representation of weighting functions in the form of matrices of partial derivatives of grid limb radiances with respect to the grid values of atmospheric parameters is used for a convolution with the finite field of view of the instrument.

Energy spectra and wave function of trigonometric Rosen-Morse potential as an effective quantum chromodynamics potential in D-dimensions

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

Deta, U. A., E-mail: utamaalan@yahoo.co.id; Suparmi,; Cari,

2014-09-30

The Energy Spectra and Wave Function of Schrodinger equation in D-Dimensions for trigonometric Rosen-Morse potential were investigated analytically using Nikiforov-Uvarov method. This potential captures the essential traits of the quark-gluon dynamics of Quantum Chromodynamics. The approximate energy spectra are given in the close form and the corresponding approximate wave function for arbitrary l-state (l ≠ 0) in D-dimensions are formulated in the form of differential polynomials. The wave function of this potential unnormalizable for general case. The wave function of this potential unnormalizable for general case. The existence of extra dimensions (centrifugal factor) and this potential increase the energy spectramore » of system.« less

Collision-induced dissociation analysis of negative atmospheric ion adducts in atmospheric pressure corona discharge ionization mass spectrometry.

PubMed

Sekimoto, Kanako; Takayama, Mitsuo

2013-05-01

Collision-induced dissociation (CID) experiments were performed on atmospheric ion adducts [M + R](-) formed between various types of organic compounds M and atmospheric negative ions R(-) [such as O2(-), HCO3(-), COO(-)(COOH), NO2(-), NO3(-), and NO3(-)(HNO3)] in negative-ion mode atmospheric pressure corona discharge ionization (APCDI) mass spectrometry. All of the [M + R](-) adducts were fragmented to form deprotonated analytes [M - H](-) and/or atmospheric ions R(-), whose intensities in the CID spectra were dependent on the proton affinities of the [M - H](-) and R(-) fragments. Precursor ions [M + R](-) for which R(-) have higher proton affinities than [M - H](-) formed [M - H](-) as the dominant product. Furthermore, the CID of the adducts with HCO3(-) and NO3(-)(HNO3) led to other product ions such as [M + HO](-) and NO3(-), respectively. The fragmentation behavior of [M + R](-) for each R(-) observed was independent of analyte type (e.g., whether the analyte was aliphatic or aromatic, or possessed certain functional groups).

Motions about a fixed point by hypergeometric functions: new non-complex analytical solutions and integration of the herpolhode

NASA Astrophysics Data System (ADS)

Mingari Scarpello, Giovanni; Ritelli, Daniele

2018-06-01

The present study highlights the dynamics of a body moving about a fixed point and provides analytical closed form solutions. Firstly, for the symmetrical heavy body, that is the Lagrange-Poisson case, we compute the second (precession, ψ ) and third (spin, φ) Euler angles in explicit and real form by means of multiple hypergeometric (Lauricella) functions. Secondly, releasing the weight assumption but adding the complication of the asymmetry, by means of elliptic integrals of third kind, we provide the precession angle ψ completing the treatment of the Euler-Poinsot case. Thirdly, by integrating the relevant differential equation, we reach the finite polar equation of a special motion trajectory named the herpolhode. Finally, we keep the symmetry of the first problem, but without weight, and take into account a viscous dissipation. The use of motion first integrals—adopted for the first two problems—is no longer practicable in this situation; therefore, the Euler equations, faced directly, are driving to particular occurrences of Bessel functions of order - 1/2.

"You Know Doctor, I Need to Tell You Something": A Discourse Analytical Study of Patients' Voices in the Medical Consultation

ERIC Educational Resources Information Center

Cordella, Marisa

2004-01-01

Most studies in the area of doctor-patient communication focus on the talk that doctors perform during the consultation, leaving under-researched the discourse developed by patients. This article deconstructs and identifies the functions and forms of the voices (i.e. specific forms of talk) that Chilean patients employ in their interactions with…

Simple Analytic Formula for the Period of the Nonlinear Pendulum via the Struve Function: Connection to Acoustical Impedance Matching

ERIC Educational Resources Information Center

Douvropoulos, Theodosios G.

2012-01-01

An approximate formula for the period of pendulum motion beyond the small amplitude regime is obtained based on physical arguments. Two different schemes of different accuracy are developed: in the first less accurate scheme, emphasis is given on the non-quadratic form of the potential in connection to isochronism, and a specific form of a generic…

Comparison of three methods for wind turbine capacity factor estimation.

PubMed

Ditkovich, Y; Kuperman, A

2014-01-01

Three approaches to calculating capacity factor of fixed speed wind turbines are reviewed and compared using a case study. The first "quasiexact" approach utilizes discrete wind raw data (in the histogram form) and manufacturer-provided turbine power curve (also in discrete form) to numerically calculate the capacity factor. On the other hand, the second "analytic" approach employs a continuous probability distribution function, fitted to the wind data as well as continuous turbine power curve, resulting from double polynomial fitting of manufacturer-provided power curve data. The latter approach, while being an approximation, can be solved analytically thus providing a valuable insight into aspects, affecting the capacity factor. Moreover, several other merits of wind turbine performance may be derived based on the analytical approach. The third "approximate" approach, valid in case of Rayleigh winds only, employs a nonlinear approximation of the capacity factor versus average wind speed curve, only requiring rated power and rotor diameter of the turbine. It is shown that the results obtained by employing the three approaches are very close, enforcing the validity of the analytically derived approximations, which may be used for wind turbine performance evaluation.

The maximal-density mass function for primordial black hole dark matter

NASA Astrophysics Data System (ADS)

Lehmann, Benjamin V.; Profumo, Stefano; Yant, Jackson

2018-04-01

The advent of gravitational wave astronomy has rekindled interest in primordial black holes (PBH) as a dark matter candidate. As there are many different observational probes of the PBH density across different masses, constraints on PBH models are dependent on the functional form of the PBH mass function. This complicates general statements about the mass functions allowed by current data, and, in particular, about the maximum total density of PBH. Numerical studies suggest that some forms of extended mass functions face tighter constraints than monochromatic mass functions, but they do not preclude the existence of a functional form for which constraints are relaxed. We use analytical arguments to show that the mass function which maximizes the fraction of the matter density in PBH subject to all constraints is a finite linear combination of monochromatic mass functions. We explicitly compute the maximum fraction of dark matter in PBH for different combinations of current constraints, allowing for total freedom of the mass function. Our framework elucidates the dependence of the maximum PBH density on the form of observational constraints, and we discuss the implications of current and future constraints for the viability of the PBH dark matter paradigm.

Ringo: Interactive Graph Analytics on Big-Memory Machines

PubMed Central

Perez, Yonathan; Sosič, Rok; Banerjee, Arijit; Puttagunta, Rohan; Raison, Martin; Shah, Pararth; Leskovec, Jure

2016-01-01

We present Ringo, a system for analysis of large graphs. Graphs provide a way to represent and analyze systems of interacting objects (people, proteins, webpages) with edges between the objects denoting interactions (friendships, physical interactions, links). Mining graphs provides valuable insights about individual objects as well as the relationships among them. In building Ringo, we take advantage of the fact that machines with large memory and many cores are widely available and also relatively affordable. This allows us to build an easy-to-use interactive high-performance graph analytics system. Graphs also need to be built from input data, which often resides in the form of relational tables. Thus, Ringo provides rich functionality for manipulating raw input data tables into various kinds of graphs. Furthermore, Ringo also provides over 200 graph analytics functions that can then be applied to constructed graphs. We show that a single big-memory machine provides a very attractive platform for performing analytics on all but the largest graphs as it offers excellent performance and ease of use as compared to alternative approaches. With Ringo, we also demonstrate how to integrate graph analytics with an iterative process of trial-and-error data exploration and rapid experimentation, common in data mining workloads. PMID:27081215

Ringo: Interactive Graph Analytics on Big-Memory Machines.

PubMed

Perez, Yonathan; Sosič, Rok; Banerjee, Arijit; Puttagunta, Rohan; Raison, Martin; Shah, Pararth; Leskovec, Jure

2015-01-01

We present Ringo, a system for analysis of large graphs. Graphs provide a way to represent and analyze systems of interacting objects (people, proteins, webpages) with edges between the objects denoting interactions (friendships, physical interactions, links). Mining graphs provides valuable insights about individual objects as well as the relationships among them. In building Ringo, we take advantage of the fact that machines with large memory and many cores are widely available and also relatively affordable. This allows us to build an easy-to-use interactive high-performance graph analytics system. Graphs also need to be built from input data, which often resides in the form of relational tables. Thus, Ringo provides rich functionality for manipulating raw input data tables into various kinds of graphs. Furthermore, Ringo also provides over 200 graph analytics functions that can then be applied to constructed graphs. We show that a single big-memory machine provides a very attractive platform for performing analytics on all but the largest graphs as it offers excellent performance and ease of use as compared to alternative approaches. With Ringo, we also demonstrate how to integrate graph analytics with an iterative process of trial-and-error data exploration and rapid experimentation, common in data mining workloads.

Identification of Carboxylate, Phosphate, and Phenoxide Functionalities in Deprotonated Molecules Related to Drug Metabolites via Ion-Molecule Reactions with water and Diethylhydroxyborane

NASA Astrophysics Data System (ADS)

Zhu, Hanyu; Ma, Xin; Kong, John Y.; Zhang, Minli; Kenttämaa, Hilkka I.

2017-10-01

Tandem mass spectrometry based on ion-molecule reactions has emerged as a powerful tool for structural elucidation of ionized analytes. However, most currently used reagents were designed to react with protonated analytes, making them suboptimal for acidic analytes that are preferentially detected in negative ion mode. In this work we demonstrate that the phenoxide, carboxylate, and phosphate functionalities can be identified in deprotonated molecules by use of a combination of two reagents, diethylmethoxyborane (DEMB) and water. A novel reagent introduction setup that allowed DEMB and water to be separately introduced into the ion trap region of the mass spectrometer was developed to facilitate fundamental studies of this reaction. A new reagent, diethylhydroxyborane (DEHB), was generated inside the ion trap by hydrolysis of DEMB on introduction of water. Most carboxylates and phenoxides formed a DEHB adduct, followed by addition of one water molecule and subsequent ethane elimination (DEHB adduct +H2O - CH3CH3) as the major product ion. Phenoxides with a hydroxy group adjacent to the deprotonation site and phosphates formed a DEHB adduct, followed by ethane elimination (DEHB adduct - CH3CH3). Deprotonated molecules with strong intramolecular hydrogen bonds or without the aforementioned functionalities, including sulfates, were unreactive toward DEHB/H2O. Reaction mechanisms were explored via isotope labeling experiments and quantum chemical calculations. The mass spectrometry method allowed the differentiation of phenoxide-, carboxylate-, phosphate-, and sulfate-containing analytes. Finally, it was successfully coupled with high-performance liquid chromatography for the analysis of a mixture containing hymecromone, a biliary spasm drug, and its three possible metabolites. [Figure not available: see fulltext.

Quantitative Methods Based on Twisted Nematic Liquid Crystals for Mapping Surfaces Patterned with Bio/Chemical Functionality Relevant to Bioanalytical Assays

PubMed Central

Lowe, Aaron M.; Bertics, Paul J.; Abbott, Nicholas L.

2009-01-01

We report methods for the acquisition and analysis of optical images formed by thin films of twisted nematic liquid crystals (LCs) placed into contact with surfaces patterned with bio/chemical functionality relevant to surface-based assays. The methods are simple to implement and are shown to provide easily interpreted maps of chemical transformations on surfaces that are widely exploited in the preparation of analytic devices. The methods involve acquisition of multiple images of the LC as a function of the orientation of a polarizer; data analysis condenses the information present in the stack of images into a spatial map of the twist angle of the LC on the analytic surface. The potential utility of the methods is illustrated by mapping (i) the displacement of a monolayer formed from one alkanethiol on a gold film by a second thiol in solution, (ii) coadsorption of mixtures of amine-terminated and ethyleneglycol-terminated alkanethiols on gold films, which leads to a type of mixed monolayer that is widely exploited for immobilization of proteins on analytic surfaces, and (iii) patterns of antibodies printed onto surfaces. These results show that maps of the twist angle of the LC constructed from families of optical images can be used to reveal surface features that are not apparent in a single image of the LC film. Furthermore, the twist angles of the LC can be used to quantify the energy of interaction of the LC with the surface with a spatial resolution of <10 µm. When combined, the results described in this paper suggest non-destructive methods to monitor and validate chemical transformations on surfaces of the type that are routinely employed in the preparation of surface-based analytic technologies. PMID:18355089

Flexible aircraft dynamic modeling for dynamic analysis and control synthesis

NASA Technical Reports Server (NTRS)

Schmidt, David K.

1989-01-01

The linearization and simplification of a nonlinear, literal model for flexible aircraft is highlighted. Areas of model fidelity that are critical if the model is to be used for control system synthesis are developed and several simplification techniques that can deliver the necessary model fidelity are discussed. These techniques include both numerical and analytical approaches. An analytical approach, based on first-order sensitivity theory is shown to lead not only to excellent numerical results, but also to closed-form analytical expressions for key system dynamic properties such as the pole/zero factors of the vehicle transfer-function matrix. The analytical results are expressed in terms of vehicle mass properties, vibrational characteristics, and rigid-body and aeroelastic stability derivatives, thus leading to the underlying causes for critical dynamic characteristics.

Multidimensional Extension of the Generalized Chowla-Selberg Formula

NASA Astrophysics Data System (ADS)

Elizalde, E.

After recalling the precise existence conditions of the zeta function of a pseudodifferential operator, and the concept of reflection formula, an exponentially convergent expression for the analytic continuation of a multidimensional inhomogeneous Epstein-type zeta function of the general form with A the p×p$ matrix of a quadratic form, a p vector and q a constant, is obtained. It is valid on the whole complex s-plane, is exponentially convergent and provides the residua at the poles explicitly. It reduces to the famous formula of Chowla and Selberg in the particular case p=2, , q=0. Some variations of the formula and physical applications are considered.

Extending existing structural identifiability analysis methods to mixed-effects models.

PubMed

Janzén, David L I; Jirstrand, Mats; Chappell, Michael J; Evans, Neil D

2018-01-01

The concept of structural identifiability for state-space models is expanded to cover mixed-effects state-space models. Two methods applicable for the analytical study of the structural identifiability of mixed-effects models are presented. The two methods are based on previously established techniques for non-mixed-effects models; namely the Taylor series expansion and the input-output form approach. By generating an exhaustive summary, and by assuming an infinite number of subjects, functions of random variables can be derived which in turn determine the distribution of the system's observation function(s). By considering the uniqueness of the analytical statistical moments of the derived functions of the random variables, the structural identifiability of the corresponding mixed-effects model can be determined. The two methods are applied to a set of examples of mixed-effects models to illustrate how they work in practice. Copyright © 2017 Elsevier Inc. All rights reserved.

Gluon fragmentation into quarkonium at next-to-leading order

DOE PAGES

Artoisenet, Pierre; Braaten, Eric

2015-04-22

Here, we present the first calculation at next-to-leading order (NLO) in α s of a fragmentation function into quarkonium whose form at leading order is a nontrivial function of z, namely the fragmentation function for a gluon into a spin-singlet S-wave state at leading order in the relative velocity. To calculate the real NLO corrections, we introduce a new subtraction scheme that allows the phase-space integrals to be evaluated in 4 dimensions. We extract all ultraviolet and infrared divergences in the real NLO corrections analytically by calculating the phase-space integrals of the subtraction terms in 4 – 2ϵ dimensions. Wemore » also extract the divergences in the virtual NLO corrections analytically, and detail the cancellation of all divergences after renormalization. The NLO corrections have a dramatic effect on the shape of the fragmentation function, and they significantly increase the fragmentation probability.« less

Computer-Assisted Microscopy in Science Teaching and Research.

ERIC Educational Resources Information Center

Radice, Gary P.

1997-01-01

Describes a technological approach to teaching the relationships between biological form and function. Computer-assisted image analysis was integrated into a microanatomy course. Students spend less time memorizing and more time observing, measuring, and interpreting, building technical and analytical skills. Appendices list hardware and software…

The statistical theory of the fracture of fragile bodies. Part 2: The integral equation method

NASA Technical Reports Server (NTRS)

Kittl, P.

1984-01-01

It is demonstrated how with the aid of a bending test, the Weibull fracture risk function can be determined - without postulating its analytical form - by resolving an integral equation. The respective solutions for rectangular and circular section beams are given. In the first case the function is expressed as an algorithm and in the second, in the form of series. Taking into account that the cumulative fracture probability appearing in the solution to the integral equation must be continuous and monotonically increasing, any case of fabrication or selection of samples can be treated.

Bending elasticity of macromolecules: analytic predictions from the wormlike chain model.

PubMed

Polley, Anirban; Samuel, Joseph; Sinha, Supurna

2013-01-01

We present a study of the bend angle distribution of semiflexible polymers of short and intermediate lengths within the wormlike chain model. This enables us to calculate the elastic response of a stiff molecule to a bending moment. Our results go beyond the Hookean regime and explore the nonlinear elastic behavior of a single molecule. We present analytical formulas for the bend angle distribution and for the moment-angle relation. Our analytical study is compared against numerical Monte Carlo simulations. The functional forms derived here can be applied to fluorescence microscopic studies on actin and DNA. Our results are relevant to recent studies of "kinks" and cyclization in short and intermediate length DNA strands.

Applications of δ-function perturbation to the pricing of derivative securities

NASA Astrophysics Data System (ADS)

Decamps, Marc; De Schepper, Ann; Goovaerts, Marc

2004-11-01

In the recent econophysics literature, the use of functional integrals is widespread for the calculation of option prices. In this paper, we extend this approach in several directions by means of δ-function perturbations. First, we show that results about infinitely repulsive δ-function are applicable to the pricing of barrier options. We also introduce functional integrals over skew paths that give rise to a new European option formula when combined with δ-function potential. We propose accurate closed-form approximations based on the theory of comonotonic risks in case the functional integrals are not analytically computable.

Analytical transition-matrix treatment of electric multipole polarizabilities of hydrogen-like atoms

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

Kharchenko, V.F., E-mail: vkharchenko@bitp.kiev.ua

2015-04-15

The direct transition-matrix approach to the description of the electric polarization of the quantum bound system of particles is used to determine the electric multipole polarizabilities of the hydrogen-like atoms. It is shown that in the case of the bound system formed by the Coulomb interaction the corresponding inhomogeneous integral equation determining an off-shell scattering function, which consistently describes virtual multiple scattering, can be solved exactly analytically for all electric multipole polarizabilities. Our method allows to reproduce the known Dalgarno–Lewis formula for electric multipole polarizabilities of the hydrogen atom in the ground state and can also be applied to determinemore » the polarizability of the atom in excited bound states. - Highlights: • A new description for electric polarization of hydrogen-like atoms. • Expression for multipole polarizabilities in terms of off-shell scattering functions. • Derivation of integral equation determining the off-shell scattering function. • Rigorous analytic solving the integral equations both for ground and excited states. • Study of contributions of virtual multiple scattering to electric polarizabilities.« less

On The Sfr-M* Main Sequence Archetypal Star-Formation History And Analytical Models

NASA Astrophysics Data System (ADS)

Ciesla, Laure; Elbaz, David; Fensch, Jeremy

2017-06-01

From the evolution of the main sequence we can build the star formation history (SFH) of MS galaxies, assuming that they follow this relation all their life. We show that this SFH is not only a function of cosmic time but also involve the seed mass of the galaxy. We discuss the implications of this MS SFH on the stellar mass growth, and the entry in the passive region of the UVJ diagram, while the galaxy is still forming stars. We test the ability of different analytical SFH forms found in the literature to probe the SFR of all type of galaxies. Using a sample of GOODS-South galaxies, we show that these SFHs artificially enhance or create a gradient of age, parallel to the MS. A simple model of a MS galaxy, such as those expected from compaction or variation in gas accretion, undergoing some fluctuations provide does not predict such a gradient, that we show is due to SFH assumptions. We propose an improved analytical form, taking into account a flexibility in the recent SFH that we calibrate as a diagnostic to identify rapidly quenched galaxies from large photometric survey.

Fractional Fourier transform of truncated elliptical Gaussian beams.

PubMed

Du, Xinyue; Zhao, Daomu

2006-12-20

Based on the fact that a hard-edged elliptical aperture can be expanded approximately as a finite sum of complex Gaussian functions in tensor form, an analytical expression for an elliptical Gaussian beam (EGB) truncated by an elliptical aperture and passing through a fractional Fourier transform system is derived by use of vector integration. The approximate analytical results provide more convenience for studying the propagation and transformation of truncated EGBs than the usual way by using the integral formula directly, and the efficiency of numerical calculation is significantly improved.

Approximate analytical solutions in the analysis of thin elastic plates

NASA Astrophysics Data System (ADS)

Goloskokov, Dmitriy P.; Matrosov, Alexander V.

2018-05-01

Two approaches to the construction of approximate analytical solutions for bending of a rectangular thin plate are presented: the superposition method based on the method of initial functions (MIF) and the one built using the Green's function in the form of orthogonal series. Comparison of two approaches is carried out by analyzing a square plate clamped along its contour. Behavior of the moment and the shear force in the neighborhood of the corner points is discussed. It is shown that both solutions give identical results at all points of the plate except for the neighborhoods of the corner points. There are differences in the values of bending moments and generalized shearing forces in the neighborhoods of the corner points.

Phenomenological model to fit complex permittivity data of water from radio to optical frequencies.

PubMed

Shubitidze, Fridon; Osterberg, Ulf

2007-04-01

A general factorized form of the dielectric function together with a fractional model-based parameter estimation method is used to provide an accurate analytical formula for the complex refractive index in water for the frequency range 10(8)-10(16)Hz . The analytical formula is derived using a combination of a microscopic frequency-dependent rational function for adjusting zeros and poles of the dielectric dispersion together with the macroscopic statistical Fermi-Dirac distribution to provide a description of both the real and imaginary parts of the complex permittivity for water. The Fermi-Dirac distribution allows us to model the dramatic reduction in the imaginary part of the permittivity in the visible window of the water spectrum.

Characterization of electrokinetic gating valve in microfluidic channels.

PubMed

Zhang, Guiseng; Du, Wei; Liu, Bi-Feng; Hisamoto, Hideaki; Terabe, Shigeru

2007-02-12

Electrokinetic gating, functioning as a micro-valve, has been widely employed in microfluidic chips for sample injection and flow switch. Investigating its valving performance is fundamentally vital for microfluidics and microfluidics-based chemical analysis. In this paper, electrokinetic gating valve in microchannels was evaluated using optical imaging technique. Microflow profiles at channels junction were examined, revealing that molecular diffusion played a significant role in the valving disable; which could cause analyte leakage in sample injection. Due to diffusion, the analyte crossed the interface of the analyte flow and gating flow, and then formed a cometic tail-like diffusion area at channels junction. From theoretical calculation and some experimental evidences, the size of the area was related to the diffusion coefficient and the velocity of analytes. Additionally, molecular diffusion was also believed to be another reason of sampling bias in gated injection.

Analytic Wave Functions for the Half-Filled Lowest Landau Level

NASA Astrophysics Data System (ADS)

Ciftja, Orion

We consider a two-dimensional strongly correlated electronic system in a strong perpendicular magnetic field at half-filling of the lowest Landau level (LLL). We seek to build a wave function that, by construction, lies entirely in the Hilbert space of the LLL. Quite generally, a wave function of this nature can be built as a linear combination of all possible Slater determinants formed by using the complete set of single-electron states that belong to the LLL. However, due to the vast number of Slater determinant states required to form such basis functions, the expansion is impractical for any but the smallest systems. Thus, in practice, the expansion must be truncated to a small number of Slater determinants. Among many possible LLL Slater determinant states, we note a particular special class of such wave functions in which electrons occupy either only even, or only odd angular momentum states. We focus on such a class of wave functions and obtain analytic expressions for various quantities of interest. Results seem to suggest that these special wave functions, while interesting and physically appealing, are unlikely to be a very good approximation for the exact ground state at half-filling factor. The overall quality of the description can be improved by including other additional LLL Slater determinant states. It is during this process that we identify another special family of suitable LLL Slater determinant states to be used in an enlarged expansion.

Bounds of the error of Gauss-Turan-type quadratures

NASA Astrophysics Data System (ADS)

Milovanovic, Gradimir V.; Spalevic, Miodrag M.

2005-06-01

We consider the remainder term of the Gauss-Turan quadrature formulaefor analytic functions in some region of the complex plane containing the interval [-1,1] in its interior. The remainder term is presented in the form of a contour integral over confocal ellipses or circles. A strong error analysis is given for the case with a generalized class of weight functions, introduced recently by Gori and Micchelli. Also, we discuss a general case with an even weight function defined on [-1,1]. Numerical results are included.

Finite word length effects on digital filter implementation.

NASA Technical Reports Server (NTRS)

Bowman, J. D.; Clark, F. H.

1972-01-01

This paper is a discussion of two known techniques to analyze finite word length effects on digital filters. These techniques are extended to several additional programming forms and the results verified experimentally. A correlation of the analytical weighting functions for the two methods is made through the Mason Gain Formula.

The Relationship between Psychiatric Symptomatology and Motivation of Challenging Behaviour: A Preliminary Study

ERIC Educational Resources Information Center

Holden, Borge; Gitlesen, Jens Petter

2008-01-01

In addition to explaining challenging behaviour by way of behaviour analytic, functional analyses, challenging behaviour is increasingly explained by way of psychiatric symptomatology. According to some researchers, the two approaches complement each other, as psychiatric symptomatology may form a motivational basis for the individual's response…

Cartan symmetries and global dynamical systems analysis in a higher-order modified teleparallel theory

NASA Astrophysics Data System (ADS)

Karpathopoulos, L.; Basilakos, S.; Leon, G.; Paliathanasis, A.; Tsamparlis, M.

2018-07-01

In a higher-order modified teleparallel theory cosmological we present analytical cosmological solutions. In particular we determine forms of the unknown potential which drives the scalar field such that the field equations form a Liouville integrable system. For the determination of the conservation laws we apply the Cartan symmetries. Furthermore, inspired from our solutions, a toy model is studied and it is shown that it can describe the Supernova data, while at the same time introduces dark matter components in the Hubble function. When the extra matter source is a stiff fluid then we show how analytical solutions for Bianchi I universes can be constructed from our analysis. Finally, we perform a global dynamical analysis of the field equations by using variables different from that of the Hubble-normalization.

Interactively Open Autonomy Unifies Two Approaches to Function

NASA Astrophysics Data System (ADS)

Collier, John

2004-08-01

Functionality is essential to any form of anticipation beyond simple directedness at an end. In the literature on function in biology, there are two distinct approaches. One, the etiological view, places the origin of function in selection, while the other, the organizational view, individuates function by organizational role. Both approaches have well-known advantages and disadvantages. I propose a reconciliation of the two approaches, based in an interactivist approach to the individuation and stability of organisms. The approach was suggested by Kant in the Critique of Judgment, but since it requires, on his account, the identification a new form of causation, it has not been accessible by analytical techniques. I proceed by construction of the required concept to fit certain design requirements. This construction builds on concepts introduced in my previous four talks to these meetings.

Dimensional transitions in thermodynamic properties of ideal Maxwell-Boltzmann gases

NASA Astrophysics Data System (ADS)

Aydin, Alhun; Sisman, Altug

2015-04-01

An ideal Maxwell-Boltzmann gas confined in various rectangular nanodomains is considered under quantum size effects. Thermodynamic quantities are calculated from their relations with the partition function, which consists of triple infinite summations over momentum states in each direction. To obtain analytical expressions, summations are converted to integrals for macrosystems by a continuum approximation, which fails at the nanoscale. To avoid both the numerical calculation of summations and the failure of their integral approximations at the nanoscale, a method which gives an analytical expression for a single particle partition function (SPPF) is proposed. It is shown that a dimensional transition in momentum space occurs at a certain magnitude of confinement. Therefore, to represent the SPPF by lower-dimensional analytical expressions becomes possible, rather than numerical calculation of summations. Considering rectangular domains with different aspect ratios, a comparison of the results of derived expressions with those of summation forms of the SPPF is made. It is shown that analytical expressions for the SPPF give very precise results with maximum relative errors of around 1%, 2% and 3% at exactly the transition point for single, double and triple transitions, respectively. Based on dimensional transitions, expressions for free energy, entropy, internal energy, chemical potential, heat capacity and pressure are given analytically valid for any scale.

Capillary waveguide optrodes: an approach to optical sensing in medical diagnostics

NASA Astrophysics Data System (ADS)

Lippitsch, Max E.; Draxler, Sonja; Kieslinger, Dietmar; Lehmann, Hartmut; Weigl, Bernhard H.

1996-07-01

Glass capillaries with a chemically sensitive coating on the inner surface are used as optical sensors for medical diagnostics. A capillary simultaneously serves as a sample compartment, a sensor element, and an inhomogeneous optical waveguide. Various detection schemes based on absorption, fluorescence intensity, or fluorescence lifetime are described. In absorption-based capillary waveguide optrodes the absorption in the sensor layer is analyte dependent; hence light transmission along the inhomogeneous waveguiding structure formed by the capillary wall and the sensing layer is a function of the analyte concentration. Similarly, in fluorescence-based capillary optrodes the fluorescence intensity or the fluorescence lifetime of an indicator dye fixed in the sensing layer is analyte dependent; thus the specific property of fluorescent light excited in the sensing layer and thereafter guided along the inhomogeneous waveguiding structure is a function of the analyte concentration. Both schemes are experimentally demonstrated, one with carbon dioxide as the analyte and the other one with oxygen. The device combines optical sensors with the standard glass capillaries usually applied to gather blood drops from fingertips, to yield a versatile diagnostic instrument, integrating the sample compartment, the optical sensor, and the light-collecting optics into a single piece. This ensures enhanced sensor performance as well as improved handling compared with other sensors. waveguide, blood gases, medical diagnostics.

Sinusoidal input describing function for hysteresis followed by elementary backlash

NASA Technical Reports Server (NTRS)

Ringland, R. F.

1976-01-01

The author proposes a new sinusoidal input describing function which accounts for the serial combination of hysteresis followed by elementary backlash in a single nonlinear element. The output of the hysteresis element drives the elementary backlash element. Various analytical forms of the describing function are given, depending on the a/A ratio, where a is the half width of the hysteresis band or backlash gap, and A is the amplitude of the assumed input sinusoid, and on the value of the parameter representing the fraction of a attributed to the backlash characteristic. The negative inverse describing function is plotted on a gain-phase plot, and it is seen that a relatively small amount of backlash leads to domination of the backlash character in the describing function. The extent of the region of the gain-phase plane covered by the describing function is such as to guarantee some form of limit cycle behavior in most closed-loop systems.

Structure Shapes Dynamics and Directionality in Diverse Brain Networks: Mathematical Principles and Empirical Confirmation in Three Species

NASA Astrophysics Data System (ADS)

Moon, Joon-Young; Kim, Junhyeok; Ko, Tae-Wook; Kim, Minkyung; Iturria-Medina, Yasser; Choi, Jee-Hyun; Lee, Joseph; Mashour, George A.; Lee, Uncheol

2017-04-01

Identifying how spatially distributed information becomes integrated in the brain is essential to understanding higher cognitive functions. Previous computational and empirical studies suggest a significant influence of brain network structure on brain network function. However, there have been few analytical approaches to explain the role of network structure in shaping regional activities and directionality patterns. In this study, analytical methods are applied to a coupled oscillator model implemented in inhomogeneous networks. We first derive a mathematical principle that explains the emergence of directionality from the underlying brain network structure. We then apply the analytical methods to the anatomical brain networks of human, macaque, and mouse, successfully predicting simulation and empirical electroencephalographic data. The results demonstrate that the global directionality patterns in resting state brain networks can be predicted solely by their unique network structures. This study forms a foundation for a more comprehensive understanding of how neural information is directed and integrated in complex brain networks.

Practical guidelines for the characterization and quality control of pure drug nanoparticles and nano-cocrystals in the pharmaceutical industry.

PubMed

Peltonen, Leena

2018-06-16

The number of poorly soluble drug candidates is increasing, and this is also seen in the research interest towards drug nanoparticles and (nano-)cocrystals; improved solubility is the most important application of these nanosystems. In order to confirm the functionality of these nanoparticles throughout their lifecycle, repeatability of the formulation processes, functional performance of the formed systems in pre-determined way and system stability, a thorough physicochemical understanding with the aid of necessary analytical techniques is needed. Even very minor deviations in for example particle size or size deviation in nanoscale can alter the product bioavailability, and the effect is even more dramatic with the smallest particle size fractions. Also, small particle size sets special requirements for the analytical techniques. In this review most important physicochemical properties of drug nanocrystals and nano-cocrystals are presented, suitable analytical techniques, their pros and cons, are described with the extra input on practical point of view. Copyright © 2018. Published by Elsevier B.V.

Bivariate extreme value distributions

NASA Technical Reports Server (NTRS)

Elshamy, M.

1992-01-01

In certain engineering applications, such as those occurring in the analyses of ascent structural loads for the Space Transportation System (STS), some of the load variables have a lower bound of zero. Thus, the need for practical models of bivariate extreme value probability distribution functions with lower limits was identified. We discuss the Gumbel models and present practical forms of bivariate extreme probability distributions of Weibull and Frechet types with two parameters. Bivariate extreme value probability distribution functions can be expressed in terms of the marginal extremel distributions and a 'dependence' function subject to certain analytical conditions. Properties of such bivariate extreme distributions, sums and differences of paired extremals, as well as the corresponding forms of conditional distributions, are discussed. Practical estimation techniques are also given.

Dark matter in 3D

DOE PAGES

Alves, Daniele S. M.; El Hedri, Sonia; Wacker, Jay G.

2016-03-21

We discuss the relevance of directional detection experiments in the post-discovery era and propose a method to extract the local dark matter phase space distribution from directional data. The first feature of this method is a parameterization of the dark matter distribution function in terms of integrals of motion, which can be analytically extended to infer properties of the global distribution if certain equilibrium conditions hold. The second feature of our method is a decomposition of the distribution function in moments of a model independent basis, with minimal reliance on the ansatz for its functional form. We illustrate our methodmore » using the Via Lactea II N-body simulation as well as an analytical model for the dark matter halo. Furthermore, we conclude that O(1000) events are necessary to measure deviations from the Standard Halo Model and constrain or measure the presence of anisotropies.« less

Definition and characterization of an extended social-affective default network.

PubMed

Amft, Maren; Bzdok, Danilo; Laird, Angela R; Fox, Peter T; Schilbach, Leonhard; Eickhoff, Simon B

2015-03-01

Recent evidence suggests considerable overlap between the default mode network (DMN) and regions involved in social, affective and introspective processes. We considered these overlapping regions as the social-affective part of the DMN. In this study, we established a robust mapping of the underlying brain network formed by these regions and those strongly connected to them (the extended social-affective default network). We first seeded meta-analytic connectivity modeling and resting-state analyses in the meta-analytically defined DMN regions that showed statistical overlap with regions associated with social and affective processing. Consensus connectivity of each seed was subsequently delineated by a conjunction across both connectivity analyses. We then functionally characterized the ensuing regions and performed several cluster analyses. Among the identified regions, the amygdala/hippocampus formed a cluster associated with emotional processes and memory functions. The ventral striatum, anterior cingulum, subgenual cingulum and ventromedial prefrontal cortex formed a heterogeneous subgroup associated with motivation, reward and cognitive modulation of affect. Posterior cingulum/precuneus and dorsomedial prefrontal cortex were associated with mentalizing, self-reference and autobiographic information. The cluster formed by the temporo-parietal junction and anterior middle temporal sulcus/gyrus was associated with language and social cognition. Taken together, the current work highlights a robustly interconnected network that may be central to introspective, socio-affective, that is, self- and other-related mental processes.

A study of nondiffracting Lommel beams propagating in a medium containing spherical scatterers

NASA Astrophysics Data System (ADS)

Belafhal, A.; Ez-zariy, L.; Hricha, Z.

2016-11-01

By means of the expansion of the nondiffracting beams on plane waves with help of the Whittaker integral, an exact analytical expression of the far-field form function of the scattering of the acoustic and optical nondiffracting Lommel beams propagating in a medium containing spherical particles, considered as rigid and single spheres, is investigated in this work. The form function of the scattering of the high order Bessel beam by a rigid and isolated sphere is deduced, from our finding, as a special case. The effects of the wave number-sphere radius product (ka) , the polar angle (φ) , the propagation half-cone angle (β) and the scattering angle (θ) on the far-field form function of the scattered wave have been analyzed and discussed numerically. The numerical results show that the illumination of a rigid sphere by Lommel beams produces asymmetrical scattering.

Eshelby problem of polygonal inclusions in anisotropic piezoelectric full- and half-planes

NASA Astrophysics Data System (ADS)

Pan, E.

2004-03-01

This paper presents an exact closed-form solution for the Eshelby problem of polygonal inclusion in anisotropic piezoelectric full- and half-planes. Based on the equivalent body-force concept of eigenstrain, the induced elastic and piezoelectric fields are first expressed in terms of line integral on the boundary of the inclusion with the integrand being the Green's function. Using the recently derived exact closed-form line-source Green's function, the line integral is then carried out analytically, with the final expression involving only elementary functions. The exact closed-form solution is applied to a square-shaped quantum wire within semiconductor GaAs full- and half-planes, with results clearly showing the importance of material orientation and piezoelectric coupling. While the elastic and piezoelectric fields within the square-shaped quantum wire could serve as benchmarks to other numerical methods, the exact closed-form solution should be useful to the analysis of nanoscale quantum-wire structures where large strain and electric fields could be induced by the misfit strain.

General method of solving the Schroedinger equation of atoms and molecules

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

Nakatsuji, Hiroshi

2005-12-15

We propose a general method of solving the Schroedinger equation of atoms and molecules. We first construct the wave function having the exact structure, using the ICI (iterative configuration or complement interaction) method and then optimize the variables involved by the variational principle. Based on the scaled Schroedinger equation and related principles, we can avoid the singularity problem of atoms and molecules and formulate a general method of calculating the exact wave functions in an analytical expansion form. We choose initial function {psi}{sub 0} and scaling g function, and then the ICI method automatically generates the wave function that hasmore » the exact structure by using the Hamiltonian of the system. The Hamiltonian contains all the information of the system. The free ICI method provides a flexible and variationally favorable procedure of constructing the exact wave function. We explain the computational procedure of the analytical ICI method routinely performed in our laboratory. Simple examples are given using hydrogen atom for the nuclear singularity case, the Hooke's atom for the electron singularity case, and the helium atom for both cases.« less

Computing the Evans function via solving a linear boundary value ODE

NASA Astrophysics Data System (ADS)

Wahl, Colin; Nguyen, Rose; Ventura, Nathaniel; Barker, Blake; Sandstede, Bjorn

2015-11-01

Determining the stability of traveling wave solutions to partial differential equations can oftentimes be computationally intensive but of great importance to understanding the effects of perturbations on the physical systems (chemical reactions, hydrodynamics, etc.) they model. For waves in one spatial dimension, one may linearize around the wave and form an Evans function - an analytic Wronskian-like function which has zeros that correspond in multiplicity to the eigenvalues of the linearized system. If eigenvalues with a positive real part do not exist, the traveling wave will be stable. Two methods exist for calculating the Evans function numerically: the exterior-product method and the method of continuous orthogonalization. The first is numerically expensive, and the second reformulates the originally linear system as a nonlinear system. We develop a new algorithm for computing the Evans function through appropriate linear boundary-value problems. This algorithm is cheaper than the previous methods, and we prove that it preserves analyticity of the Evans function. We also provide error estimates and implement it on some classical one- and two-dimensional systems, one being the Swift-Hohenberg equation in a channel, to show the advantages.

A strategy for reducing gross errors in the generalized Born models of implicit solvation

PubMed Central

Onufriev, Alexey V.; Sigalov, Grigori

2011-01-01

The “canonical” generalized Born (GB) formula [C. Still, A. Tempczyk, R. C. Hawley, and T. Hendrickson, J. Am. Chem. Soc. 112, 6127 (1990)] is known to provide accurate estimates for total electrostatic solvation energies ΔGel of biomolecules if the corresponding effective Born radii are accurate. Here we show that even if the effective Born radii are perfectly accurate, the canonical formula still exhibits significant number of gross errors (errors larger than 2kBT relative to numerical Poisson equation reference) in pairwise interactions between individual atomic charges. Analysis of exact analytical solutions of the Poisson equation (PE) for several idealized nonspherical geometries reveals two distinct spatial modes of the PE solution; these modes are also found in realistic biomolecular shapes. The canonical GB Green function misses one of two modes seen in the exact PE solution, which explains the observed gross errors. To address the problem and reduce gross errors of the GB formalism, we have used exact PE solutions for idealized nonspherical geometries to suggest an alternative analytical Green function to replace the canonical GB formula. The proposed functional form is mathematically nearly as simple as the original, but depends not only on the effective Born radii but also on their gradients, which allows for better representation of details of nonspherical molecular shapes. In particular, the proposed functional form captures both modes of the PE solution seen in nonspherical geometries. Tests on realistic biomolecular structures ranging from small peptides to medium size proteins show that the proposed functional form reduces gross pairwise errors in all cases, with the amount of reduction varying from more than an order of magnitude for small structures to a factor of 2 for the largest ones. PMID:21528947

Who do we think we are? Analysing the content and form of identity work in the English National Health Service.

PubMed

McDermott, Imelda; Checkland, Kath; Harrison, Stephen; Snow, Stephanie; Coleman, Anna

2013-01-01

The language used by National Health Service (NHS) "commissioning" managers when discussing their roles and responsibilities can be seen as a manifestation of "identity work", defined as a process of identifying. This paper aims to offer a novel approach to analysing "identity work" by triangulation of multiple analytical methods, combining analysis of the content of text with analysis of its form. Fairclough's discourse analytic methodology is used as a framework. Following Fairclough, the authors use analytical methods associated with Halliday's systemic functional linguistics. While analysis of the content of interviews provides some information about NHS Commissioners' perceptions of their roles and responsibilities, analysis of the form of discourse that they use provides a more detailed and nuanced view. Overall, the authors found that commissioning managers have a higher level of certainty about what commissioning is not rather than what commissioning is; GP managers have a high level of certainty of their identity as a GP rather than as a manager; and both GP managers and non-GP managers oscillate between multiple identities depending on the different situations they are in. This paper offers a novel approach to triangulation, based not on the usual comparison of multiple data sources, but rather based on the application of multiple analytical methods to a single source of data. This paper also shows the latent uncertainty about the nature of commissioning enterprise in the English NHS.

Detection of VX Simulants Using Piezoresistive Microcantilever Sensors

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

Porter, Timothy L.; Venedam, Richard J.; Kyle, Kyle

2011-05-28

Piezoresistive microcantilever sensors may be used in a variety of sensing applications, including chemical analytes and some types of biological species. These sensors employ a tiny piezoresistive microcantilever functionalized with a “sensing material” that acts as a probe for the desired analyte. In this study, the microcantilever was partially embedded into the sensing material, producing a sensor element that is highly rigid and resistant to shock, making it suitable for portable or handheld operation. The sensing material matrix used was Hypol, a hydrogel capable of preserving the bio-functionality of molecules embedded into it. This matrix was combined with acetylcholinesterase tomore » form the finished sensing material. Results of exposing these sensors to a VX simulant, malathion, are presented for both vapor and liquid environments.« less

A result on quasi-periodic solutions of a nonlinear beam equation with a quasi-periodic forcing term

NASA Astrophysics Data System (ADS)

Wang, Yi; Si, Jianguo

2012-02-01

In this paper, a quasi-periodically forced nonlinear beam equation {u_{tt}+u_{xxxx}+μ u+\\varepsilonφ(t)h(u)=0} with hinged boundary conditions is considered, where μ > 0, {\\varepsilon} is a small positive parameter, {φ} is a real analytic quasi-periodic function in t with a frequency vector ω = ( ω 1, ω 2 . . . , ω m ), and the nonlinearity h is a real analytic odd function of the form {h(u)=η_1u+η_{2bar{r}+1}u^{2bar{r}+1}+sum_{k≥ bar{r}+1}η_{2k+1}u^{2k+1},η_1,η_{2bar{r}+1} neq0, bar{r} in {mathbb {N}}.} The above equation admits a quasi-periodic solution.

Universal binding energy relation for cleaved and structurally relaxed surfaces.

PubMed

Srirangarajan, Aarti; Datta, Aditi; Gandi, Appala Naidu; Ramamurty, U; Waghmare, U V

2014-02-05

The universal binding energy relation (UBER), derived earlier to describe the cohesion between two rigid atomic planes, does not accurately capture the cohesive properties when the cleaved surfaces are allowed to relax. We suggest a modified functional form of UBER that is analytical and at the same time accurately models the properties of surfaces relaxed during cleavage. We demonstrate the generality as well as the validity of this modified UBER through first-principles density functional theory calculations of cleavage in a number of crystal systems. Our results show that the total energies of all the relaxed surfaces lie on a single (universal) energy surface, that is given by the proposed functional form which contains an additional length-scale associated with structural relaxation. This functional form could be used in modelling the cohesive zones in crack growth simulation studies. We find that the cohesive law (stress-displacement relation) differs significantly in the case where cracked surfaces are allowed to relax, with lower peak stresses occurring at higher displacements.

A closed-form solution for steady-state coupled phloem/xylem flow using the Lambert-W function.

PubMed

Hall, A J; Minchin, P E H

2013-12-01

A closed-form solution for steady-state coupled phloem/xylem flow is presented. This incorporates the basic Münch flow model of phloem transport, the cohesion model of xylem flow, and local variation in the xylem water potential and lateral water flow along the transport pathway. Use of the Lambert-W function allows this solution to be obtained under much more general and realistic conditions than has previously been possible. Variation in phloem resistance (i.e. viscosity) with solute concentration, and deviations from the Van't Hoff expression for osmotic potential are included. It is shown that the model predictions match those of the equilibrium solution of a numerical time-dependent model based upon the same mechanistic assumptions. The effect of xylem flow upon phloem flow can readily be calculated, which has not been possible in any previous analytical model. It is also shown how this new analytical solution can handle multiple sources and sinks within a complex architecture, and can describe competition between sinks. The model provides new insights into Münch flow by explicitly including interactions with xylem flow and water potential in the closed-form solution, and is expected to be useful as a component part of larger numerical models of entire plants. © 2013 John Wiley & Sons Ltd.

Bogoliubov theory of acoustic Hawking radiation in Bose-Einstein condensates

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

Recati, A.; Physik-Department, Technische Universitaet Muenchen, D-85748 Garching; Pavloff, N.

2009-10-15

We apply the microscopic Bogoliubov theory of dilute Bose-Einstein condensates to analyze quantum and thermal fluctuations in a flowing atomic condensate in the presence of a sonic horizon. For the simplest case of a step-like horizon, closed-form analytical expressions are found for the spectral distribution of the analog Hawking radiation and for the density correlation function. The peculiar long-distance density correlations that appear as a consequence of the Hawking emission features turns out to be reinforced by a finite initial temperature of the condensate. The analytical results are in good quantitative agreement with first principle numerical calculations.

Analysis of dual coupler nested coupled cavities.

PubMed

Adib, George A; Sabry, Yasser M; Khalil, Diaa

2017-12-01

Coupled ring resonators are now forming the basic building blocks in several optical systems serving different applications. In many of these applications, a small full width at half maximum is required, along with a large free spectral range. In this work, a configuration of passive coupled cavities constituting dual coupler nested cavities is proposed. A theoretical study of the configuration is presented allowing us to obtain analytical expressions of its different spectral characteristics. The transfer function of the configuration is also used to generate design curves while comparing these results with analytical expressions. Finally, the configuration is compared with other coupled cavity configurations.

Solar radiation - to - power generation models for one-axis tracking PV system with on-site measurements from Eskisehir, Turkey

NASA Astrophysics Data System (ADS)

Filik, Tansu; Başaran Filik, Ümmühan; Nezih Gerek, Ömer

2017-11-01

In this study, new analytic models are proposed for mapping on-site global solar radiation values to electrical power output values in solar photovoltaic (PV) panels. The model extraction is achieved by simultaneously recording solar radiation and generated power from fixed and tracking panels, each with capacity of 3 kW, in Eskisehir (Turkey) region. It is shown that the relation between the solar radiation and the corresponding electric power is not only nonlinear, but it also exhibits an interesting time-varying characteristic in the form of a hysteresis function. This observed radiation-to-power relation is, then, analytically modelled with three piece-wise function parts (corresponding to morning, noon and evening times), which is another novel contribution of this work. The model is determined for both fixed panels and panels with a tracking system. Especially the panel system with a dynamic tracker produces a harmonically richer (with higher values in general) characteristic, so higher order polynomial models are necessary for the construction of analytical solar radiation models. The presented models, characteristics of the hysteresis functions, and differences in the fixed versus solar-tracking panels are expected to provide valuable insight for further model based researches.

Random matrix theory of singular values of rectangular complex matrices I: Exact formula of one-body distribution function in fixed-trace ensemble

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

Adachi, Satoshi; Toda, Mikito; Kubotani, Hiroto

The fixed-trace ensemble of random complex matrices is the fundamental model that excellently describes the entanglement in the quantum states realized in a coupled system by its strongly chaotic dynamical evolution [see H. Kubotani, S. Adachi, M. Toda, Phys. Rev. Lett. 100 (2008) 240501]. The fixed-trace ensemble fully takes into account the conservation of probability for quantum states. The present paper derives for the first time the exact analytical formula of the one-body distribution function of singular values of random complex matrices in the fixed-trace ensemble. The distribution function of singular values (i.e. Schmidt eigenvalues) of a quantum state ismore » so important since it describes characteristics of the entanglement in the state. The derivation of the exact analytical formula utilizes two recent achievements in mathematics, which appeared in 1990s. The first is the Kaneko theory that extends the famous Selberg integral by inserting a hypergeometric type weight factor into the integrand to obtain an analytical formula for the extended integral. The second is the Petkovsek-Wilf-Zeilberger theory that calculates definite hypergeometric sums in a closed form.« less

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.

Asymptotic co- and post-seismic displacements in a homogeneous Maxwell sphere

NASA Astrophysics Data System (ADS)

Tang, He; Sun, Wenke

2018-07-01

The deformations of the Earth caused by internal and external forces are usually expressed through Green's functions or the superposition of normal modes, that is, via numerical methods, which are applicable for computing both co- and post-seismic deformations. It is difficult to express these deformations in an analytical form, even for a uniform viscoelastic sphere. In this study, we present a set of asymptotic solutions for computing co- and post-seismic displacements; these solutions can be further applied to solving co- and post-seismic geoid, gravity and strain changes. Expressions are derived for a uniform Maxwell Earth by combining the reciprocity theorem, which links earthquake, tidal, shear and loading deformations, with the asymptotic solutions of these three external forces (tidal, shear and loading) and analytical inverse Laplace transformation formulae. Since the asymptotic solutions are given in a purely analytical form without series summations or extra convergence skills, they can be practically applied in an efficient way, especially when computing post-seismic deformations and glacial isotactic adjustments of the Earth over long timescales.

Asymptotic Co- and Post-seismic displacements in a homogeneous Maxwell sphere

NASA Astrophysics Data System (ADS)

Tang, He; Sun, Wenke

2018-05-01

The deformations of the Earth caused by internal and external forces are usually expressed through Green's functions or the superposition of normal modes, i.e. via numerical methods, which are applicable for computing both co- and post-seismic deformations. It is difficult to express these deformations in an analytical form, even for a uniform viscoelastic sphere. In this study, we present a set of asymptotic solutions for computing co- and post-seismic displacements; these solutions can be further applied to solving co- and post-seismic geoid, gravity, and strain changes. Expressions are derived for a uniform Maxwell Earth by combining the reciprocity theorem, which links earthquake, tidal, shear and loading deformations, with the asymptotic solutions of these three external forces (tidal, shear and loading) and analytical inverse Laplace transformation formulae. Since the asymptotic solutions are given in a purely analytical form without series summations or extra convergence skills, they can be practically applied in an efficient way, especially when computing post-seismic deformations and glacial isotactic adjustments of the Earth over long timescales.

Magnetohydrodynamic viscous flow over a nonlinearly moving surface: Closed-form solutions

NASA Astrophysics Data System (ADS)

Fang, Tiegang

2014-05-01

In this paper, the magnetohydrodynamic (MHD) flow over a nonlinearly (power-law velocity) moving surface is investigated analytically and solutions are presented for a few special conditions. The solutions are obtained in closed forms with hyperbolic functions. The effects of the magnetic, the wall moving, and the mass transpiration parameters are discussed. These solutions are important to show the flow physics as well as to be used as bench mark problems for numerical validation and development of new solution schemes.

Linear modeling of steady-state behavioral dynamics.

PubMed Central

Palya, William L; Walter, Donald; Kessel, Robert; Lucke, Robert

2002-01-01

The observed steady-state behavioral dynamics supported by unsignaled periods of reinforcement within repeating 2,000-s trials were modeled with a linear transfer function. These experiments employed improved schedule forms and analytical methods to improve the precision of the measured transfer function, compared to previous work. The refinements include both the use of multiple reinforcement periods that improve spectral coverage and averaging of independently determined transfer functions. A linear analysis was then used to predict behavior observed for three different test schedules. The fidelity of these predictions was determined. PMID:11831782

The Laughlin liquid in an external potential

NASA Astrophysics Data System (ADS)

Rougerie, Nicolas; Yngvason, Jakob

2018-04-01

We study natural perturbations of the Laughlin state arising from the effects of trapping and disorder. These are N-particle wave functions that have the form of a product of Laughlin states and analytic functions of the N variables. We derive an upper bound to the ground state energy in a confining external potential, matching exactly a recently derived lower bound in the large N limit. Irrespective of the shape of the confining potential, this sharp upper bound can be achieved through a modification of the Laughlin function by suitably arranged quasi-holes.

Evaluation of geopotential and luni-solar perturbations by a recursive algorithm

NASA Technical Reports Server (NTRS)

Giacaglia, G. E. O.

1975-01-01

The disturbing functions due to the geopotential and Luni-solar attractions are linear and bilinear forms in spherical harmonics. Making use of recurrence relations for the solid spherical harmonics and their derivatives, recurrence formulas are obtained for high degree terms as function of lower degree for any term of those disturbing functions and their derivative with respect to any element. The equations obtained are effective when a numerical integration of the equations of motion is appropriate. In analytical theories, they provide a fast way of obtaining high degree terms starting from initial very simple functions.

Analytic integrable systems: Analytic normalization and embedding flows

NASA Astrophysics Data System (ADS)

Zhang, Xiang

In this paper we mainly study the existence of analytic normalization and the normal form of finite dimensional complete analytic integrable dynamical systems. More details, we will prove that any complete analytic integrable diffeomorphism F(x)=Bx+f(x) in (Cn,0) with B having eigenvalues not modulus 1 and f(x)=O(|) is locally analytically conjugate to its normal form. Meanwhile, we also prove that any complete analytic integrable differential system x˙=Ax+f(x) in (Cn,0) with A having nonzero eigenvalues and f(x)=O(|) is locally analytically conjugate to its normal form. Furthermore we will prove that any complete analytic integrable diffeomorphism defined on an analytic manifold can be embedded in a complete analytic integrable flow. We note that parts of our results are the improvement of Moser's one in J. Moser, The analytic invariants of an area-preserving mapping near a hyperbolic fixed point, Comm. Pure Appl. Math. 9 (1956) 673-692 and of Poincaré's one in H. Poincaré, Sur l'intégration des équations différentielles du premier order et du premier degré, II, Rend. Circ. Mat. Palermo 11 (1897) 193-239. These results also improve the ones in Xiang Zhang, Analytic normalization of analytic integrable systems and the embedding flows, J. Differential Equations 244 (2008) 1080-1092 in the sense that the linear part of the systems can be nonhyperbolic, and the one in N.T. Zung, Convergence versus integrability in Poincaré-Dulac normal form, Math. Res. Lett. 9 (2002) 217-228 in the way that our paper presents the concrete expression of the normal form in a restricted case.

ATMOSPHERIC CHEMISTRY FOR ASTROPHYSICISTS: A SELF-CONSISTENT FORMALISM AND ANALYTICAL SOLUTIONS FOR ARBITRARY C/O

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

Heng, Kevin; Tsai, Shang-Min; Lyons, James R., E-mail: kevin.heng@csh.unibe.ch

2016-01-10

We present a self-consistent formalism for computing and understanding the atmospheric chemistry of exoplanets from the viewpoint of an astrophysicist. Starting from the first law of thermodynamics, we demonstrate that the van’t Hoff equation (which describes the equilibrium constant), Arrhenius equation (which describes the rate coefficients), and procedures associated with the Gibbs free energy (minimization, rescaling) have a common physical and mathematical origin. We address an ambiguity associated with the equilibrium constant, which is used to relate the forward and reverse rate coefficients, and restate its two definitions. By necessity, one of the equilibrium constants must be dimensionless and equatemore » to an exponential function involving the Gibbs free energy, while the other is a ratio of rate coefficients and must therefore possess physical units. We demonstrate that the Arrhenius equation takes on a functional form that is more general than previously stated without recourse to tagging on ad hoc functional forms. Finally, we derive analytical models of chemical systems, in equilibrium, with carbon, hydrogen, and oxygen. We include acetylene and are able to reproduce several key trends, versus temperature and carbon-to-oxygen ratio, published in the literature. The rich variety of behavior that mixing ratios exhibit as a function of the carbon-to-oxygen ratio is merely the outcome of stoichiometric book-keeping and not the direct consequence of temperature or pressure variations.« less

Atmospheric Chemistry for Astrophysicists: A Self-consistent Formalism and Analytical Solutions for Arbitrary C/O

NASA Astrophysics Data System (ADS)

Heng, Kevin; Lyons, James R.; Tsai, Shang-Min

2016-01-01

We present a self-consistent formalism for computing and understanding the atmospheric chemistry of exoplanets from the viewpoint of an astrophysicist. Starting from the first law of thermodynamics, we demonstrate that the van’t Hoff equation (which describes the equilibrium constant), Arrhenius equation (which describes the rate coefficients), and procedures associated with the Gibbs free energy (minimization, rescaling) have a common physical and mathematical origin. We address an ambiguity associated with the equilibrium constant, which is used to relate the forward and reverse rate coefficients, and restate its two definitions. By necessity, one of the equilibrium constants must be dimensionless and equate to an exponential function involving the Gibbs free energy, while the other is a ratio of rate coefficients and must therefore possess physical units. We demonstrate that the Arrhenius equation takes on a functional form that is more general than previously stated without recourse to tagging on ad hoc functional forms. Finally, we derive analytical models of chemical systems, in equilibrium, with carbon, hydrogen, and oxygen. We include acetylene and are able to reproduce several key trends, versus temperature and carbon-to-oxygen ratio, published in the literature. The rich variety of behavior that mixing ratios exhibit as a function of the carbon-to-oxygen ratio is merely the outcome of stoichiometric book-keeping and not the direct consequence of temperature or pressure variations.

Analytical model for the radio-frequency sheath

NASA Astrophysics Data System (ADS)

Czarnetzki, Uwe

2013-12-01

A simple analytical model for the planar radio-frequency (rf) sheath in capacitive discharges is developed that is based on the assumptions of a step profile for the electron front, charge exchange collisions with constant cross sections, negligible ionization within the sheath, and negligible ion dynamics. The continuity, momentum conservation, and Poisson equations are combined in a single integro-differential equation for the square of the ion drift velocity, the so called sheath equation. Starting from the kinetic Boltzmann equation, special attention is paid to the derivation and the validity of the approximate fluid equation for momentum balance. The integrals in the sheath equation appear in the screening function which considers the relative contribution of the temporal mean of the electron density to the space charge in the sheath. It is shown that the screening function is quite insensitive to variations of the effective sheath parameters. The two parameters defining the solution are the ratios of the maximum sheath extension to the ion mean free path and the Debye length, respectively. A simple general analytic expression for the screening function is introduced. By means of this expression approximate analytical solutions are obtained for the collisionless as well as the highly collisional case that compare well with the exact numerical solution. A simple transition formula allows application to all degrees of collisionality. In addition, the solutions are used to calculate all static and dynamic quantities of the sheath, e.g., the ion density, fields, and currents. Further, the rf Child-Langmuir laws for the collisionless as well as the collisional case are derived. An essential part of the model is the a priori knowledge of the wave form of the sheath voltage. This wave form is derived on the basis of a cubic charge-voltage relation for individual sheaths, considering both sheaths and the self-consistent self-bias in a discharge with arbitrary symmetry. The externally applied rf voltage is assumed to be sinusoidal, although the model can be extended to arbitrary wave forms, e.g., for dual-frequency discharges. The model calculates explicitly the cubic correction parameter in the charge-voltage relation for the case of highly asymmetric discharges. It is shown that the cubic correction is generally moderate but more pronounced in the collisionless case. The analytical results are compared to experimental data from the literature obtained by laser electric field measurements of the mean and dynamic fields in the capacitive sheath for various gases and pressures. Very good agreement is found throughout.

Analytical model for the radio-frequency sheath.

PubMed

Czarnetzki, Uwe

2013-12-01

A simple analytical model for the planar radio-frequency (rf) sheath in capacitive discharges is developed that is based on the assumptions of a step profile for the electron front, charge exchange collisions with constant cross sections, negligible ionization within the sheath, and negligible ion dynamics. The continuity, momentum conservation, and Poisson equations are combined in a single integro-differential equation for the square of the ion drift velocity, the so called sheath equation. Starting from the kinetic Boltzmann equation, special attention is paid to the derivation and the validity of the approximate fluid equation for momentum balance. The integrals in the sheath equation appear in the screening function which considers the relative contribution of the temporal mean of the electron density to the space charge in the sheath. It is shown that the screening function is quite insensitive to variations of the effective sheath parameters. The two parameters defining the solution are the ratios of the maximum sheath extension to the ion mean free path and the Debye length, respectively. A simple general analytic expression for the screening function is introduced. By means of this expression approximate analytical solutions are obtained for the collisionless as well as the highly collisional case that compare well with the exact numerical solution. A simple transition formula allows application to all degrees of collisionality. In addition, the solutions are used to calculate all static and dynamic quantities of the sheath, e.g., the ion density, fields, and currents. Further, the rf Child-Langmuir laws for the collisionless as well as the collisional case are derived. An essential part of the model is the a priori knowledge of the wave form of the sheath voltage. This wave form is derived on the basis of a cubic charge-voltage relation for individual sheaths, considering both sheaths and the self-consistent self-bias in a discharge with arbitrary symmetry. The externally applied rf voltage is assumed to be sinusoidal, although the model can be extended to arbitrary wave forms, e.g., for dual-frequency discharges. The model calculates explicitly the cubic correction parameter in the charge-voltage relation for the case of highly asymmetric discharges. It is shown that the cubic correction is generally moderate but more pronounced in the collisionless case. The analytical results are compared to experimental data from the literature obtained by laser electric field measurements of the mean and dynamic fields in the capacitive sheath for various gases and pressures. Very good agreement is found throughout.

Lattice QCD and the timelike pion form factor.

PubMed

Meyer, Harvey B

2011-08-12

We present a formula that allows one to calculate the pion form factor in the timelike region 2m(π) ≤ √(s) ≤ 4m(π) in lattice QCD. The form factor quantifies the contribution of two-pion states to the vacuum polarization. It must be known very accurately in order to reduce the theoretical uncertainty on the anomalous magnetic moment of the muon. At the same time, the formula constitutes a rare example where, in a restricted kinematic regime, the spectral function of a conserved current can be determined from Euclidean observables without an explicit analytic continuation.

Derivation of a closed form analytical expression for fluorescence recovery after photo bleaching in the case of continuous bleaching during read out

NASA Astrophysics Data System (ADS)

Endress, E.; Weigelt, S.; Reents, G.; Bayerl, T. M.

2005-01-01

Measurements of very slow diffusive processes in membranes, like the diffusion of integral membrane proteins, by fluorescence recovery after photo bleaching (FRAP) are hampered by bleaching of the probe during the read out of the fluorescence recovery. In the limit of long observation time (very slow diffusion as in the case of large membrane proteins), this bleaching may cause errors to the recovery function and thus provides error-prone diffusion coefficients. In this work we present a new approach to a two-dimensional closed form analytical solution of the reaction-diffusion equation, based on the addition of a dissipative term to the conventional diffusion equation. The calculation was done assuming (i) a Gaussian laser beam profile for bleaching the spot and (ii) that the fluorescence intensity profile emerging from the spot can be approximated by a two-dimensional Gaussian. The detection scheme derived from the analytical solution allows for diffusion measurements without the constraint of observation bleaching. Recovery curves of experimental FRAP data obtained under non-negligible read-out bleaching for native membranes (rabbit endoplasmic reticulum) on a planar solid support showed excellent agreement with the analytical solution and allowed the calculation of the lipid diffusion coefficient.

Periodontal Ligament Entheses and their Adaptive Role in the Context of Dentoalveolar Joint Function

PubMed Central

Lin, Jeremy D.; Jang, Andrew T.; Kurylo, Michael P.; Hurng, Jonathan; Yang, Feifei; Yang, Lynn; Pal, Arvin; Chen, Ling; Ho, Sunita P.

2017-01-01

Objectives The dynamic bone-periodontal ligament (PDL)-tooth fibrous joint consists of two adaptive functionally graded interfaces (FGI), the PDL-bone and PDL-cementum that respond to mechanical strain transmitted during mastication. In general, from a materials and mechanics perspective, FGI prevent catastrophic failure during prolonged cyclic loading. This review is a discourse of results gathered from literature to illustrate the dynamic adaptive nature of the fibrous joint in response to physiologic and pathologic simulated functions, and experimental tooth movement. Methods Historically, studies have investigated soft to hard tissue transitions through analytical techniques that provided insights into structural, biochemical, and mechanical characterization methods. Experimental approaches included two dimensional to three dimensional advanced in situ imaging and analytical techniques. These techniques allowed mapping and correlation of deformations to physicochemical and mechanobiological changes within volumes of the complex subjected to concentric and eccentric loading regimes respectively. Results Tooth movement is facilitated by mechanobiological activity at the interfaces of the fibrous joint and generates elastic discontinuities at these interfaces in response to eccentric loading. Both concentric and eccentric loads mediated cellular responses to strains, and prompted self-regulating mineral forming and resorbing zones that in turn altered the functional space of the joint. Significance A multiscale biomechanics and mechanobiology approach is important for correlating joint function to tissue-level strain-adaptive properties with overall effects on joint form as related to physiologic and pathologic functions. Elucidating the shift in localization of biomolecules specifically at interfaces during development, function, and therapeutic loading of the joint is critical for developing “functional regeneration and adaptation” strategies with an emphasis on restoring physiologic joint function. PMID:28476202

Analytically derived switching functions for exact H2+ eigenstates

NASA Astrophysics Data System (ADS)

Thorson, W. R.; Kimura, M.; Choi, J. H.; Knudson, S. K.

1981-10-01

Electron translation factors (ETF's) appropriate for slow atomic collisions may be constructed using switching functions. In this paper we derive a set of switching functions for the H2+ system by an analytical "two-center decomposition" of the exact molecular eigenstates. These switching functions are closely approximated by the simple form f=bη, where η is the "angle variable" of prolate spheroidal coordinates. For given united atom angular momentum quantum numbers (l,m), the characteristic parameter blm depends only on the quantity c2=-ɛR22, where ɛ is the electronic binding energy and R the internuclear distance in a.u. The resulting parameters are in excellent agreement with those found in our earlier work by a heuristic "optimization" scheme based on a study of coupling matrix-element behavior for a number of H2+ states. An approximate extension to asymmetric cases (HeH2+) has also been made. Nonadiabatic couplings based on these switching functions have been used in recent close-coupling calculations for H+-H(1s) collisions and He2+-H(1s) collisions at energies 1.0-20 keV.

Temperature field determination in slabs, circular plates and spheres with saw tooth heat generating sources

NASA Astrophysics Data System (ADS)

Diestra Cruz, Heberth Alexander

The Green's functions integral technique is used to determine the conduction heat transfer temperature field in flat plates, circular plates, and solid spheres with saw tooth heat generating sources. In all cases the boundary temperature is specified (Dirichlet's condition) and the thermal conductivity is constant. The method of images is used to find the Green's function in infinite solids, semi-infinite solids, infinite quadrants, circular plates, and solid spheres. The saw tooth heat generation source has been modeled using Dirac delta function and Heaviside step function. The use of Green's functions allows obtain the temperature distribution in the form of an integral that avoids the convergence problems of infinite series. For the infinite solid and the sphere, the temperature distribution is three-dimensional and in the cases of semi-infinite solid, infinite quadrant and circular plate the distribution is two-dimensional. The method used in this work is superior to other methods because it obtains elegant analytical or quasi-analytical solutions to complex heat conduction problems with less computational effort and more accuracy than the use of fully numerical methods.

Analytical formulation of impulsive collision avoidance dynamics

NASA Astrophysics Data System (ADS)

Bombardelli, Claudio

2014-02-01

The paper deals with the problem of impulsive collision avoidance between two colliding objects in three dimensions and assuming elliptical Keplerian orbits. Closed-form analytical expressions are provided that accurately predict the relative dynamics of the two bodies in the encounter b-plane following an impulsive delta-V manoeuvre performed by one object at a given orbit location prior to the impact and with a generic three-dimensional orientation. After verifying the accuracy of the analytical expressions for different orbital eccentricities and encounter geometries the manoeuvre direction that maximises the miss distance is obtained numerically as a function of the arc length separation between the manoeuvre point and the predicted collision point. The provided formulas can be used for high-accuracy instantaneous estimation of the outcome of a generic impulsive collision avoidance manoeuvre and its optimisation.

Evaluation of cluster expansions and correlated one-body properties of nuclei

NASA Astrophysics Data System (ADS)

Moustakidis, Ch. C.; Massen, S. E.; Panos, C. P.; Grypeos, M. E.; Antonov, A. N.

2001-07-01

Three different cluster expansions for the evaluation of correlated one-body properties of s-p and s-d shell nuclei are compared. Harmonic oscillator wave functions and Jastrow-type correlations are used, while analytical expressions are obtained for the charge form factor, density distribution, and momentum distribution by truncating the expansions and using a standard Jastrow correlation function f. The harmonic oscillator parameter b and the correlation parameter β have been determined by a least-squares fit to the experimental charge form factors in each case. The information entropy of nuclei in position space (Sr) and momentum space (Sk) according to the three methods are also calculated. It is found that the larger the entropy sum, S=Sr+Sk (the net information content of the system), the smaller the values of χ2. This indicates that maximal S is a criterion of the quality of a given nuclear model, according to the maximum entropy principle. Only two exceptions to this rule, out of many cases examined, were found. Finally an analytic expression for the so-called ``healing'' or ``wound'' integrals is derived with the function f considered, for any state of the relative two-nucleon motion, and their values in certain cases are computed and compared.

Numerically stable formulas for a particle-based explicit exponential integrator

NASA Astrophysics Data System (ADS)

Nadukandi, Prashanth

2015-05-01

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

Sensing based on surface-enhanced Raman scattering using self-forming ZnO nanoarrays coated with gold as substrates

NASA Astrophysics Data System (ADS)

Tang, Feng; Adam, Pierre-Michel; Rogers, David J.; Sandana, Vinod E.; Bove, Philippe; Teherani, Ferechteh H.

2018-03-01

Surface-Enhanced Raman spectroscopy (SERS) is a widely used technique adopted in both academia and industry for the detection of trace quantities of Raman active molecules. This is usually accomplished by functionalizing distributions of plasmonic metal nanoparticles with the analyte molecules. Recently metal-coated nanostructures have been investigated as alternatives to dispersions of metal nanoparticles in order to avoid clustering and homogeneity/reproducibility issues. In this paper, several samples of Au-coated ZnO nanoarrays are adopted as SERS substrates in order to investigate the molecular sensing capacity for methylene blue (MB) molecules. Self-forming ZnO nanoarrays were grown on both c-sapphire and silicon substrates by pulsed laser deposition. The nanoarrays were then coated with 30 nm of gold using thermal evaporation and the SERS signals of MB functionalized samples were obtained with a Raman microspectrometer. The ratio of SERS intensity to that of an MB functionalized glass substrate (ISERS/IRaman) was calculated based on the averaged SERS signals. A relatively good within-wafer homogeneity of the enhancement effect was found with ISERS/IRaman values as high as 64.2 for Au-coated nano ZnO grown on silicon substrates. The experimental results show that the Au-coated ZnO nanoarrays can be excellent SERS substrates for molecular/chemical analyte sensing.

Ion/Ion Reactions with "Onium" Reagents: An Approach for the Gas-phase Transfer of Organic Cations to Multiply-Charged Anions

NASA Astrophysics Data System (ADS)

Gilbert, Joshua D.; Prentice, Boone M.; McLuckey, Scott A.

2015-05-01

The use of ion/ion reactions to effect gas-phase alkylation is demonstrated. Commonly used fixed-charge "onium" cations are well-suited for ion/ion reactions with multiply deprotonated analytes because of their tendency to form long-lived electrostatic complexes. Activation of these complexes results in an SN2 reaction that yields an alkylated anion with the loss of a neutral remnant of the reagent. This alkylation process forms the basis of a general method for alkylation of deprotonated analytes generated via electrospray, and is demonstrated on a variety of anionic sites. SN2 reactions of this nature are demonstrated empirically and characterized using density functional theory (DFT). This method for modification in the gas phase is extended to the transfer of larger and more complex R groups that can be used in later gas-phase synthesis steps. For example, N-cyclohexyl- N'-(2-morpholinoethyl)carbodiimide (CMC) is used to transfer a carbodiimide functionality to a peptide anion containing a carboxylic acid. Subsequent activation yields a selective reaction between the transferred carbodiimide group and a carboxylic acid, suggesting the carbodiimide functionality is retained through the transfer process. Many different R groups are transferable using this method, allowing for new possibilities for charge manipulation and derivatization in the gas phase.

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

NASA Astrophysics Data System (ADS)

Lau, Chun Sing

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

Nonlinear Schroedinger Approximations for Partial Differential Equations with Quadratic and Quasilinear Terms

NASA Astrophysics Data System (ADS)

Cummings, Patrick

We consider the approximation of solutions of two complicated, physical systems via the nonlinear Schrodinger equation (NLS). In particular, we discuss the evolution of wave packets and long waves in two physical models. Due to the complicated nature of the equations governing many physical systems and the in-depth knowledge we have for solutions of the nonlinear Schrodinger equation, it is advantageous to use approximation results of this kind to model these physical systems. The approximations are simple enough that we can use them to understand the qualitative and quantitative behavior of the solutions, and by justifying them we can show that the behavior of the approximation captures the behavior of solutions to the original equation, at least for long, but finite time. We first consider a model of the water wave equations which can be approximated by wave packets using the NLS equation. We discuss a new proof that both simplifies and strengthens previous justification results of Schneider and Wayne. Rather than using analytic norms, as was done by Schneider and Wayne, we construct a modified energy functional so that the approximation holds for the full interval of existence of the approximate NLS solution as opposed to a subinterval (as is seen in the analytic case). Furthermore, the proof avoids problems associated with inverting the normal form transform by working with a modified energy functional motivated by Craig and Hunter et al. We then consider the Klein-Gordon-Zakharov system and prove a long wave approximation result. In this case there is a non-trivial resonance that cannot be eliminated via a normal form transform. By combining the normal form transform for small Fourier modes and using analytic norms elsewhere, we can get a justification result on the order 1 over epsilon squared time scale.

Analytic solution of the Spencer-Lewis angular-spatial moments equations

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

Filippone, W.L.

A closed-form solution for the angular-spatial moments of the Spencer-Lewis equation is presented that is valid for infinite homogeneous media. From the moments, the electron density distribution as a function of position and path length (energy) is reconstructed for several sample problems involving plane isotropic sources of electrons in aluminium. The results are in excellent agreement with those determined numerically using the streaming ray method. The primary use of the closed form solution will most likely be to generate accurate electron transport benchmark solutions. In principle, the electron density as a function of space, path length, and direction can bemore » determined for planar sources of arbitrary angular distribution.« less

Theory for solubility in static systems

NASA Astrophysics Data System (ADS)

Gusev, Andrei A.; Suter, Ulrich W.

1991-06-01

A theory for the solubility of small particles in static structures has been developed. The distribution function of the solute in a frozen solid has been derived in analytical form for the quantum and the quasiclassical cases. The solubility at infinitesimal gas pressure (Henry's constant) as well as the pressure dependence of the solute concentration at elevated pressures has been found from the statistical equilibrium between the solute in the static matrix and the ideal-gas phase. The distribution function of a solute containing different particles has been evaluated in closed form. An application of the theory to the sorption of methane in the computed structures of glassy polycarbonate has resulted in a satisfactory agreement with experimental data.

Electron scattering intensities and Patterson functions of Skyrmions

NASA Astrophysics Data System (ADS)

Karliner, M.; King, C.; Manton, N. S.

2016-06-01

The scattering of electrons off nuclei is one of the best methods of probing nuclear structure. In this paper we focus on electron scattering off nuclei with spin and isospin zero within the Skyrme model. We consider two distinct methods and simplify our calculations by use of the Born approximation. The first method is to calculate the form factor of the spherically averaged Skyrmion charge density; the second uses the Patterson function to calculate the scattering intensity off randomly oriented Skyrmions, and spherically averages at the end. We compare our findings with experimental scattering data. We also find approximate analytical formulae for the first zero and first stationary point of a form factor.

An Empirical Model of Body Image Disturbance Using Behavioral Principles Found in Functional Analytic Psychotherapy and Acceptance and Commitment Therapy

ERIC Educational Resources Information Center

Callaghan, Glenn M.; Duenas, Julissa A.; Nadeau, Sarah E.; Darrow, Sabrina M.; Van der Merwe, Jessica; Misko, Jennifer

2012-01-01

The literature examining body image disturbance and Body Dysmorphic Disorder (BDD) is fraught with competing theoretical constructions of the etiology and nosology of these problems. Recent studies on various forms of psychopathology suggest that intrapersonal processes, including experiential avoidance, and interpersonal processes such as…

The MGGB equation-of-state for multifield applications: a numerical recipe for analytic expression of sesame EOS data

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

Kashiwa, B. A.

2010-12-01

Abstract A thermodynamically consistent and fully general equation–of– state (EOS) for multifield applications is described. EOS functions are derived from a Helmholtz free energy expressed as the sum of thermal (fluctuational) and collisional (condensed–phase) contributions; thus the free energy is of the Mie–Gr¨uneisen1 form. The phase–coexistence region is defined using a parameterized saturation curve by extending the form introduced by Guggenheim,2 which scales the curve relative to conditions at the critical point. We use the zero–temperature condensed–phase contribution developed by Barnes,3 which extends the Thomas–Fermi–Dirac equation to zero pressure. Thus, the functional form of the EOS could be called MGGBmore » (for Mie– Gr¨uneisen–Guggenheim–Barnes). Substance–specific parameters are obtained by fitting the low–density energy to data from the Sesame4 library; fitting the zero–temperature pressure to the Sesame cold curve; and fitting the saturation curve and latent heat to laboratory data,5 if available. When suitable coexistence data, or Sesame data, are not available, then we apply the Principle of Corresponding States.2 Thus MGGB can be thought of as a numerical recipe for rendering the tabular Sesame EOS data in an analytic form that includes a proper coexistence region, and which permits the accurate calculation of derivatives associated with compressibility, expansivity, Joule coefficient, and specific heat, all of which are required for multifield applications. 1« less

Nonclassical thermal-state superpositions: Analytical evolution law and decoherence behavior

NASA Astrophysics Data System (ADS)

Meng, Xiang-guo; Goan, Hsi-Sheng; Wang, Ji-suo; Zhang, Ran

2018-03-01

Employing the integration technique within normal products of bosonic operators, we present normal product representations of thermal-state superpositions and investigate their nonclassical features, such as quadrature squeezing, sub-Poissonian distribution, and partial negativity of the Wigner function. We also analytically and numerically investigate their evolution law and decoherence characteristics in an amplitude-decay model via the variations of the probability distributions and the negative volumes of Wigner functions in phase space. The results indicate that the evolution formulas of two thermal component states for amplitude decay can be viewed as the same integral form as a displaced thermal state ρ(V , d) , but governed by the combined action of photon loss and thermal noise. In addition, the larger values of the displacement d and noise V lead to faster decoherence for thermal-state superpositions.

Performance evaluation soil samples utilizing encapsulation technology

DOEpatents

Dahlgran, J.R.

1999-08-17

Performance evaluation soil samples and method of their preparation uses encapsulation technology to encapsulate analytes which are introduced into a soil matrix for analysis and evaluation by analytical laboratories. Target analytes are mixed in an appropriate solvent at predetermined concentrations. The mixture is emulsified in a solution of polymeric film forming material. The emulsified solution is polymerized to form microcapsules. The microcapsules are recovered, quantitated and introduced into a soil matrix in a predetermined ratio to form soil samples with the desired analyte concentration. 1 fig.

Performance evaluation soil samples utilizing encapsulation technology

DOEpatents

Dahlgran, James R.

1999-01-01

Performance evaluation soil samples and method of their preparation using encapsulation technology to encapsulate analytes which are introduced into a soil matrix for analysis and evaluation by analytical laboratories. Target analytes are mixed in an appropriate solvent at predetermined concentrations. The mixture is emulsified in a solution of polymeric film forming material. The emulsified solution is polymerized to form microcapsules. The microcapsules are recovered, quantitated and introduced into a soil matrix in a predetermined ratio to form soil samples with the desired analyte concentration.

Analytic model of a multi-electron atom

NASA Astrophysics Data System (ADS)

Skoromnik, O. D.; Feranchuk, I. D.; Leonau, A. U.; Keitel, C. H.

2017-12-01

A fully analytical approximation for the observable characteristics of many-electron atoms is developed via a complete and orthonormal hydrogen-like basis with a single-effective charge parameter for all electrons of a given atom. The basis completeness allows us to employ the secondary-quantized representation for the construction of regular perturbation theory, which includes in a natural way correlation effects, converges fast and enables an effective calculation of the subsequent corrections. The hydrogen-like basis set provides a possibility to perform all summations over intermediate states in closed form, including both the discrete and continuous spectra. This is achieved with the help of the decomposition of the multi-particle Green function in a convolution of single-electronic Coulomb Green functions. We demonstrate that our fully analytical zeroth-order approximation describes the whole spectrum of the system, provides accuracy, which is independent of the number of electrons and is important for applications where the Thomas-Fermi model is still utilized. In addition already in second-order perturbation theory our results become comparable with those via a multi-configuration Hartree-Fock approach.

Differentiation of regioisomeric aromatic ketocarboxylic acids by atmospheric pressure chemical ionization CAD tandem mass spectrometry in a linear quadrupole ion trap mass spectrometer

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

Amundson, Lucas M.; Owen, Ben C.; Gallardo, Vanessa A.

2011-01-01

Positive-mode atmospheric pressure chemical ionization tandem mass spectrometry (APCI-MS n ) was tested for the differentiation of regioisomeric aromatic ketocarboxylic acids. Each analyte forms exclusively an abundant protonated molecule upon ionization via positive-mode APCI in a commercial linear quadrupole ion trap (LQIT) mass spectrometer. Energy-resolved collision-activated dissociation (CAD) experiments carried out on the protonated analytes revealed fragmentation patterns that varied based on the location of the functional groups. Unambiguous differentiation between the regioisomers was achieved in each case by observing different fragmentation patterns, different relative abundances of ion-molecule reaction products, or different relative abundances of fragment ions formed at differentmore » collision energies. The mechanisms of some of the reactions were examined by H/D exchange reactions and molecular orbital calculations.« less

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

Xantheas, Sotiris S.; Werhahn, Jasper C.

Based on the formulation of the analytical expression of the potential V(r) describing intermolecular interactions in terms of the dimensionless variables r*=r/rm and !*=V/!, where rm is the separation at the minimum and ! the well depth, we propose more generalized scalable forms for the commonly used Lennard-Jones, Mie, Morse and Buckingham exponential-6 potential energy functions (PEFs). These new generalized forms have an additional parameter from and revert to the original ones for some choice of that parameter. In this respect, the original forms can be considered as special cases of the more general forms that are introduced. We alsomore » propose a scalable, but nonrevertible to the original one, 4-parameter extended Morse potential.« less

Cumulant-based expressions for the multibody terms for the correlation between local and electrostatic interactions in the united-residue force field

NASA Astrophysics Data System (ADS)

Liwo, Adam; Czaplewski, Cezary; Pillardy, Jarosław; Scheraga, Harold A.

2001-08-01

A general method to derive site-site or united-residue potentials is presented. The basic principle of the method is the separation of the degrees of freedom of a system into the primary and secondary ones. The primary degrees of freedom describe the basic features of the system, while the secondary ones are averaged over when calculating the potential of mean force, which is hereafter referred to as the restricted free energy (RFE) function. The RFE can be factored into one-, two-, and multibody terms, using the cluster-cumulant expansion of Kubo. These factors can be assigned the functional forms of the corresponding lowest-order nonzero generalized cumulants, which can, in most cases, be evaluated analytically, after making some simplifying assumptions. This procedure to derive coarse-grain force fields is very valuable when applied to multibody terms, whose functional forms are hard to deduce in another way (e.g., from structural databases). After the functional forms have been derived, they can be parametrized based on the RFE surfaces of model systems obtained from all-atom models or on the statistics derived from structural databases. The approach has been applied to our united-residue force field for proteins. Analytical expressions were derived for the multibody terms pertaining to the correlation between local and electrostatic interactions within the polypeptide backbone; these expressions correspond to up to sixth-order terms in the cumulant expansion of the RFE. These expressions were subsequently parametrized by fitting to the RFEs of selected peptide fragments, calculated with the empirical conformational energy program for peptides force field. The new multibody terms enable not only the heretofore predictable α-helical segments, but also regular β-sheets, to form as the lowest-energy structures, as assessed by test calculations on a model helical protein A, as well as a model 20-residue polypeptide (betanova); the latter was not possible without introducing these new terms.

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Comment on "A note on generalized radial mesh generation for plasma electronic structure"

NASA Astrophysics Data System (ADS)

Pain, J.-Ch.

2011-12-01

In a recent note, B.G. Wilson and V. Sonnad [1] proposed a very useful closed form expression for the efficient generation of analytic log-linear radial meshes. The central point of the note is an implicit equation for the parameter h, involving Lambert's function W[x]. The authors mention that they are unaware of any direct proof of this equation (they obtained it by re-summing the Taylor expansion of h[α] using high-order coefficients obtained by analytic differentiation of the implicit definition using symbolic manipulation). In the present comment, we propose a direct proof of that equation.

Analytical skin friction and heat transfer formula for compressible internal flows

NASA Technical Reports Server (NTRS)

Dechant, Lawrence J.; Tattar, Marc J.

1994-01-01

An analytic, closed-form friction formula for turbulent, internal, compressible, fully developed flow was derived by extending the incompressible law-of-the-wall relation to compressible cases. The model is capable of analyzing heat transfer as a function of constant surface temperatures and surface roughness as well as analyzing adiabatic conditions. The formula reduces to Prandtl's law of friction for adiabatic, smooth, axisymmetric flow. In addition, the formula reduces to the Colebrook equation for incompressible, adiabatic, axisymmetric flow with various roughnesses. Comparisons with available experiments show that the model averages roughly 12.5 percent error for adiabatic flow and 18.5 percent error for flow involving heat transfer.

An analytical solution for Dean flow in curved ducts with rectangular cross section

NASA Astrophysics Data System (ADS)

Norouzi, M.; Biglari, N.

2013-05-01

In this paper, a full analytical solution for incompressible flow inside the curved ducts with rectangular cross-section is presented for the first time. The perturbation method is applied to solve the governing equations and curvature ratio is considered as the perturbation parameter. The previous perturbation solutions are usually restricted to the flow in curved circular or annular pipes related to the overly complex form of solutions or singularity situation for flow in curved ducts with non-circular shapes of cross section. This issue specifies the importance of analytical studies in the field of Dean flow inside the non-circular ducts. In this study, the main flow velocity, stream function of lateral velocities (secondary flows), and flow resistance ratio in rectangular curved ducts are obtained analytically. The effect of duct curvature and aspect ratio on flow field is investigated as well. Moreover, it is important to mention that the current analytical solution is able to simulate the Taylor-Görtler and Dean vortices (vortices in stable and unstable situations) in curved channels.

Statistical theory on the analytical form of cloud particle size distributions

NASA Astrophysics Data System (ADS)

Wu, Wei; McFarquhar, Greg

2017-11-01

Several analytical forms of cloud particle size distributions (PSDs) have been used in numerical modeling and remote sensing retrieval studies of clouds and precipitation, including exponential, gamma, lognormal, and Weibull distributions. However, there is no satisfying physical explanation as to why certain distribution forms preferentially occur instead of others. Theoretically, the analytical form of a PSD can be derived by directly solving the general dynamic equation, but no analytical solutions have been found yet. Instead of using a process level approach, the use of the principle of maximum entropy (MaxEnt) for determining the analytical form of PSDs from the perspective of system is examined here. Here, the issue of variability under coordinate transformations that arises using the Gibbs/Shannon definition of entropy is identified, and the use of the concept of relative entropy to avoid these problems is discussed. Focusing on cloud physics, the four-parameter generalized gamma distribution is proposed as the analytical form of a PSD using the principle of maximum (relative) entropy with assumptions on power law relations between state variables, scale invariance and a further constraint on the expectation of one state variable (e.g. bulk water mass). DOE ASR.

Analyticity in Time and Smoothing Effect of Solutions to Nonlinear Schrödinger Equations

NASA Astrophysics Data System (ADS)

Hayashi, Nakao; Kato, Keiichi

In this paper we consider analyticity in time and smoothing effect of solutions to nonlinear Schrödinger equations where . We prove that if φ satisfies then there exists a unique solution of (1) and positive constants T, C0, C1 such that is analytic in time and space variables for and and has an analytic continuation on and In the case the condition (2) can be relaxed as follows: where m= 0 if n= 1, p= 1, m= 1 if n= 2, and m= 1 if n= 3, p= 1.

Quantum currents and pair correlation of electrons in a chain of localized dots

NASA Astrophysics Data System (ADS)

Morawetz, Klaus

2017-03-01

The quantum transport of electrons in a wire of localized dots by hopping, interaction and dissipation is calculated and a representation by an equivalent RCL circuit is found. The exact solution for the electric-field induced currents allows to discuss the role of virtual currents to decay initial correlations and Bloch oscillations. The dynamical response function in random phase approximation (RPA) is calculated analytically with the help of which the static structure function and pair correlation function are determined. The pair correlation function contains a form factor from the Brillouin zone and a structure factor caused by the localized dots in the wire.

The Analytical Solution of the Transient Radial Diffusion Equation with a Nonuniform Loss Term.

NASA Astrophysics Data System (ADS)

Loridan, V.; Ripoll, J. F.; De Vuyst, F.

2017-12-01

Many works have been done during the past 40 years to perform the analytical solution of the radial diffusion equation that models the transport and loss of electrons in the magnetosphere, considering a diffusion coefficient proportional to a power law in shell and a constant loss term. Here, we propose an original analytical method to address this challenge with a nonuniform loss term. The strategy is to match any L-dependent electron losses with a piecewise constant function on M subintervals, i.e., dealing with a constant lifetime on each subinterval. Applying an eigenfunction expansion method, the eigenvalue problem becomes presently a Sturm-Liouville problem with M interfaces. Assuming the continuity of both the distribution function and its first spatial derivatives, we are able to deal with a well-posed problem and to find the full analytical solution. We further show an excellent agreement between both the analytical solutions and the solutions obtained directly from numerical simulations for different loss terms of various shapes and with a diffusion coefficient DLL L6. We also give two expressions for the required number of eigenmodes N to get an accurate snapshot of the analytical solution, highlighting that N is proportional to 1/√t0, where t0 is a time of interest, and that N increases with the diffusion power. Finally, the equilibrium time, defined as the time to nearly reach the steady solution, is estimated by a closed-form expression and discussed. Applications to Earth and also Jupiter and Saturn are discussed.

Variational model for one-dimensional quantum magnets

NASA Astrophysics Data System (ADS)

Kudasov, Yu. B.; Kozabaranov, R. V.

2018-04-01

A new variational technique for investigation of the ground state and correlation functions in 1D quantum magnets is proposed. A spin Hamiltonian is reduced to a fermionic representation by the Jordan-Wigner transformation. The ground state is described by a new non-local trial wave function, and the total energy is calculated in an analytic form as a function of two variational parameters. This approach is demonstrated with an example of the XXZ-chain of spin-1/2 under a staggered magnetic field. Generalizations and applications of the variational technique for low-dimensional magnetic systems are discussed.

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

NASA Astrophysics Data System (ADS)

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

2007-03-01

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

Analytical derivatives of the individual state energies in ensemble density functional theory method. I. General formalism

DOE PAGES

Filatov, Michael; Liu, Fang; Martínez, Todd J.

2017-07-21

The state-averaged (SA) spin restricted ensemble referenced Kohn-Sham (REKS) method and its state interaction (SI) extension, SI-SA-REKS, enable one to describe correctly the shape of the ground and excited potential energy surfaces of molecules undergoing bond breaking/bond formation reactions including features such as conical intersections crucial for theoretical modeling of non-adiabatic reactions. Until recently, application of the SA-REKS and SI-SA-REKS methods to modeling the dynamics of such reactions was obstructed due to the lack of the analytical energy derivatives. Here, the analytical derivatives of the individual SA-REKS and SI-SA-REKS energies are derived. The final analytic gradient expressions are formulated entirelymore » in terms of traces of matrix products and are presented in the form convenient for implementation in the traditional quantum chemical codes employing basis set expansions of the molecular orbitals. Finally, we will describe the implementation and benchmarking of the derived formalism in a subsequent article of this series.« less

General minimal surface solution for gravitational instantons

NASA Astrophysics Data System (ADS)

Aliev, A. N.; Kalaycı, J.; Nutku, Y.

1997-07-01

We construct the general instanton metric obtained from Weierstrass' general local solution for minimal surfaces using the correspondence between minimal surfaces in three-dimensional Euclidean space and gravitational instantons admitting two Killing vectors. The resulting metric contains one arbitrary analytic function and we show that it can be transformed to the Gibbons-Hawking form of an instanton metric that was reported earlier.

The Analytic Reconciliation of Classic Mayan Elite Pottery: Squaring Pottery Function with Form, Adornment, and Residual Contents

ERIC Educational Resources Information Center

Loughmiller-Newman, Jennifer Ann

2012-01-01

This dissertation presents a multidisciplinary means of determining the actual content (foodstuff, non-foodstuff, or lack of contents) of Classic Mayan (A.D. 250-900) vessels. Based on previous studies that have identified the residues of foodstuffs named in hieroglyphic texts (e.g. cacao), this study is designed to further investigate foodstuff…

Exact solutions for the selection-mutation equilibrium in the Crow-Kimura evolutionary model.

PubMed

Semenov, Yuri S; Novozhilov, Artem S

2015-08-01

We reformulate the eigenvalue problem for the selection-mutation equilibrium distribution in the case of a haploid asexually reproduced population in the form of an equation for an unknown probability generating function of this distribution. The special form of this equation in the infinite sequence limit allows us to obtain analytically the steady state distributions for a number of particular cases of the fitness landscape. The general approach is illustrated by examples; theoretical findings are compared with numerical calculations. Copyright © 2015. Published by Elsevier Inc.

Vapor sensing using polymer/carbon black composites in the percolative conduction regime.

PubMed

Sisk, Brian C; Lewis, Nathan S

2006-08-29

To investigate the behavior of chemiresistive vapor sensors operating below or around the percolation threshold, chemiresistors have been formed from composites of insulating organic polymers and low mass fractions of conductive carbon black (CB, 1-12% w/w). Such sensors produced extremely large relative differential resistance changes above certain threshold vapor concentrations. At high analyte partial pressures, these sensors exhibited better signal/noise characteristics and were typically less mutually correlated in their vapor response properties than composites formed using higher mass fractions of CB in the same set of polymer sorption layers. The responses of the low-mass-fraction CB sensors were, however, less repeatable, and their nonlinear response as a function of analyte concentration required more complicated calibration schemes to identify and quantify analyte vapors to compensate for drift of a sensor array and to compensate for variability in response between sensor arrays. Because of their much larger response signals, the low-mass-fraction CB sensors might be especially well suited for use with low-precision analog-to-digital signal readout electronics. These sensors serve well as a complement to composites formed from higher mass fractions of CB and have yielded insight into the tradeoffs of signal-to-noise improvements vs complexity of signal processing algorithms necessitated by the use of nonlinearly responding detectors in array-based sensing schemes.

Improved Analytical Potentials for the a ^3Σu+ and X ^1Σg+ States of {Cs_2}

NASA Astrophysics Data System (ADS)

Baldwin, Jesse; Le Roy, Robert J.

2012-06-01

Recent studies of the collisional properties of ultracold Cs atoms have led to a renewed interest in the singlet and triplet ground-state potential energy functions of Cs_2. Coxon and Hajigeorgiou recently determined an analytic potential function for the X ^1Σ_g^+ state that accurately reproduces a large body of spectroscopic data that spanned 99.45% of the potential well. However, their potential explicitly incorporates only the three leading inverse-power terms in the long-range potential, and does not distinguish between the three asymptotes associated with the different Cs atom spin states. Similarly, Xie et al. have reported two versions of an analytic potential energy function for the a ^3Σ_u^+ state that they determined from direct potential fits to emission data that spanned 93 % of its potential energy well. However, the tail of their potential function model was not constrained to have the inverse-power-sum form required by theory. Moreover, a physically correct description of cold atom collision phenomena requires the long-range inverse-power tails of these two potentials to be identical, and they are not. Thus, these functions cannot be expected to describe cold atom collision properties correctly. The present paper describes our efforts to determine improved analytic potential energy functions for these states that have identical long-range tails, and fully represent all of the spectroscopic data used in the earlier worka,b,c as well as photoassociation data that was not considered there and experimental values of the collisional scattering lengths for the two states. J. A. Coxon and P. Hajigeorgiou, J. Chem. Phys. 132, 09105 (2010). F. Xie et al. J. Chem. Phys. 130 051102 (2009). F. Xie et al. J. Chem. Phys. 135, 024303 (2011) J. G. Danzl et al., Science, 321, 1062 (2008). C. Chin, et al., Phys. Rev. Lett. 85, 2717 (2000) P. J. Leo, C. J. Williams, and P. S. Julienne, Phys. Rev. Lett. 85, 2721 (2000)

Collision-Induced Dissociation Study of the Adduct Ions Produced in NO3−-Free Area of Atmospheric Pressure Negative Corona Discharges under Ambient Air Conditions

PubMed Central

Sekimoto, Kanako; Matsuda, Natsuki; Takayama, Mitsuo

2013-01-01

Collision-induced dissociation (CID) experiments of adducts [M+R]− with negative atmospheric ions R− (O2−, HCO3− and COO−(COOH)) produced in NO3−-free discharge area in atmospheric pressure corona discharge ionization (APCDI) method were performed using aliphatic and aromatic compounds M. The [M+R]− adducts for individual R− fragmented to form deprotonated analytes [M−H]− as well as the specific product ions which also occurred in the CID of [M−H]−, independent of analytes with several different functional groups. The results obtained suggested that the specific product ions formed in the CID of [M+R]−, as well as CID of [M−H]−, are generated due to further fragmentation of the product ions [M−H]−. It was concluded, therefore, that CID of [M+R]− formed in NO3−-free discharge area can indirectly lead to the formation of the product ions originating from [M−H]−. PMID:24860710

An analytically solvable three-body break-up model problem in hyperspherical coordinates

NASA Astrophysics Data System (ADS)

Ancarani, L. U.; Gasaneo, G.; Mitnik, D. M.

2012-10-01

An analytically solvable S-wave model for three particles break-up processes is presented. The scattering process is represented by a non-homogeneous Coulombic Schrödinger equation where the driven term is given by a Coulomb-like interaction multiplied by the product of a continuum wave function and a bound state in the particles coordinates. The closed form solution is derived in hyperspherical coordinates leading to an analytic expression for the associated scattering transition amplitude. The proposed scattering model contains most of the difficulties encountered in real three-body scattering problem, e.g., non-separability in the electrons' spherical coordinates and Coulombic asymptotic behavior. Since the coordinates' coupling is completely different, the model provides an alternative test to that given by the Temkin-Poet model. The knowledge of the analytic solution provides an interesting benchmark to test numerical methods dealing with the double continuum, in particular in the asymptotic regions. An hyperspherical Sturmian approach recently developed for three-body collisional problems is used to reproduce to high accuracy the analytical results. In addition to this, we generalized the model generating an approximate wave function possessing the correct radial asymptotic behavior corresponding to an S-wave three-body Coulomb problem. The model allows us to explore the typical structure of the solution of a three-body driven equation, to identify three regions (the driven, the Coulombic and the asymptotic), and to analyze how far one has to go to extract the transition amplitude.

Comparison of Three Methods for Wind Turbine Capacity Factor Estimation

PubMed Central

Ditkovich, Y.; Kuperman, A.

2014-01-01

Three approaches to calculating capacity factor of fixed speed wind turbines are reviewed and compared using a case study. The first “quasiexact” approach utilizes discrete wind raw data (in the histogram form) and manufacturer-provided turbine power curve (also in discrete form) to numerically calculate the capacity factor. On the other hand, the second “analytic” approach employs a continuous probability distribution function, fitted to the wind data as well as continuous turbine power curve, resulting from double polynomial fitting of manufacturer-provided power curve data. The latter approach, while being an approximation, can be solved analytically thus providing a valuable insight into aspects, affecting the capacity factor. Moreover, several other merits of wind turbine performance may be derived based on the analytical approach. The third “approximate” approach, valid in case of Rayleigh winds only, employs a nonlinear approximation of the capacity factor versus average wind speed curve, only requiring rated power and rotor diameter of the turbine. It is shown that the results obtained by employing the three approaches are very close, enforcing the validity of the analytically derived approximations, which may be used for wind turbine performance evaluation. PMID:24587755

Line-source excitation of realistic conformal metasurface cloaks

NASA Astrophysics Data System (ADS)

Padooru, Yashwanth R.; Yakovlev, Alexander B.; Chen, Pai-Yen; Alù, Andrea

2012-11-01

Following our recently introduced analytical tools to model and design conformal mantle cloaks based on metasurfaces [Padooru et al., J. Appl. Phys. 112, 034907 (2012)], we investigate their performance and physical properties when excited by an electric line source placed in their close proximity. We consider metasurfaces formed by 2-D arrays of slotted (meshes and Jerusalem cross slots) and printed (patches and Jerusalem crosses) sub-wavelength elements. The electromagnetic scattering analysis is carried out using a rigorous analytical model, which utilizes the two-sided impedance boundary conditions at the interface of the sub-wavelength elements. It is shown that the homogenized grid-impedance expressions, originally derived for planar arrays of sub-wavelength elements and plane-wave excitation, may be successfully used to model and tailor the surface reactance of cylindrical conformal mantle cloaks illuminated by near-field sources. Our closed-form analytical results are in good agreement with full-wave numerical simulations, up to sub-wavelength distances from the metasurface, confirming that mantle cloaks may be very effective to suppress the scattering of moderately sized objects, independent of the type of excitation and point of observation. We also discuss the dual functionality of these metasurfaces to boost radiation efficiency and directivity from confined near-field sources.

Why noise is useful in functional and neural mechanisms of interval timing?

PubMed Central

2013-01-01

Background The ability to estimate durations in the seconds-to-minutes range - interval timing - is essential for survival, adaptation and its impairment leads to severe cognitive and/or motor dysfunctions. The response rate near a memorized duration has a Gaussian shape centered on the to-be-timed interval (criterion time). The width of the Gaussian-like distribution of responses increases linearly with the criterion time, i.e., interval timing obeys the scalar property. Results We presented analytical and numerical results based on the striatal beat frequency (SBF) model showing that parameter variability (noise) mimics behavioral data. A key functional block of the SBF model is the set of oscillators that provide the time base for the entire timing network. The implementation of the oscillators block as simplified phase (cosine) oscillators has the additional advantage that is analytically tractable. We also checked numerically that the scalar property emerges in the presence of memory variability by using biophysically realistic Morris-Lecar oscillators. First, we predicted analytically and tested numerically that in a noise-free SBF model the output function could be approximated by a Gaussian. However, in a noise-free SBF model the width of the Gaussian envelope is independent of the criterion time, which violates the scalar property. We showed analytically and verified numerically that small fluctuations of the memorized criterion time leads to scalar property of interval timing. Conclusions Noise is ubiquitous in the form of small fluctuations of intrinsic frequencies of the neural oscillators, the errors in recording/retrieving stored information related to criterion time, fluctuation in neurotransmitters’ concentration, etc. Our model suggests that the biological noise plays an essential functional role in the SBF interval timing. PMID:23924391

Investigation of chaos and its control in a Duffing-type nano beam model

NASA Astrophysics Data System (ADS)

Jha, Abhishek Kumar; Dasgupta, Sovan Sundar

2018-04-01

The prediction of chaos of a nano beam with harmonic excitation is investigated. Using the Galerkin method the nonlinear lumped model of a clamped-clamped nano beam with nonlinear cubic stiffness is obtained. This is a Duffing system with hardening type of nonlinearity. Based on the energy function and the phase portrait of the system, the resonator dynamics is categorized into four situations in which Using Malnikov function, an analytical criterion for homoclinic intersection in the form of inequality is written in terms of the system parameters. A numerical study including largest lyapunov exponent, Poincare diagram and phase portrait confirm the analytical prediction of chaos and effect of forcing amplitude. Subsequently, a linear velocity feedback controller is introduced into the system to successfully control the chaotic motion of the system at a faster rate at larger value of gain parameter.

Enhancement of Raman scattering in dielectric nanostructures with electric and magnetic Mie resonances

NASA Astrophysics Data System (ADS)

Frizyuk, Kristina; Hasan, Mehedi; Krasnok, Alex; Alú, Andrea; Petrov, Mihail

2018-02-01

Resonantly enhanced Raman scattering in dielectric nanostructures has been recently proven to be an efficient tool for nanothermometry and for the experimental determination of their mode composition. In this paper we develop a rigorous analytical theory based on the Green's function approach to calculate the Raman emission from crystalline high-index dielectric nanoparticles. As an example, we consider silicon nanoparticles which have a strong Raman response due to active optical phonon modes. We relate enhancement of Raman signal emission to the Purcell effect due to the excitation of Mie modes inside the nanoparticles. We also employ our numerical approach to calculate inelastic Raman emission in more sophisticated geometries, which do not allow a straightforward analytical form of the Green's function. The Raman response from a silicon nanodisk has been analyzed with the proposed method, and the contribution of various Mie modes has been revealed.

Characterization and prediction of the backscattered form function of an immersed cylindrical shell using hybrid fuzzy clustering and bio-inspired algorithms.

PubMed

Agounad, Said; Aassif, El Houcein; Khandouch, Younes; Maze, Gérard; Décultot, Dominique

2018-02-01

The acoustic scattering of a plane wave by an elastic cylindrical shell is studied. A new approach is developed to predict the form function of an immersed cylindrical shell of the radius ratio b/a ('b' is the inner radius and 'a' is the outer radius). The prediction of the backscattered form function is investigated by a combined approach between fuzzy clustering algorithms and bio-inspired algorithms. Four famous fuzzy clustering algorithms: the fuzzy c-means (FCM), the Gustafson-Kessel algorithm (GK), the fuzzy c-regression model (FCRM) and the Gath-Geva algorithm (GG) are combined with particle swarm optimization and genetic algorithm. The symmetric and antisymmetric circumferential waves A, S 0 , A 1 , S 1 and S 2 are investigated in a reduced frequency (k 1 a) range extends over 0.1

dPotFit: A computer program to fit diatomic molecule spectral data to potential energy functions

NASA Astrophysics Data System (ADS)

Le Roy, Robert J.

2017-01-01

This paper describes program dPotFit, which performs least-squares fits of diatomic molecule spectroscopic data consisting of any combination of microwave, infrared or electronic vibrational bands, fluorescence series, and tunneling predissociation level widths, involving one or more electronic states and one or more isotopologs, and for appropriate systems, second virial coefficient data, to determine analytic potential energy functions defining the observed levels and other properties of each state. Four families of analytical potential functions are available for fitting in the current version of dPotFit: the Expanded Morse Oscillator (EMO) function, the Morse/Long-Range (MLR) function, the Double-Exponential/Long-Range (DELR) function, and the 'Generalized Potential Energy Function' (GPEF) of Šurkus, which incorporates a variety of polynomial functional forms. In addition, dPotFit allows sets of experimental data to be tested against predictions generated from three other families of analytic functions, namely, the 'Hannover Polynomial' (or "X-expansion") function, and the 'Tang-Toennies' and Scoles-Aziz 'HFD', exponential-plus-van der Waals functions, and from interpolation-smoothed pointwise potential energies, such as those obtained from ab initio or RKR calculations. dPotFit also allows the fits to determine atomic-mass-dependent Born-Oppenheimer breakdown functions, and singlet-state Λ-doubling, or 2Σ splitting radial strength functions for one or more electronic states. dPotFit always reports both the 95% confidence limit uncertainty and the "sensitivity" of each fitted parameter; the latter indicates the number of significant digits that must be retained when rounding fitted parameters, in order to ensure that predictions remain in full agreement with experiment. It will also, if requested, apply a "sequential rounding and refitting" procedure to yield a final parameter set defined by a minimum number of significant digits, while ensuring no significant loss of accuracy in the predictions yielded by those parameters.

Spatially resolved thermal desorption/ionization coupled with mass spectrometry

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

Jesse, Stephen; Van Berkel, Gary J; Ovchinnikova, Olga S

2013-02-26

A system and method for sub-micron analysis of a chemical composition of a specimen are described. The method includes providing a specimen for evaluation and a thermal desorption probe, thermally desorbing an analyte from a target site of said specimen using the thermally active tip to form a gaseous analyte, ionizing the gaseous analyte to form an ionized analyte, and analyzing a chemical composition of the ionized analyte. The thermally desorbing step can include heating said thermally active tip to above 200.degree. C., and positioning the target site and the thermally active tip such that the heating step forms themore » gaseous analyte. The thermal desorption probe can include a thermally active tip extending from a cantilever body and an apex of the thermally active tip can have a radius of 250 nm or less.« less

Sample distribution in peak mode isotachophoresis

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

Rubin, Shimon; Schwartz, Ortal; Bercovici, Moran, E-mail: mberco@technion.ac.il

We present an analytical study of peak mode isotachophoresis (ITP), and provide closed form solutions for sample distribution and electric field, as well as for leading-, trailing-, and counter-ion concentration profiles. Importantly, the solution we present is valid not only for the case of fully ionized species, but also for systems of weak electrolytes which better represent real buffer systems and for multivalent analytes such as proteins and DNA. The model reveals two major scales which govern the electric field and buffer distributions, and an additional length scale governing analyte distribution. Using well-controlled experiments, and numerical simulations, we verify andmore » validate the model and highlight its key merits as well as its limitations. We demonstrate the use of the model for determining the peak concentration of focused sample based on known buffer and analyte properties, and show it differs significantly from commonly used approximations based on the interface width alone. We further apply our model for studying reactions between multiple species having different effective mobilities yet co-focused at a single ITP interface. We find a closed form expression for an effective-on rate which depends on reactants distributions, and derive the conditions for optimizing such reactions. Interestingly, the model reveals that maximum reaction rate is not necessarily obtained when the concentration profiles of the reacting species perfectly overlap. In addition to the exact solutions, we derive throughout several closed form engineering approximations which are based on elementary functions and are simple to implement, yet maintain the interplay between the important scales. Both the exact and approximate solutions provide insight into sample focusing and can be used to design and optimize ITP-based assays.« less

Acid-Base Properties of Azo Dyes in Solution Studied Using Spectrophotometry and Colorimetry

NASA Astrophysics Data System (ADS)

Snigur, D. V.; Chebotarev, A. N.; Bevziuk, K. V.

2018-03-01

Colorimetry and spectrophotometry with chemometric data processing were used to study the acid-base properties of azo dyes in aqueous solution. The capabilities of both methods were compared. Ionization constants of all the functional groups of the azo compounds studied could be determined relative to the change in the specific color difference depending on the acidity of the medium. The colorimetric functions of ion-molecular forms of azo compounds used as an analytical signal allow us to obtain complete information on the acid-base equilibrium in a wide acidity range.

Noise kernels of stochastic gravity in conformally-flat spacetimes

NASA Astrophysics Data System (ADS)

Cho, H. T.; Hu, B. L.

2015-03-01

The central object in the theory of semiclassical stochastic gravity is the noise kernel, which is the symmetric two point correlation function of the stress-energy tensor. Using the corresponding Wightman functions in Minkowski, Einstein and open Einstein spaces, we construct the noise kernels of a conformally coupled scalar field in these spacetimes. From them we show that the noise kernels in conformally-flat spacetimes, including the Friedmann-Robertson-Walker universes, can be obtained in closed analytic forms by using a combination of conformal and coordinate transformations.

The simultaneous integration of many trajectories using nilpotent normal forms

NASA Technical Reports Server (NTRS)

Grayson, Matthew A.; Grossman, Robert

1990-01-01

Taylor's formula shows how to approximate a certain class of functions by polynomials. The approximations are arbitrarily good in some neighborhood whenever the function is analytic and they are easy to compute. The main goal is to give an efficient algorithm to approximate a neighborhood of the configuration space of a dynamical system by a nilpotent, explicitly integrable dynamical system. The major areas covered include: an approximating map; the generalized Baker-Campbell-Hausdorff formula; the Picard-Taylor method; the main theorem; simultaneous integration of trajectories; and examples.

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

NASA Astrophysics Data System (ADS)

Grants, Ilmārs; Bojarevičs, Andris; Gerbeth, Gunter

2016-06-01

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

Generalized constitutive equations for piezo-actuated compliant mechanism

NASA Astrophysics Data System (ADS)

Cao, Junyi; Ling, Mingxiang; Inman, Daniel J.; Lin, Jin

2016-09-01

This paper formulates analytical models to describe the static displacement and force interactions between generic serial-parallel compliant mechanisms and their loads by employing the matrix method. In keeping with the familiar piezoelectric constitutive equations, the generalized constitutive equations of compliant mechanism represent the input-output displacement and force relations in the form of a generalized Hooke’s law and as analytical functions of physical parameters. Also significantly, a new model of output displacement for compliant mechanism interacting with piezo-stacks and elastic loads is deduced based on the generalized constitutive equations. Some original findings differing from the well-known constitutive performance of piezo-stacks are also given. The feasibility of the proposed models is confirmed by finite element analysis and by experiments under various elastic loads. The analytical models can be an insightful tool for predicting and optimizing the performance of a wide class of compliant mechanisms that simultaneously consider the influence of loads and piezo-stacks.

Analytic double product integrals for all-frequency relighting.

PubMed

Wang, Rui; Pan, Minghao; Chen, Weifeng; Ren, Zhong; Zhou, Kun; Hua, Wei; Bao, Hujun

2013-07-01

This paper presents a new technique for real-time relighting of static scenes with all-frequency shadows from complex lighting and highly specular reflections from spatially varying BRDFs. The key idea is to depict the boundaries of visible regions using piecewise linear functions, and convert the shading computation into double product integrals—the integral of the product of lighting and BRDF on visible regions. By representing lighting and BRDF with spherical Gaussians and approximating their product using Legendre polynomials locally in visible regions, we show that such double product integrals can be evaluated in an analytic form. Given the precomputed visibility, our technique computes the visibility boundaries on the fly at each shading point, and performs the analytic integral to evaluate the shading color. The result is a real-time all-frequency relighting technique for static scenes with dynamic, spatially varying BRDFs, which can generate more accurate shadows than the state-of-the-art real-time PRT methods.

DROMO formulation for planar motions: solution to the Tsien problem

NASA Astrophysics Data System (ADS)

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

2015-06-01

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

Computer modeling of a two-junction, monolithic cascade solar cell

NASA Technical Reports Server (NTRS)

Lamorte, M. F.; Abbott, D.

1979-01-01

The theory and design criteria for monolithic, two-junction cascade solar cells are described. The departure from the conventional solar cell analytical method and the reasons for using the integral form of the continuity equations are briefly discussed. The results of design optimization are presented. The energy conversion efficiency that is predicted for the optimized structure is greater than 30% at 300 K, AMO and one sun. The analytical method predicts device performance characteristics as a function of temperature. The range is restricted to 300 to 600 K. While the analysis is capable of determining most of the physical processes occurring in each of the individual layers, only the more significant device performance characteristics are presented.

A coupled analytical model for hydrostatic response of 1-3 piezocomposites.

PubMed

Rajapakse, Nimal; Chen, Yue

2008-08-01

This study presents a fully coupled analysis of a unit cell of a 1-3 piezocomposite under hydrostatic loading. The governing equations for coupled axisymmetric electroelastic field of a transversely isotropic piezoelectric medium and a transversely isotropic elastic medium are used. A reduced form of the analytical general solutions expressed in terms of series of modified Bessel functions of the first and second kind are used. The solution of the boundary-value problem corresponding to a unit cell is presented. The effective properties of a 1-3 piezocomposite are obtained for different fiber volume fractions, polymer and piezoceramic properties, and fiber aspect ratios. Comparisons with previously reported simplified and uncoupled models are made.

A simplified analytic form for generation of axisymmetric plasma boundaries

DOE PAGES

Luce, Timothy C.

2017-02-23

An improved method has been formulated for generating analytic boundary shapes as input for axisymmetric MHD equilibria. This method uses the family of superellipses as the basis function, as previously introduced. The improvements are a simplified notation, reduction of the number of simultaneous nonlinear equations to be solved, and the realization that not all combinations of input parameters admit a solution to the nonlinear constraint equations. The method tests for the existence of a self-consistent solution and, when no solution exists, it uses a deterministic method to find a nearby solution. As a result, examples of generation of boundaries, includingmore » tests with an equilibrium solver, are given.« less

A simplified analytic form for generation of axisymmetric plasma boundaries

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

Luce, Timothy C.

An improved method has been formulated for generating analytic boundary shapes as input for axisymmetric MHD equilibria. This method uses the family of superellipses as the basis function, as previously introduced. The improvements are a simplified notation, reduction of the number of simultaneous nonlinear equations to be solved, and the realization that not all combinations of input parameters admit a solution to the nonlinear constraint equations. The method tests for the existence of a self-consistent solution and, when no solution exists, it uses a deterministic method to find a nearby solution. As a result, examples of generation of boundaries, includingmore » tests with an equilibrium solver, are given.« less

Analytical approximations to seawater optical phase functions of scattering

NASA Astrophysics Data System (ADS)

Haltrin, Vladimir I.

2004-11-01

This paper proposes a number of analytical approximations to the classic and recently measured seawater light scattering phase functions. The three types of analytical phase functions are derived: individual representations for 15 Petzold, 41 Mankovsky, and 91 Gulf of Mexico phase functions; collective fits to Petzold phase functions; and analytical representations that take into account dependencies between inherent optical properties of seawater. The proposed phase functions may be used for problems of radiative transfer, remote sensing, visibility and image propagation in natural waters of various turbidity.

Dpf Analyses Yield Fully Analytic Potentials for the B ^1Πu ``BARRIER'' States of {Rb}_2 and {Li}_2 and AN Improved Ground-State Well Depth for {Rb}_2

NASA Astrophysics Data System (ADS)

Slaughter, Kai; Dattani, Nikesh S.; Amiot, Claude S.; Ross, Amanda J.; Le Roy, Robert J.

2015-06-01

Determining full model potential energy functions for molecular states that have a `natural' rotationless barrier which protrudes above the potential asymptote, such as the B ^1Π_u states of alkali dimers, is a challenging problem. The present work extends our previous Direct-Potential-Fit (DPF) analysis of data for the B ^1Π_u state of Li_2 by introducing a more sophisticated model for the long-range tail of the fully analytic `Double Exponential Long-Range' (DELR) potential function form^a that takes account of the interstate coupling that occurs near the asymptotes of nS+nP alkali dimers. This type of analysis is then applied to data for the B ^1Π_u state of Rb_2, and a concurrent extension of the DPF analysis of Seto and Le Roy yields an improved fully analytic potential energy function for its ground X ^1σ_g^+ state. The effect of taking account of the long-range inter-state coupling on the shapes of the outer walls of the B ^1Π_u state potential functions for these two species will also be examined. Y. Huang and R.J. Le Roy, J. Chem. Phys., 119, 7398 (2003) M. Aubert-Frécon and G. Hadinger and S. Magnier and S. Rousseau, J. Mol. Spectosc., 288, 182 (1998). J.Y. Seto and R.J. Le Roy, J. Chem. Phys., 113, 3067 (2000).

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

NASA Astrophysics Data System (ADS)

Engelmann, Matthias; Rasmussen, Morten Grud

2016-12-01

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

Kinetics of diffusional droplet growth in a liquid/liquid two-phase system

NASA Technical Reports Server (NTRS)

Baird, James K.; Cain, Judith B.

1993-01-01

This report contains experimental results for the interdiffusion coefficient of the system, succinonitrile plus water, at a number of compositions and temperatures in the single phase region of the phase diagram. The concentration and temperature dependence of the measured diffusion coefficient has been analyzed in terms of Landau - Ginzburg theory, which assumes that the Gibb free energy is an analytic function of its variables, and can be expanded in a Taylor series about any point in the phase diagram. At most points in the single phase region this is adequate. Near the consolute point (critical point of solution), however, the free energy is non-analytic, and the Landau - Ginzburg theory fails. The solution to this problem dictates that the Landau - Ginzburg form of the free energy be replaced by Widom scaling functions with irrational values for the scaling exponents. As our measurements of the diffusion coefficient near the critical point reflect this non-analytic character, we are preparing for publication in a refereed journal a separate analysis of some of the data contained herein as well as some additional measurements we have just completed. When published, reprints of this article will be furnished to NASA.

Analytical modelling of temperature effects on an AMPA-type synapse.

PubMed

Kufel, Dominik S; Wojcik, Grzegorz M

2018-05-11

It was previously reported, that temperature may significantly influence neural dynamics on the different levels of brain function. Thus, in computational neuroscience, it would be useful to make models scalable for a wide range of various brain temperatures. However, lack of experimental data and an absence of temperature-dependent analytical models of synaptic conductance does not allow to include temperature effects at the multi-neuron modeling level. In this paper, we propose a first step to deal with this problem: A new analytical model of AMPA-type synaptic conductance, which is able to incorporate temperature effects in low-frequency stimulations. It was constructed based on Markov model description of AMPA receptor kinetics using the set of coupled ODEs. The closed-form solution for the set of differential equations was found using uncoupling assumption (introduced in the paper) with few simplifications motivated both from experimental data and from Monte Carlo simulation of synaptic transmission. The model may be used for computationally efficient and biologically accurate implementation of temperature effects on AMPA receptor conductance in large-scale neural network simulations. As a result, it may open a wide range of new possibilities for researching the influence of temperature on certain aspects of brain functioning.

An exactly solvable coarse-grained model for species diversity

NASA Astrophysics Data System (ADS)

Suweis, Samir; Rinaldo, Andrea; Maritan, Amos

2012-07-01

We present novel analytical results concerning ecosystem species diversity that stem from a proposed coarse-grained neutral model based on birth-death processes. The relevance of the problem lies in the urgency for understanding and synthesizing both theoretical results from ecological neutral theory and empirical evidence on species diversity preservation. The neutral model of biodiversity deals with ecosystems at the same trophic level, where per capita vital rates are assumed to be species independent. Closed-form analytical solutions for the neutral theory are obtained within a coarse-grained model, where the only input is the species persistence time distribution. Our results pertain to: the probability distribution function of the number of species in the ecosystem, both in transient and in stationary states; the n-point connected time correlation function; and the survival probability, defined as the distribution of time spans to local extinction for a species randomly sampled from the community. Analytical predictions are also tested on empirical data from an estuarine fish ecosystem. We find that emerging properties of the ecosystem are very robust and do not depend on specific details of the model, with implications for biodiversity and conservation biology.

Blade Tip Rubbing Stress Prediction

NASA Technical Reports Server (NTRS)

Davis, Gary A.; Clough, Ray C.

1991-01-01

An analytical model was constructed to predict the magnitude of stresses produced by rubbing a turbine blade against its tip seal. This model used a linearized approach to the problem, after a parametric study, found that the nonlinear effects were of insignificant magnitude. The important input parameters to the model were: the arc through which rubbing occurs, the turbine rotor speed, normal force exerted on the blade, and the rubbing coefficient of friction. Since it is not possible to exactly specify some of these parameters, values were entered into the model which bracket likely values. The form of the forcing function was another variable which was impossible to specify precisely, but the assumption of a half-sine wave with a period equal to the duration of the rub was taken as a realistic assumption. The analytical model predicted resonances between harmonics of the forcing function decomposition and known harmonics of the blade. Thus, it seemed probable that blade tip rubbing could be at least a contributor to the blade-cracking phenomenon. A full-scale, full-speed test conducted on the space shuttle main engine high pressure fuel turbopump Whirligig tester was conducted at speeds between 33,000 and 28,000 RPM to confirm analytical predictions.

Approximation solution of Schrodinger equation for Q-deformed Rosen-Morse using supersymmetry quantum mechanics (SUSY QM)

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

Alemgadmi, Khaled I. K., E-mail: azozkied@yahoo.com; Suparmi; Cari

2015-09-30

The approximate analytical solution of Schrodinger equation for Q-Deformed Rosen-Morse potential was investigated using Supersymmetry Quantum Mechanics (SUSY QM) method. The approximate bound state energy is given in the closed form and the corresponding approximate wave function for arbitrary l-state given for ground state wave function. The first excited state obtained using upper operator and ground state wave function. The special case is given for the ground state in various number of q. The existence of Rosen-Morse potential reduce energy spectra of system. The larger value of q, the smaller energy spectra of system.

Solution of D dimensional Dirac equation for coulombic potential using NU method and its thermodynamics properties

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

Cari, C., E-mail: cari@staff.uns.ac.id; Suparmi, A., E-mail: soeparmi@staff.uns.ac.id; Yunianto, M., E-mail: muhtaryunianto@staff.uns.ac.id

2016-02-08

The analytical solution of Ddimensional Dirac equation for Coulombic potential is investigated using Nikiforov-Uvarov method. The D dimensional relativistic energy spectra are obtained from relativistic energy eigenvalue equation by using Mat Lab software.The corresponding D dimensional radial wave functions are formulated in the form of generalized Jacobi and Laguerre Polynomials. In the non-relativistic limit, the relativistic energy equation reduces to the non-relativistic energy which will be applied to determine some thermodynamical properties of the system. The thermodynamical properties of the system are expressed in terms of error function and imaginary error function.

Low-Cost Chemical-Responsive Adhesive Sensing Chips.

PubMed

Tan, Weirui; Zhang, Liyuan; Shen, Wei

2017-12-06

Chemical-responsive adhesive sensing chip is a new low-cost analytical platform that uses adhesive tape loaded with indicator reagents to detect or quantify the target analytes by directly sticking the tape to the samples of interest. The chemical-responsive adhesive sensing chips can be used with paper to analyze aqueous samples; they can also be used to detect and quantify solid, particulate, and powder analytes. The colorimetric indicators become immediately visible as the contact between the functionalized adhesives and target samples is made. The chemical-responsive adhesive sensing chip expands the capability of paper-based analytical devices to analyze solid, particulate, or powder materials via one-step operation. It is also a simpler alternative way, to the covalent chemical modification of paper, to eliminate indicator leaching from the dipstick-style paper sensors. Chemical-responsive adhesive chips can display analytical results in the form of colorimetric dot patterns, symbols, and texts, enabling clear understanding of assay results by even nonprofessional users. In this work, we demonstrate the analyses of heavy metal salts in silica powder matrix, heavy metal ions in water, and bovine serum albumin in an aqueous solution. The detection is one-step, specific, sensitive, and easy-to-operate.

Development of an analytical solution for the Budyko watershed parameter in terms of catchment physical features

NASA Astrophysics Data System (ADS)

Reaver, N.; Kaplan, D. A.; Jawitz, J. W.

2017-12-01

The Budyko hypothesis states that a catchment's long-term water and energy balances are dependent on two relatively easy to measure quantities: rainfall depth and potential evaporation. This hypothesis is expressed as a simple function, the Budyko equation, which allows for the prediction of a catchment's actual evapotranspiration and discharge from measured rainfall depth and potential evaporation, data which are widely available. However, the two main analytically derived forms of the Budyko equation contain a single unknown watershed parameter, whose value varies across catchments; variation in this parameter has been used to explain the hydrological behavior of different catchments. The watershed parameter is generally thought of as a lumped quantity that represents the influence of all catchment biophysical features (e.g. soil type and depth, vegetation type, timing of rainfall, etc). Previous work has shown that the parameter is statistically correlated with catchment properties, but an explicit expression has been elusive. While the watershed parameter can be determined empirically by fitting the Budyko equation to measured data in gauged catchments where actual evapotranspiration can be estimated, this limits the utility of the framework for predicting impacts to catchment hydrology due to changing climate and land use. In this study, we developed an analytical solution for the lumped catchment parameter for both forms of the Budyko equation. We combined these solutions with a statistical soil moisture model to obtain analytical solutions for the Budyko equation parameter as a function of measurable catchment physical features, including rooting depth, soil porosity, and soil wilting point. We tested the predictive power of these solutions using the U.S. catchments in the MOPEX database. We also compared the Budyko equation parameter estimates generated from our analytical solutions (i.e. predicted parameters) with those obtained through the calibration of the Budyko equation to discharge data (i.e. empirical parameters), and found good agreement. These results suggest that it is possible to predict the Budyko equation watershed parameter directly from physical features, even for ungauged catchments.

Unfolding the laws of star formation: the density distribution of molecular clouds.

PubMed

Kainulainen, Jouni; Federrath, Christoph; Henning, Thomas

2014-04-11

The formation of stars shapes the structure and evolution of entire galaxies. The rate and efficiency of this process are affected substantially by the density structure of the individual molecular clouds in which stars form. The most fundamental measure of this structure is the probability density function of volume densities (ρ-PDF), which determines the star formation rates predicted with analytical models. This function has remained unconstrained by observations. We have developed an approach to quantify ρ-PDFs and establish their relation to star formation. The ρ-PDFs instigate a density threshold of star formation and allow us to quantify the star formation efficiency above it. The ρ-PDFs provide new constraints for star formation theories and correctly predict several key properties of the star-forming interstellar medium.

The D-dimensional non-relativistic particle in the Scarf Trigonometry plus Non-Central Rosen-Morse Potentials

NASA Astrophysics Data System (ADS)

Deta, U. A.; Lestari, N. A.; Yantidewi, M.; Suparmi, A.; Cari, C.

2018-03-01

The D-Dimensional Non-Relativistic Particle Properties in the Scarf Trigonometry plus Non-Central Rosen-Morse Potentials was investigated using an analytical method. The bound state energy is given approximately in the closed form. The approximate wave function for arbitrary l-state in D-dimensions are expressed in the form of generalised Jacobi Polynomials. The energy spectra of the particle are increased when the dimensions are higher. The relationship between the orbital number in each dimension is recursive. The special case in 3 dimensions is given to the ground state.

A Novel Capacity Analysis for Wireless Backhaul Mesh Networks

NASA Astrophysics Data System (ADS)

Chung, Tein-Yaw; Lee, Kuan-Chun; Lee, Hsiao-Chih

This paper derived a closed-form expression for inter-flow capacity of a backhaul wireless mesh network (WMN) with centralized scheduling by employing a ring-based approach. Through the definition of an interference area, we are able to accurately describe a bottleneck collision area for a WMN and calculate the upper bound of inter-flow capacity. The closed-form expression shows that the upper bound is a function of the ratio between transmission range and network radius. Simulations and numerical analysis show that our analytic solution can better estimate the inter-flow capacity of WMNs than that of previous approach.

Dynamic Response of Layered TiB/Ti Functionally Graded Material Specimens

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

Byrd, Larry; Beberniss, Tim; Chapman, Ben

2008-02-15

This paper covers the dynamic response of rectangular (25.4x101.6x3.175 mm) specimens manufactured from layers of TiB/Ti. The layers contained volume fractions of TiB that varied from 0 to 85% and thus formed a functionally graded material. Witness samples of the 85% TiB material were also tested to provide a baseline for the statistical variability of the test techniques. Static and dynamic tests were performed to determine the in situ material properties and fundamental frequencies. Damping in the material/ fixture was also found from the dynamic response. These tests were simulated using composite beam theory which gave an analytical solution, andmore » using finite element analysis. The response of the 85% TiB specimens was found to be much more uniform than the functionally graded material and the dynamic response more uniform than the static response. A least squares analysis of the data using the analytical solutions were used to determine the elastic modulus and Poisson's ratio of each layer. These results were used to model the response in the finite element analysis. The results indicate that current analytical and numerical methods for modeling the material give similar and adequate predictions for natural frequencies if the measured property values were used. The models did not agree as well if the properties from the manufacturer or those of Hill and Linn were used.« less

Universal behaviour of interoccurrence times between losses in financial markets: An analytical description

NASA Astrophysics Data System (ADS)

Ludescher, J.; Tsallis, C.; Bunde, A.

2011-09-01

We consider 16 representative financial records (stocks, indices, commodities, and exchange rates) and study the distribution PQ(r) of the interoccurrence times r between daily losses below negative thresholds -Q, for fixed mean interoccurrence time RQ. We find that in all cases, PQ(r) follows the form PQ(r)~1/[(1+(q- 1)βr]1/(q-1), where β and q are universal constants that depend only on RQ, but not on a specific asset. While β depends only slightly on RQ, the q-value increases logarithmically with RQ, q=1+q0 ln(RQ/2), such that for RQ→2, PQ(r) approaches a simple exponential, PQ(r)cong2-r. The fact that PQ does not scale with RQ is due to the multifractality of the financial markets. The analytic form of PQ allows also to estimate both the risk function and the Value-at-Risk, and thus to improve the estimation of the financial risk.

CHARACTERIZING THE BROWN DWARF FORMATION CHANNELS FROM THE INITIAL MASS FUNCTION AND BINARY-STAR DYNAMICS

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

Thies, Ingo; Pflamm-Altenburg, Jan; Kroupa, Pavel

2015-02-10

The stellar initial mass function (IMF) is a key property of stellar populations. There is growing evidence that the classical star-formation mechanism by the direct cloud fragmentation process has difficulties reproducing the observed abundance and binary properties of brown dwarfs and very-low-mass stars. In particular, recent analytical derivations of the stellar IMF exhibit a deficit of brown dwarfs compared to observational data. Here we derive the residual mass function of brown dwarfs as an empirical measure of the brown dwarf deficiency in recent star-formation models with respect to observations and show that it is compatible with the substellar part ofmore » the Thies-Kroupa IMF and the mass function obtained by numerical simulations. We conclude that the existing models may be further improved by including a substellar correction term that accounts for additional formation channels like disk or filament fragmentation. The term ''peripheral fragmentation'' is introduced here for such additional formation channels. In addition, we present an updated analytical model of stellar and substellar binarity. The resulting binary fraction and the dynamically evolved companion mass-ratio distribution are in good agreement with observational data on stellar and very-low-mass binaries in the Galactic field, in clusters, and in dynamically unprocessed groups of stars if all stars form as binaries with stellar companions. Cautionary notes are given on the proper analysis of mass functions and the companion mass-ratio distribution and the interpretation of the results. The existence of accretion disks around young brown dwarfs does not imply that these form just like stars in direct fragmentation.« less

High-beta analytic equilibria in circular, elliptical, and D-shaped large aspect ratio axisymmetric configurations with poloidal and toroidal flows

NASA Astrophysics Data System (ADS)

López, O. E.; Guazzotto, L.

2017-03-01

The Grad-Shafranov-Bernoulli system of equations is a single fluid magnetohydrodynamical description of axisymmetric equilibria with mass flows. Using a variational perturbative approach [E. Hameiri, Phys. Plasmas 20, 024504 (2013)], analytic approximations for high-beta equilibria in circular, elliptical, and D-shaped cross sections in the high aspect ratio approximation are found, which include finite toroidal and poloidal flows. Assuming a polynomial dependence of the free functions on the poloidal flux, the equilibrium problem is reduced to an inhomogeneous Helmholtz partial differential equation (PDE) subject to homogeneous Dirichlet conditions. An application of the Green's function method leads to a closed form for the circular solution and to a series solution in terms of Mathieu functions for the elliptical case, which is valid for arbitrary elongations. To extend the elliptical solution to a D-shaped domain, a boundary perturbation in terms of the triangularity is used. A comparison with the code FLOW [L. Guazzotto et al., Phys. Plasmas 11(2), 604-614 (2004)] is presented for relevant scenarios.

Cascaded analysis of signal and noise propagation through a heterogeneous breast model.

PubMed

Mainprize, James G; Yaffe, Martin J

2010-10-01

The detectability of lesions in radiographic images can be impaired by patterns caused by the surrounding anatomic structures. The presence of such patterns is often referred to as anatomic noise. Others have previously extended signal and noise propagation theory to include variable background structure as an additional noise term and used in simulations for analysis by human and ideal observers. Here, the analytic forms of the signal and noise transfer are derived to obtain an exact expression for any input random distribution and the "power law" filter used to generate the texture of the tissue distribution. A cascaded analysis of propagation through a heterogeneous model is derived for x-ray projection through simulated heterogeneous backgrounds. This is achieved by considering transmission through the breast as a correlated amplification point process. The analytic forms of the cascaded analysis were compared to monoenergetic Monte Carlo simulations of x-ray propagation through power law structured backgrounds. As expected, it was found that although the quantum noise power component scales linearly with the x-ray signal, the anatomic noise will scale with the square of the x-ray signal. There was a good agreement between results obtained using analytic expressions for the noise power and those from Monte Carlo simulations for different background textures, random input functions, and x-ray fluence. Analytic equations for the signal and noise properties of heterogeneous backgrounds were derived. These may be used in direct analysis or as a tool to validate simulations in evaluating detectability.

Analytical excited state forces for the time-dependent density-functional tight-binding method.

PubMed

Heringer, D; Niehaus, T A; Wanko, M; Frauenheim, Th

2007-12-01

An analytical formulation for the geometrical derivatives of excitation energies within the time-dependent density-functional tight-binding (TD-DFTB) method is presented. The derivation is based on the auxiliary functional approach proposed in [Furche and Ahlrichs, J Chem Phys 2002, 117, 7433]. To validate the quality of the potential energy surfaces provided by the method, adiabatic excitation energies, excited state geometries, and harmonic vibrational frequencies were calculated for a test set of molecules in excited states of different symmetry and multiplicity. According to the results, the TD-DFTB scheme surpasses the performance of configuration interaction singles and the random phase approximation but has a lower quality than ab initio time-dependent density-functional theory. As a consequence of the special form of the approximations made in TD-DFTB, the scaling exponent of the method can be reduced to three, similar to the ground state. The low scaling prefactor and the satisfactory accuracy of the method makes TD-DFTB especially suitable for molecular dynamics simulations of dozens of atoms as well as for the computation of luminescence spectra of systems containing hundreds of atoms. (c) 2007 Wiley Periodicals, Inc.

Non-analytic terms from nested divergences in maximal supergravity

NASA Astrophysics Data System (ADS)

Basu, Anirban

2016-07-01

The {D}4{{ R }}4 and {D}6{{ R }}4 coefficient functions in the effective action of type II string theory compactified on T d contain terms of the form {{ E }}1{{ln}}{g}d and {{ E }}2{({{ln}}{g}d)}2 in specific dimensions, where g d is the T-duality invariant string coupling, and {{ E }}1 and {{ E }}2 are U-duality invariant coefficient functions. We derive these non-analytic terms from nested ultraviolet divergences in two and three loop maximal supergravity. For the {D}4{{ R }}4 coupling, the contribution involves {{ E }}{{ R }4}{{ln}}{g}d, while for the {D}6{{ R }}4 coupling, it involves {{ E }}{{ R }4}{{ln}}{g}d, {{ E }}{D2{{ R }}4}{({{ln}}{g}d)}2 and {{ E }}{D4{{ R }}4}{{ln}}{g}d; where {{ E }}{{ R }4}, {{ E }}{D2{{ R }}4} and {{ E }}{D4{{ R }}4} are the {{ R }}4, {D}2{{ R }}4 and {D}4{{ R }}4 coefficient functions respectively. The contribution from {{ E }}{D2{{ R }}4}, the coefficient function of an amplitude that vanishes onshell, arises from a two loop nested subdivergence of the three loop amplitude.

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

Zegadlo, Krzysztof B., E-mail: zegadlo@if.pw.edu.pl; Karpierz, Miroslaw A.; Wasak, Tomasz

We report results of the analysis for families of one-dimensional (1D) trapped solitons, created by competing self-focusing (SF) quintic and self-defocusing (SDF) cubic nonlinear terms. Two trapping potentials are considered, the harmonic-oscillator (HO) and delta-functional ones. The models apply to optical solitons in colloidal waveguides and other photonic media, and to matter-wave solitons in Bose-Einstein condensates loaded into a quasi-1D trap. For the HO potential, the results are obtained in an approximate form, using the variational and Thomas-Fermi approximations, and in a full numerical form, including the ground state and the first antisymmetric excited one. For the delta-functional attractive potential,more » the results are produced in a fully analytical form, and verified by means of numerical methods. Both exponentially localized solitons and weakly localized trapped modes are found for the delta-functional potential. The most essential conclusions concern the applicability of competing Vakhitov-Kolokolov (VK) and anti-VK criteria to the identification of the stability of solitons created under the action of the competing SF and SDF terms.« less

Stabilization of solitons under competing nonlinearities by external potentials

NASA Astrophysics Data System (ADS)

Zegadlo, Krzysztof B.; Wasak, Tomasz; Malomed, Boris A.; Karpierz, Miroslaw A.; Trippenbach, Marek

2014-12-01

We report results of the analysis for families of one-dimensional (1D) trapped solitons, created by competing self-focusing (SF) quintic and self-defocusing (SDF) cubic nonlinear terms. Two trapping potentials are considered, the harmonic-oscillator (HO) and delta-functional ones. The models apply to optical solitons in colloidal waveguides and other photonic media, and to matter-wave solitons in Bose-Einstein condensates loaded into a quasi-1D trap. For the HO potential, the results are obtained in an approximate form, using the variational and Thomas-Fermi approximations, and in a full numerical form, including the ground state and the first antisymmetric excited one. For the delta-functional attractive potential, the results are produced in a fully analytical form, and verified by means of numerical methods. Both exponentially localized solitons and weakly localized trapped modes are found for the delta-functional potential. The most essential conclusions concern the applicability of competing Vakhitov-Kolokolov (VK) and anti-VK criteria to the identification of the stability of solitons created under the action of the competing SF and SDF terms.

Of ens 'n' ands: observations on the phonetic make-up of a coordinator and its uses in talk-in-interaction.

PubMed

Barth-Weingarten, Dagmar

2012-03-01

In grammar books, the various functions of and as phrasal coordinator and clausal conjunction are treated as standard knowledge. In addition, studies on the uses of and in everyday talk-in-interaction have described its discourse-organizational functions on a more global level. In the phonetic literature, in turn, a range of phonetic forms of and have been listed. Yet, so far few studies have related the phonetic features of and to its function. This contribution surveys a range of phonetic forms of and in a corpus of private American English telephone conversations. It shows that the use of forms such as [ænd], [εn], or [en], among others, is not random but, in essence, correlates with the syntactic-pragmatic scope of and and the cognitive closeness of the items the and connects. This, in turn, allows the phonetic design of and to contribute to the organization of turn-taking. The findings presented are based on conversation-analytic and interactional-linguistic methodology, which includes quantitative analyses.

Nursing's ways of knowing and dual process theories of cognition.

PubMed

Paley, John; Cheyne, Helen; Dalgleish, Len; Duncan, Edward A S; Niven, Catherine A

2007-12-01

This paper is a comparison of nursing's patterns of knowing with the systems identified by cognitive science, and evaluates claims about the equal-status relation between scientific and non-scientific knowledge. Ever since Carper's seminal paper in 1978, it has been taken for granted in the nursing literature that there are ways of knowing, or patterns of knowing, that are not scientific. This idea has recently been used to argue that the concept of evidence, typically associated with evidence-based practice, is inappropriately restricted because it is identified exclusively with scientific research. The paper reviews literature in psychology which appears to draw a comparable distinction between rule-based, analytical cognitive processes and other forms of cognitive processing which are unconscious, holistic and intuitive. There is a convincing parallel between the 'patterns of knowing' distinction in nursing and the 'cognitive processing' distinction in psychology. However, there is an important difference in the way the relation between different forms of knowing (or cognitive processing) is depicted. In nursing, it is argued that the different patterns of knowing have equal status and weight. In cognitive science, it is suggested that the rule-based, analytical form of cognition has a supervisory and corrective function with respect to the other forms. Scientific reasoning and evidence-based knowledge have epistemological priority over the other forms of nursing knowledge. The implications of this claim for healthcare practice are briefly indicated.

Nonperturbative confinement in quantum chromodynamics. I. Study of an approximate equation of Mandelstam

NASA Astrophysics Data System (ADS)

Atkinson, D.; Drohm, J. K.; Johnson, P. W.; Stam, K.

1981-11-01

An approximated form of the Dyson-Schwinger equation for the gluon propagator in quarkless QCD is subjected to nonlinear functional and numerical analysis. It is found that solutions exist, and that these have a double pole at the origin of the square of the propagator momentum, together with an accumulation of soft branch points. This analytic structure is strongly suggestive of confinement by infrared slavery.

Development and study of a parallel algorithm of iteratively forming latent functionally-determined structures for classification and analysis of meteorological data

NASA Astrophysics Data System (ADS)

Sorokin, V. A.; Volkov, Yu V.; Sherstneva, A. I.; Botygin, I. A.

2016-11-01

This paper overviews a method of generating climate regions based on an analytic signal theory. When applied to atmospheric surface layer temperature data sets, the method allows forming climatic structures with the corresponding changes in the temperature to make conclusions on the uniformity of climate in an area and to trace the climate changes in time by analyzing the type group shifts. The algorithm is based on the fact that the frequency spectrum of the thermal oscillation process is narrow-banded and has only one mode for most weather stations. This allows using the analytic signal theory, causality conditions and introducing an oscillation phase. The annual component of the phase, being a linear function, was removed by the least squares method. The remaining phase fluctuations allow consistent studying of their coordinated behavior and timing, using the Pearson correlation coefficient for dependence evaluation. This study includes program experiments to evaluate the calculation efficiency in the phase grouping task. The paper also overviews some single-threaded and multi-threaded computing models. It is shown that the phase grouping algorithm for meteorological data can be parallelized and that a multi-threaded implementation leads to a 25-30% increase in the performance.

Differentiation of protonated aromatic regioisomers related to lignin by reactions with trimethylborate in a fourier-transform ion cyclotron resonance mass spectrometer

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

Somuramasami, J; Duan, P; Amundson, Lucas M

2011-04-06

Several lignin model compounds were examined to test whether gas-phase ion–molecule reactions of trimethylborate (TMB) in a FTICR can be used to differentiate the ortho-, meta-, and para-isomers of protonated aromatic compounds, such as those formed during degradation of lignin. All three regioisomers could be differentiated for methoxyphenols and hydroxyphenols. However, only the differentiation of the ortho-isomer from the meta- and para-isomers was possible for hydroxyacetophenones and hydroxybenzoic acids. Consideration of the previously reported proton affinities at all basic sites in the isomeric hydroxyphenols, and the calculated proton affinities at all basic sites in the three methoxyphenol isomers, revealed thatmore » the proton affinities of the analytes relative to that of TMB play an important role in determining whether and how they react with TMB. The loss of two methanol molecules (instead of one) from the adducts formed with TMB either during ion–molecule reactions, or during sustained-off resonance irradiated collision-activated dissociation of the ion–molecule reaction products, revealed the presence of two functionalities in almost all the isomers. This finding supports earlier results suggesting that TMB can be used to count the functionalities in unknown oxygen-containing analytes.« less

The roles of teachers' science talk in revealing language demands within diverse elementary school classrooms: a study of teaching heat and temperature in Singapore

NASA Astrophysics Data System (ADS)

Seah, Lay Hoon; Yore, Larry D.

2017-01-01

This study of three science teachers' lessons on heat and temperature seeks to characterise classroom talk that highlighted the ways language is used and to examine the nature of the language demands revealed in constructing, negotiating, arguing and communicating science ideas. The transcripts from the entire instructional units for these teachers' four culturally and linguistically diverse Grade 4 classes (10 years old) with English as the language of instruction constitute the data for this investigation. Analysis of these transcripts focused on teachers' talk that made explicit reference to the form or function of the language of science and led to the inductive development of the 'Attending to Language Demands in Science' analytical framework. This framework in turn revealed that the major foregrounding purposes of teachers' talk include labelling, explaining, differentiating, selecting and constructing. Further classification of the instances within these categories revealed the extensive and contextualised nature of the language demands. The results challenge the conventional assumption that basic literacy skills dominate over disciplinary literacy skills in primary school science. Potential uses of the analytical framework that could further expand our understanding of the forms, functions and demands of language used in elementary school science are also discussed.

Formulation of the linear model from the nonlinear simulation for the F18 HARV

NASA Technical Reports Server (NTRS)

Hall, Charles E., Jr.

1991-01-01

The F-18 HARV is a modified F-18 Aircraft which is capable of flying in the post-stall regime in order to achieve superagility. The onset of aerodynamic stall, and continued into the post-stall region, is characterized by nonlinearities in the aerodynamic coefficients. These aerodynamic coefficients are not expressed as analytic functions, but rather in the form of tabular data. The nonlinearities in the aerodynamic coefficients yield a nonlinear model of the aircraft's dynamics. Nonlinear system theory has made many advances, but this area is not sufficiently developed to allow its application to this problem, since many of the theorems are existance theorems and that the systems are composed of analytic functions. Thus, the feedback matrices and the state estimators are obtained from linear system theory techniques. It is important, in order to obtain the correct feedback matrices and state estimators, that the linear description of the nonlinear flight dynamics be as accurate as possible. A nonlinear simulation is run under the Advanced Continuous Simulation Language (ACSL). The ACSL simulation uses FORTRAN subroutines to interface to the look-up tables for the aerodynamic data. ACSL has commands to form the linear representation for the system. Other aspects of this investigation are discussed.

Advances in organic-inorganic hybrid sorbents for the extraction of organic and inorganic pollutants in different types of food and environmental samples.

PubMed

Ng, Nyuk-Ting; Kamaruddin, Amirah Farhan; Wan Ibrahim, Wan Aini; Sanagi, Mohd Marsin; Abdul Keyon, Aemi S

2018-01-01

The efficiency of the extraction and removal of pollutants from food and the environment has been an important issue in analytical science. By incorporating inorganic species into an organic matrix, a new material known as an organic-inorganic hybrid material is formed. As it possesses high selectivity, permeability, and mechanical and chemical stabilities, organic-inorganic hybrid materials constitute an emerging research field and have become popular to serve as sorbents in various separaton science methods. Here, we review recent significant advances in analytical solid-phase extraction employing organic-inorganic composite/nanocomposite sorbents for the extraction of organic and inorganic pollutants from various types of food and environmental matrices. The physicochemical characteristics, extraction properties, and analytical performances of sorbents are discussed; including morphology and surface characteristics, types of functional groups, interaction mechanism, selectivity and sensitivity, accuracy, and regeneration abilities. Organic-inorganic hybrid sorbents combined with extraction techniques are highly promising for sample preparation of various food and environmental matrixes with analytes at trace levels. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Success and failure of the plasma analogy for Laughlin states on a torus

NASA Astrophysics Data System (ADS)

Fremling, Mikael

2017-01-01

We investigate the nature of the plasma analogy for the Laughlin wave function on a torus describing the quantum Hall plateau at ν =\\frac{1}{q} . We first establish, as expected, that the plasma is screening if there are no short nontrivial paths around the torus. We also find that when one of the handles has a short circumference—i.e. the thin-torus limit—the plasma no longer screens. To quantify this we compute the normalization of the Laughlin state, both numerically and analytically. In the thin torus limit, the analytical form of the normalization simplify and we can reconstruct the normalization and analytically extend it back into the 2D regime. We find that there are geometry dependent corrections to the normalization, and this in turn implies that the plasma in the plasma analogy is not screening when in the thin torus limit. Despite the breaking of the plasma analogy in this limit, the analytical approximation is still a good description of the normalization for all tori, and also allows us to compute hall viscosity at intermediate thickness.

A Highly Flexible, Automated System Providing Reliable Sample Preparation in Element- and Structure-Specific Measurements.

PubMed

Vorberg, Ellen; Fleischer, Heidi; Junginger, Steffen; Liu, Hui; Stoll, Norbert; Thurow, Kerstin

2016-10-01

Life science areas require specific sample pretreatment to increase the concentration of the analytes and/or to convert the analytes into an appropriate form for the detection and separation systems. Various workstations are commercially available, allowing for automated biological sample pretreatment. Nevertheless, due to the required temperature, pressure, and volume conditions in typical element and structure-specific measurements, automated platforms are not suitable for analytical processes. Thus, the purpose of the presented investigation was the design, realization, and evaluation of an automated system ensuring high-precision sample preparation for a variety of analytical measurements. The developed system has to enable system adaption and high performance flexibility. Furthermore, the system has to be capable of dealing with the wide range of required vessels simultaneously, allowing for less cost and time-consuming process steps. However, the system's functionality has been confirmed in various validation sequences. Using element-specific measurements, the automated system was up to 25% more precise compared to the manual procedure and as precise as the manual procedure using structure-specific measurements. © 2015 Society for Laboratory Automation and Screening.

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

PubMed Central

Suzuki, Yoko; Noel, Jeffrey K.; Onuchic, José N.

2011-01-01

Much has been done to study the interplay between geometric and energetic effects on the protein folding energy landscape. Numerical techniques such as molecular dynamics simulations are able to maintain a precise geometrical representation of the protein. Analytical approaches, however, often focus on the energetic aspects of folding, including geometrical information only in an average way. Here, we investigate a semi-analytical expression of folding that explicitly includes geometrical effects. We consider a Hamiltonian corresponding to a Gaussian filament with structure-based interactions. The model captures local features of protein folding often averaged over by mean-field theories, for example, loop contact formation and excluded volume. We explore the thermodynamics and folding mechanisms of beta-hairpin and alpha-helical structures as functions of temperature and Q, the fraction of native contacts formed. Excluded volume is shown to be an important component of a protein Hamiltonian, since it both dominates the cooperativity of the folding transition and alters folding mechanisms. Understanding geometrical effects in analytical formulae will help illuminate the consequences of the approximations required for the study of larger proteins. PMID:21721664

Analytical solution for the normal emission portion of the averaged Yarkovsky-O'Keefe-Radzvieskii-Paddack coefficient for a single facet

NASA Astrophysics Data System (ADS)

Albuja, Antonella A.; Scheeres, Daniel J.

2015-02-01

The Yarkovsky-O'Keefe-Radzvieskii-Paddack (YORP) effect has been well studied for asteroids. This paper develops an analytic solution to find the normal emission YORP component for a single facet. The solution presented here does not account for self-shadowing or self-heating. The YORP coefficient for all facets can be summed together to find the total coefficient of the asteroid. The normal emission component of YORP has been shown to be the most important for asteroids and it directly affects the rate of change of the asteroid's spin period. The analytical solution found is a sole function of the facet's geometry and the obliquity of the asteroid. This solution is universal for any facet and its orientation. The behaviour of the coefficient is analysed with this analytical solution. The closed-form solution is used to find the total YORP coefficient for the asteroids Apollo and 1998 ML14 whose shape models are composed of different numbers of facets. The results are then compared to published results and those obtained through numerical quadrature for validation.

Design considerations of a hollow microneedle-optofluidic biosensing platform incorporating enzyme-linked assays

NASA Astrophysics Data System (ADS)

Ranamukhaarachchi, Sahan A.; Padeste, Celestino; Häfeli, Urs O.; Stoeber, Boris; Cadarso, Victor J.

2018-02-01

A hollow metallic microneedle is integrated with microfluidics and photonic components to form a microneedle-optofluidic biosensor suitable for therapeutic drug monitoring (TDM) in biological fluids, like interstitial fluid, that can be collected in a painless and minimally-invasive manner. The microneedle inner lumen surface is bio-functionalized to trap and bind target analytes on-site in a sample volume as small as 0.6 nl, and houses an enzyme-linked assay on its 0.06 mm2 wall. The optofluidic components are designed to rapidly quantify target analytes present in the sample and collected in the microneedle using a simple and sensitive absorbance scheme. This contribution describes how the biosensor components were optimized to detect in vitro streptavidin-horseradish peroxidase (Sav-HRP) as a model analyte over a large detection range (0-7.21 µM) and a very low limit of detection (60.2 nM). This biosensor utilizes the lowest analyte volume reported for TDM with microneedle technology, and presents significant avenues to improve current TDM methods for patients, by potentially eliminating blood draws for several drug candidates.

Method of and apparatus for determining the similarity of a biological analyte from a model constructed from known biological fluids

DOEpatents

Robinson, Mark R.; Ward, Kenneth J.; Eaton, Robert P.; Haaland, David M.

1990-01-01

The characteristics of a biological fluid sample having an analyte are determined from a model constructed from plural known biological fluid samples. The model is a function of the concentration of materials in the known fluid samples as a function of absorption of wideband infrared energy. The wideband infrared energy is coupled to the analyte containing sample so there is differential absorption of the infrared energy as a function of the wavelength of the wideband infrared energy incident on the analyte containing sample. The differential absorption causes intensity variations of the infrared energy incident on the analyte containing sample as a function of sample wavelength of the energy, and concentration of the unknown analyte is determined from the thus-derived intensity variations of the infrared energy as a function of wavelength from the model absorption versus wavelength function.

The importance of functional form in optimal control solutions of problems in population dynamics

USGS Publications Warehouse

Runge, M.C.; Johnson, F.A.

2002-01-01

Optimal control theory is finding increased application in both theoretical and applied ecology, and it is a central element of adaptive resource management. One of the steps in an adaptive management process is to develop alternative models of system dynamics, models that are all reasonable in light of available data, but that differ substantially in their implications for optimal control of the resource. We explored how the form of the recruitment and survival functions in a general population model for ducks affected the patterns in the optimal harvest strategy, using a combination of analytical, numerical, and simulation techniques. We compared three relationships between recruitment and population density (linear, exponential, and hyperbolic) and three relationships between survival during the nonharvest season and population density (constant, logistic, and one related to the compensatory harvest mortality hypothesis). We found that the form of the component functions had a dramatic influence on the optimal harvest strategy and the ultimate equilibrium state of the system. For instance, while it is commonly assumed that a compensatory hypothesis leads to higher optimal harvest rates than an additive hypothesis, we found this to depend on the form of the recruitment function, in part because of differences in the optimal steady-state population density. This work has strong direct consequences for those developing alternative models to describe harvested systems, but it is relevant to a larger class of problems applying optimal control at the population level. Often, different functional forms will not be statistically distinguishable in the range of the data. Nevertheless, differences between the functions outside the range of the data can have an important impact on the optimal harvest strategy. Thus, development of alternative models by identifying a single functional form, then choosing different parameter combinations from extremes on the likelihood profile may end up producing alternatives that do not differ as importantly as if different functional forms had been used. We recommend that biological knowledge be used to bracket a range of possible functional forms, and robustness of conclusions be checked over this range.

Density- and wavefunction-normalized Cartesian spherical harmonics for l ≤ 20

DOE PAGES

Michael, J. Robert; Volkov, Anatoliy

2015-03-01

The widely used pseudoatom formalism in experimental X-ray charge-density studies makes use of real spherical harmonics when describing the angular component of aspherical deformations of the atomic electron density in molecules and crystals. The analytical form of the density-normalized Cartesian spherical harmonic functions for up to l ≤ 7 and the corresponding normalization coefficients were reported previously by Paturle & Coppens. It was shown that the analytical form for normalization coefficients is available primarily forl ≤ 4. Only in very special cases it is possible to derive an analytical representation of the normalization coefficients for 4 < l ≤ 7.more » In most cases for l > 4 the density normalization coefficients were calculated numerically to within seven significant figures. In this study we review the literature on the density-normalized spherical harmonics, clarify the existing notations, use the Paturle–Coppens method in the Wolfram Mathematicasoftware to derive the Cartesian spherical harmonics for l ≤ 20 and determine the density normalization coefficients to 35 significant figures, and computer-generate a Fortran90 code. The article primarily targets researchers who work in the field of experimental X-ray electron density, but may be of some use to all who are interested in Cartesian spherical harmonics.« less

Monoenergetic ion acceleration and Rayleigh-Taylor instability of the composite target irradiated by the laser pulse

NASA Astrophysics Data System (ADS)

Khudik, Vladimir; Yi, S. Austin; Shvets, Gennady

2012-10-01

Acceleration of ions in the two-specie composite target irradiated by a circularly polarized laser pulse is studied analytically and via particle-in-cell (PIC) simulations. A self-consistent analytical model of the composite target is developed. In this model, target parameters are stationary in the center of mass of the system: heavy and light ions are completely separated from each other and form two layers, while electrons are bouncing in the potential well formed by the laser ponderomotive and electrostatic potentials. They are distributed in the direction of acceleration by the Boltzmann law and over velocities by the Maxwell-Juttner law. The laser pulse interacts directly only with electrons in a thin sheath layer, and these electrons transfer the laser pressure to the target ions. In the fluid approximation it is shown, the composite target is still susceptible to the Rayleigh-Taylor instability [1]. Using PIC simulations we found the growth rate of initially seeded perturbations as a function of their wavenumber for different composite target parameters and compare it with analytical results. Useful scaling laws between this rate and laser pulse pressure and target parameters are discussed.[4pt] [1] T.P. Yu, A. Pukhov, G. Shvets, M. Chen, T. H. Ratliff, S. A. Yi, and V. Khudik, Phys. Plasmas, 18, 043110 (2011).

Development of a point-kinetic verification scheme for nuclear reactor applications

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

Demazière, C., E-mail: demaz@chalmers.se; Dykin, V.; Jareteg, K.

In this paper, a new method that can be used for checking the proper implementation of time- or frequency-dependent neutron transport models and for verifying their ability to recover some basic reactor physics properties is proposed. This method makes use of the application of a stationary perturbation to the system at a given frequency and extraction of the point-kinetic component of the system response. Even for strongly heterogeneous systems for which an analytical solution does not exist, the point-kinetic component follows, as a function of frequency, a simple analytical form. The comparison between the extracted point-kinetic component and its expectedmore » analytical form provides an opportunity to verify and validate neutron transport solvers. The proposed method is tested on two diffusion-based codes, one working in the time domain and the other working in the frequency domain. As long as the applied perturbation has a non-zero reactivity effect, it is demonstrated that the method can be successfully applied to verify and validate time- or frequency-dependent neutron transport solvers. Although the method is demonstrated in the present paper in a diffusion theory framework, higher order neutron transport methods could be verified based on the same principles.« less

Systems and methods for laser assisted sample transfer to solution for chemical analysis

DOEpatents

Van Berkel, Gary J.; Kertesz, Vilmos; Ovchinnikova, Olga S.

2014-06-03

Systems and methods are described for laser ablation of an analyte from a specimen and capturing of the analyte in a dispensed solvent to form a testing solution. A solvent dispensing and extraction system can form a liquid microjunction with the specimen. The solvent dispensing and extraction system can include a surface sampling probe. The laser beam can be directed through the surface sampling probe. The surface sampling probe can also serve as an atomic force microscopy probe. The surface sampling probe can form a seal with the specimen. The testing solution including the analyte can then be analyzed using an analytical instrument or undergo further processing.

Systems and methods for laser assisted sample transfer to solution for chemical analysis

DOEpatents

Van Berkel, Gary J.; Kertesz, Vilmos; Ovchinnikova, Olga S.

2015-09-29

Systems and methods are described for laser ablation of an analyte from a specimen and capturing of the analyte in a dispensed solvent to form a testing solution. A solvent dispensing and extraction system can form a liquid microjunction with the specimen. The solvent dispensing and extraction system can include a surface sampling probe. The laser beam can be directed through the surface sampling probe. The surface sampling probe can also serve as an atomic force microscopy probe. The surface sampling probe can form a seal with the specimen. The testing solution including the analyte can then be analyzed using an analytical instrument or undergo further processing.

Systems and methods for laser assisted sample transfer to solution for chemical analysis

DOEpatents

Van Berkel, Gary J; Kertesz, Vilmos; Ovchinnikova, Olga S

2013-08-27

Systems and methods are described for laser ablation of an analyte from a specimen and capturing of the analyte in a dispensed solvent to form a testing solution. A solvent dispensing and extraction system can form a liquid microjunction with the specimen. The solvent dispensing and extraction system can include a surface sampling probe. The laser beam can be directed through the surface sampling probe. The surface sampling probe can also serve as an atomic force microscopy probe. The surface sampling probe can form a seal with the specimen. The testing solution including the analyte can then be analyzed using an analytical instrument or undergo further processing.

Negative effective mass in acoustic metamaterial with nonlinear mass-in-mass subsystems

NASA Astrophysics Data System (ADS)

Cveticanin, L.; Zukovic, M.

2017-10-01

In this paper the dynamics of the nonlinear mass-in-mass system as the basic subsystem of the acoustic metamaterial is investigated. The excitation of the system is in the form of the Jacobi elliptic function. The corresponding model to this forcing is the mass-in-mass system with cubic nonlinearity of the Duffing type. Mathematical model of the motion is a system of two coupled strong nonlinear and nonhomogeneous second order differential equations. Particular solution to the system is obtained. The analytical solution of the problem is based on the simple and double integral of the cosine Jacobi function. In the paper the integrals are given in the form of series of trigonometric functions. These results are new one. After some modification the simplified solution in the first approximation is obtained. The result is convenient for discussion. Conditions for elimination of the motion of the mass 1 by connection of the nonlinear dynamic absorber (mass - spring system) are defined. In the consideration the effective mass ratio is introduced in the nonlinear mass-in-mass system. Negative effective mass ratio gives the absorption of vibrations with certain frequencies. The advantage of the nonlinear subunit in comparison to the linear one is that the frequency gap is significantly wider. Nevertheless, it has to be mentioned that the amplitude of vibration differs from zero for a small value. In the paper the analytical results are compared with numerical one and are in agreement.

Scope of Gradient and Genetic Algorithms in Multivariable Function Optimization

NASA Technical Reports Server (NTRS)

Shaykhian, Gholam Ali; Sen, S. K.

2007-01-01

Global optimization of a multivariable function - constrained by bounds specified on each variable and also unconstrained - is an important problem with several real world applications. Deterministic methods such as the gradient algorithms as well as the randomized methods such as the genetic algorithms may be employed to solve these problems. In fact, there are optimization problems where a genetic algorithm/an evolutionary approach is preferable at least from the quality (accuracy) of the results point of view. From cost (complexity) point of view, both gradient and genetic approaches are usually polynomial-time; there are no serious differences in this regard, i.e., the computational complexity point of view. However, for certain types of problems, such as those with unacceptably erroneous numerical partial derivatives and those with physically amplified analytical partial derivatives whose numerical evaluation involves undesirable errors and/or is messy, a genetic (stochastic) approach should be a better choice. We have presented here the pros and cons of both the approaches so that the concerned reader/user can decide which approach is most suited for the problem at hand. Also for the function which is known in a tabular form, instead of an analytical form, as is often the case in an experimental environment, we attempt to provide an insight into the approaches focusing our attention toward accuracy. Such an insight will help one to decide which method, out of several available methods, should be employed to obtain the best (least error) output. *

Peculiarities of Forming a Multiband Transmission Function Based on Multifrequency Acousto-Optic Diffraction

NASA Astrophysics Data System (ADS)

Proklov, V. V.; Rezvov, Yu. G.

2018-01-01

An analytical solution for the transmission function of noncoherent wideband radiation is obtained under acousto-optic (AO) filtering using a discrete set of monochromatic AO waves with a small spectral overlap. We studied characteristics of the AO transformation of a continuous spectrum of noncoherent radiation into a given set of discrete narrow bands of spectral transmission by excitation of a discrete set of sound frequencies. We carried out the analysis of transmission functions of individual channels taking into account a partial overlap of their spectra and possible intermodulation distortions. It is shown that a stationary value of the root-mean-square light power is found at the electronic output due to the photoelectric transformation and detecting diffracted light. Based on this, a necessary stationary, multiband, and nearly equidistant transmission function of a device can be formed by using a relevant spectrum of acoustic excitation. Peculiarities of this way of forming the multiband transmission function are revealed: the limitation of diffraction efficiency for an individual channel, the possibility of decoupling side lobes of adjacent channels, etc. A multiband acousto-optic filter (MAOF) was simulated that was based on a paratellurite monocrystal (TeO2), which was previously used for experimental optical encoding. The theoretical and experimental results are in gratifying agreement.

Scaling and percolation in the small-world network model

NASA Astrophysics Data System (ADS)

Newman, M. E. J.; Watts, D. J.

1999-12-01

In this paper we study the small-world network model of Watts and Strogatz, which mimics some aspects of the structure of networks of social interactions. We argue that there is one nontrivial length-scale in the model, analogous to the correlation length in other systems, which is well-defined in the limit of infinite system size and which diverges continuously as the randomness in the network tends to zero, giving a normal critical point in this limit. This length-scale governs the crossover from large- to small-world behavior in the model, as well as the number of vertices in a neighborhood of given radius on the network. We derive the value of the single critical exponent controlling behavior in the critical region and the finite size scaling form for the average vertex-vertex distance on the network, and, using series expansion and Padé approximants, find an approximate analytic form for the scaling function. We calculate the effective dimension of small-world graphs and show that this dimension varies as a function of the length-scale on which it is measured, in a manner reminiscent of multifractals. We also study the problem of site percolation on small-world networks as a simple model of disease propagation, and derive an approximate expression for the percolation probability at which a giant component of connected vertices first forms (in epidemiological terms, the point at which an epidemic occurs). The typical cluster radius satisfies the expected finite size scaling form with a cluster size exponent close to that for a random graph. All our analytic results are confirmed by extensive numerical simulations of the model.

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

NASA Astrophysics Data System (ADS)

Bubin, Sergiy; Adamowicz, Ludwik

2008-03-01

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

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

PubMed

Bubin, Sergiy; Adamowicz, Ludwik

2008-03-21

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

The shape parameter and its modification for defining coastal profiles

NASA Astrophysics Data System (ADS)

Türker, Umut; Kabdaşli, M. Sedat

2009-03-01

The shape parameter is important for the theoretical description of the sandy coastal profiles. This parameter has previously been defined as a function of the sediment-settling velocity. However, the settling velocity cannot be characterized over a wide range of sediment grains. This, in turn, limits the calculation of the shape parameter over a wide range. This paper provides a simpler and faster analytical equation to describe the shape parameter. The validity of the equation has been tested and compared with the previously estimated values given in both graphical and tabular forms. The results of this study indicate that the analytical solutions of the shape parameter improved the usability of profile better than graphical solutions, predicting better results both at the surf zone and offshore.

Displacement potential solution of a guided deep beam of composite materials under symmetric three-point bending

NASA Astrophysics Data System (ADS)

Rahman, M. Muzibur; Ahmad, S. Reaz

2017-12-01

An analytical investigation of elastic fields for a guided deep beam of orthotropic composite material having three point symmetric bending is carried out using displacement potential boundary modeling approach. Here, the formulation is developed as a single function of space variables defined in terms of displacement components, which has to satisfy the mixed type of boundary conditions. The relevant displacement and stress components are derived into infinite series using Fourier integral along with suitable polynomials coincided with boundary conditions. The results are presented mainly in the form of graphs and verified with finite element solutions using ANSYS. This study shows that the analytical and numerical solutions are in good agreement and thus enhances reliability of the displacement potential approach.

Analytical bond order potential for simulations of BeO 1D and 2D nanostructures and plasma-surface interactions

NASA Astrophysics Data System (ADS)

Byggmästar, J.; Hodille, E. A.; Ferro, Y.; Nordlund, K.

2018-04-01

An analytical interatomic bond order potential for the Be-O system is presented. The potential is fitted and compared to a large database of bulk BeO and point defect properties obtained using density functional theory. Its main applications include simulations of plasma-surface interactions involving oxygen or oxide layers on beryllium, as well as simulations of BeO nanotubes and nanosheets. We apply the potential in a study of oxygen irradiation of Be surfaces, and observe the early stages of an oxide layer forming on the Be surface. Predicted thermal and elastic properties of BeO nanotubes and nanosheets are simulated and compared with published ab initio data.

Lump solutions to nonlinear partial differential equations via Hirota bilinear forms

NASA Astrophysics Data System (ADS)

Ma, Wen-Xiu; Zhou, Yuan

2018-02-01

Lump solutions are analytical rational function solutions localized in all directions in space. We analyze a class of lump solutions, generated from quadratic functions, to nonlinear partial differential equations. The basis of success is the Hirota bilinear formulation and the primary object is the class of positive multivariate quadratic functions. A complete determination of quadratic functions positive in space and time is given, and positive quadratic functions are characterized as sums of squares of linear functions. Necessary and sufficient conditions for positive quadratic functions to solve Hirota bilinear equations are presented, and such polynomial solutions yield lump solutions to nonlinear partial differential equations under the dependent variable transformations u = 2(ln ⁡ f) x and u = 2(ln ⁡ f) xx, where x is one spatial variable. Applications are made for a few generalized KP and BKP equations.

Helium Purge Flow Prevention of Atmospheric Contamination of the Cryogenically Cooled Optics of Orbiting Infrared Telescopes: Calculation of He-O Differential Cross Section,

DTIC Science & Technology

1981-06-05

interactions. Aquilanti and coworkers were able to obtain two analytic forms for the interatomic potential --a Lennard - Jones (12, 6) and an exp(a, 6) function...Sec. UI.D 38 ences between the 3R and 3E- potential functions which described the interac- tions of ground-state oxygen and helium atoms. Instead, for...AO-AIOI 152 AEROSPACE CORP EL SEUMOO CA CHEMISTRY AND PHYSICS LAD r/6 17 HELIUM PLRE FLOW PREVENTION OF ATMOSPHERIC CONTAMINATION OF TAR fTCiO )JN81

Contact problem on indentation of an elastic half-plane with an inhomogeneous coating by a flat punch in the presence of tangential stresses on a surface

NASA Astrophysics Data System (ADS)

Volkov, Sergei S.; Vasiliev, Andrey S.; Aizikovich, Sergei M.; Sadyrin, Evgeniy V.

2018-05-01

Indentation of an elastic half-space with functionally graded coating by a rigid flat punch is studied. The half-plane is additionally subjected to distributed tangential stresses. Tangential stresses are represented in a form of Fourier series. The problem is reduced to the solution of two dual integral equations over even and odd functions describing distribution of unknown normal contact stresses. The solutions of these dual integral equations are constructed by the bilateral asymptotic method. Approximated analytical expressions for contact normal stresses are provided.

A lattice Boltzmann model with an amending function for simulating nonlinear partial differential equations

NASA Astrophysics Data System (ADS)

Chen, Lin-Jie; Ma, Chang-Feng

2010-01-01

This paper proposes a lattice Boltzmann model with an amending function for one-dimensional nonlinear partial differential equations (NPDEs) in the form ut + αuux + βunux + γuxx + δuxxx + ζuxxxx = 0. This model is different from existing models because it lets the time step be equivalent to the square of the space step and derives higher accuracy and nonlinear terms in NPDEs. With the Chapman-Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. The numerical results agree well with the analytical solutions.

Unusual analyte-matrix adduct ions and mechanism of their formation in MALDI TOF MS of benzene-1,3,5-tricarboxamide and urea compounds.

PubMed

Lou, Xianwen; Fransen, Michel; Stals, Patrick J M; Mes, Tristan; Bovee, Ralf; van Dongen, Joost J L; Meijer, E W

2013-09-01

Analyte-matrix adducts are normally absent under typical matrix assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI TOF MS) conditions. Interestingly, though, in the analysis of several types of organic compounds synthesized in our laboratory, analyte-matrix adduct ion peaks were always recorded when common MALDI matrices such as 4-hydroxy-α-cyanocinnamic acid (CHCA) were used. These compounds are mainly those with a benzene-1,3,5-tricarboxamide (BTA) or urea moiety, which are important building blocks to make new functional supramolecular materials. The possible mechanism of the adduct formation was investigated. A shared feature of the compounds studied is that they can form intermolecular hydrogen bonding with matrices like CHCA. The intermolecular hydrogen bonding will make the association between analyte ions and matrix molecules stronger. As a result, the analyte ions and matrix molecules in MALDI clusters will become more difficult to be separated from each other. Furthermore, it was found that analyte ions were mainly adducted with matrix salts, which is probably due to the much lower volatility of the salts compared with that of their corresponding matrix acids. It seems that the analyte-matrix adduct formation for our compounds are caused by the incomplete evaporation of matrix molecules from the MALDI clusters because of the combined effects of enhanced intermolecular interaction between analyte-matrix and of the low volatility of matrix salts. Based on these findings, strategies to suppress the analyte-matrix adduction are briefly discussed. In return, the positive results of using these strategies support the proposed mechanism of the analyte-matrix adduct formation.

SU-G-206-06: Analytic Dose Function for CT Scans in Infinite Cylinders as a Function of Scan Length and Cylinder Radius

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

Bakalyar, D; Feng, W; McKenney, S

Purpose: The radiation dose absorbed at a particular radius ρ within the central plane of a long cylinder following a CT scan is a function of the length of the scan L and the cylinder radius R along with kVp and cylinder composition. An analytic function was created that that not only expresses these dependencies but is integrable in closed form over the area of the central plane. This feature facilitates explicit calculation of the planar average dose. The “approach to equilibrium” h(L) discussed in the TG111 report is seamlessly included in this function. Methods: For a cylindrically symmetric radiationmore » field, Monte Carlo calculations were performed to compute the dose distribution to long polyethylene cylinders for scans of varying L for cylinders ranging in radius from 5 to 20 cm. The function was developed from the resultant Monte Carlo data. In addition, the function was successfully fit to data taken from measurements on the 30 cm diameter ICRU/TG200 phantom using a real-time dosimeter. Results: Symmetry and continuity dictate a local extremum at the center which is a minimum for the larger sizes. There are competing effects as the beam penetrates the cylinder from the outside: attenuation, resulting in a decrease; scatter, abruptly increasing at the circumference. This competition may result in an absolute maximum between the center and outer edge leading to a “gull wing” shape for the radial dependence. For the smallest cylinders, scatter may dominate to the extent that there is an absolute maximum at the center. Conclusion: An integrable, analytic function has been developed that provides the radial dependency of dose for the central plane of a scan of length L for cylinders of varying diameter. Equivalently, we have developed h(L,R,ρ).« less

Outage Probability of MRC for κ-μ Shadowed Fading Channels under Co-Channel Interference.

PubMed

Chen, Changfang; Shu, Minglei; Wang, Yinglong; Yang, Ming; Zhang, Chongqing

2016-01-01

In this paper, exact closed-form expressions are derived for the outage probability (OP) of the maximal ratio combining (MRC) scheme in the κ-μ shadowed fading channels, in which both the independent and correlated shadowing components are considered. The scenario assumes the received desired signals are corrupted by the independent Rayleigh-faded co-channel interference (CCI) and background white Gaussian noise. To this end, first, the probability density function (PDF) of the κ-μ shadowed fading distribution is obtained in the form of a power series. Then the incomplete generalized moment-generating function (IG-MGF) of the received signal-to-interference-plus-noise ratio (SINR) is derived in the closed form. By using the IG-MGF results, closed-form expressions for the OP of MRC scheme are obtained over the κ-μ shadowed fading channels. Simulation results are included to validate the correctness of the analytical derivations. These new statistical results can be applied to the modeling and analysis of several wireless communication systems, such as body centric communications.

Outage Probability of MRC for κ-μ Shadowed Fading Channels under Co-Channel Interference

PubMed Central

Chen, Changfang; Shu, Minglei; Wang, Yinglong; Yang, Ming; Zhang, Chongqing

2016-01-01

In this paper, exact closed-form expressions are derived for the outage probability (OP) of the maximal ratio combining (MRC) scheme in the κ-μ shadowed fading channels, in which both the independent and correlated shadowing components are considered. The scenario assumes the received desired signals are corrupted by the independent Rayleigh-faded co-channel interference (CCI) and background white Gaussian noise. To this end, first, the probability density function (PDF) of the κ-μ shadowed fading distribution is obtained in the form of a power series. Then the incomplete generalized moment-generating function (IG-MGF) of the received signal-to-interference-plus-noise ratio (SINR) is derived in the closed form. By using the IG-MGF results, closed-form expressions for the OP of MRC scheme are obtained over the κ-μ shadowed fading channels. Simulation results are included to validate the correctness of the analytical derivations. These new statistical results can be applied to the modeling and analysis of several wireless communication systems, such as body centric communications. PMID:27851817

A class of simple bouncing and late-time accelerating cosmologies in f(R) gravity

NASA Astrophysics Data System (ADS)

Kuiroukidis, A.

We consider the field equations for a flat FRW cosmological model, given by Eq. (??), in an a priori generic f(R) gravity model and cast them into a, completely normalized and dimensionless, system of ODEs for the scale factor and the function f(R), with respect to the scalar curvature R. It is shown that under reasonable assumptions, namely for power-law functional form for the f(R) gravity model, one can produce simple analytical and numerical solutions describing bouncing cosmological models where in addition there are late-time accelerating. The power-law form for the f(R) gravity model is typically considered in the literature as the most concrete, reasonable, practical and viable assumption [see S. D. Odintsov and V. K. Oikonomou, Phys. Rev. D 90 (2014) 124083, arXiv:1410.8183 [gr-qc

A generic analytical foot rollover model for predicting translational ankle kinematics in gait simulation studies.

PubMed

Ren, Lei; Howard, David; Ren, Luquan; Nester, Chris; Tian, Limei

2010-01-19

The objective of this paper is to develop an analytical framework to representing the ankle-foot kinematics by modelling the foot as a rollover rocker, which cannot only be used as a generic tool for general gait simulation but also allows for case-specific modelling if required. Previously, the rollover models used in gait simulation have often been based on specific functions that have usually been of a simple form. In contrast, the analytical model described here is in a general form that the effective foot rollover shape can be represented by any polar function rho=rho(phi). Furthermore, a normalized generic foot rollover model has been established based on a normative foot rollover shape dataset of 12 normal healthy subjects. To evaluate model accuracy, the predicted ankle motions and the centre of pressure (CoP) were compared with measurement data for both subject-specific and general cases. The results demonstrated that the ankle joint motions in both vertical and horizontal directions (relative RMSE approximately 10%) and CoP (relative RMSE approximately 15% for most of the subjects) are accurately predicted over most of the stance phase (from 10% to 90% of stance). However, we found that the foot cannot be very accurately represented by a rollover model just after heel strike (HS) and just before toe off (TO), probably due to shear deformation of foot plantar tissues (ankle motion can occur without any foot rotation). The proposed foot rollover model can be used in both inverse and forward dynamics gait simulation studies and may also find applications in rehabilitation engineering. Copyright 2009 Elsevier Ltd. All rights reserved.

Optically controlled electrophoresis with a photoconductive substrate

NASA Astrophysics Data System (ADS)

Inami, Wataru; Nagashima, Taiki; Kawata, Yoshimasa

2018-05-01

A photoconductive substrate is used to perform electrophoresis. Light-induced micro-particle flow manipulation is demonstrated without using a fabricated flow channel. The path along which the particles were moved was formed by an illuminated light pattern on the substrate. Because the substrate conductivity and electric field distribution can be modified by light illumination, the forces acting on the particles can be controlled. This technique has potential applications as a high functionality analytical device.

Exact linearized Coulomb collision operator in the moment expansion

DOE PAGES

Ji, Jeong -Young; Held, Eric D.

2006-10-05

In the moment expansion, the Rosenbluth potentials, the linearized Coulomb collision operators, and the moments of the collision operators are analytically calculated for any moment. The explicit calculation of Rosenbluth potentials converts the integro-differential form of the Coulomb collision operator into a differential operator, which enables one to express the collision operator in a simple closed form for any arbitrary mass and temperature ratios. In addition, it is shown that gyrophase averaging the collision operator acting on arbitrary distribution functions is the same as the collision operator acting on the corresponding gyrophase averaged distribution functions. The moments of the collisionmore » operator are linear combinations of the fluid moments with collision coefficients parametrized by mass and temperature ratios. Furthermore, useful forms involving the small mass-ratio approximation are easily found since the collision operators and their moments are expressed in terms of the mass ratio. As an application, the general moment equations are explicitly written and the higher order heat flux equation is derived.« less

Investigating tautomeric polymorphism in crystalline anthranilic acid using terahertz spectroscopy and solid-state density functional theory.

PubMed

Delaney, Sean P; Witko, Ewelina M; Smith, Tiffany M; Korter, Timothy M

2012-08-02

Terahertz spectroscopy is sensitive to the interactions between molecules in the solid-state and recently has emerged as a new analytical tool for investigating polymorphism. Here, this technique is applied for the first time to the phenomenon of tautomeric polymorphism where the crystal structures of anthranilic acid (2-aminobenzoic acid) have been investigated. Three polymorphs of anthranilic acid (denoted Forms I, II and III) were studied using terahertz spectroscopy and the vibrational modes and relative polymorph stabilities analyzed using solid-state density functional theory calculations augmented with London dispersion force corrections. Form I consists of both neutral and zwitterionic molecules and was found to be the most stable polymorph as compared to Forms II and III (both containing only neutral molecules). The simulations suggest that a balance between steric interactions and electrostatic forces is responsible for the favoring of the mixed neutral/zwitterion solid over the all neutral or all zwitterion crystalline arrangements.

Characterizing nonconstant instrumental variance in emerging miniaturized analytical techniques.

PubMed

Noblitt, Scott D; Berg, Kathleen E; Cate, David M; Henry, Charles S

2016-04-07

Measurement variance is a crucial aspect of quantitative chemical analysis. Variance directly affects important analytical figures of merit, including detection limit, quantitation limit, and confidence intervals. Most reported analyses for emerging analytical techniques implicitly assume constant variance (homoskedasticity) by using unweighted regression calibrations. Despite the assumption of constant variance, it is known that most instruments exhibit heteroskedasticity, where variance changes with signal intensity. Ignoring nonconstant variance results in suboptimal calibrations, invalid uncertainty estimates, and incorrect detection limits. Three techniques where homoskedasticity is often assumed were covered in this work to evaluate if heteroskedasticity had a significant quantitative impact-naked-eye, distance-based detection using paper-based analytical devices (PADs), cathodic stripping voltammetry (CSV) with disposable carbon-ink electrode devices, and microchip electrophoresis (MCE) with conductivity detection. Despite these techniques representing a wide range of chemistries and precision, heteroskedastic behavior was confirmed for each. The general variance forms were analyzed, and recommendations for accounting for nonconstant variance discussed. Monte Carlo simulations of instrument responses were performed to quantify the benefits of weighted regression, and the sensitivity to uncertainty in the variance function was tested. Results show that heteroskedasticity should be considered during development of new techniques; even moderate uncertainty (30%) in the variance function still results in weighted regression outperforming unweighted regressions. We recommend utilizing the power model of variance because it is easy to apply, requires little additional experimentation, and produces higher-precision results and more reliable uncertainty estimates than assuming homoskedasticity. Copyright © 2016 Elsevier B.V. All rights reserved.

Analyticity without Differentiability

ERIC Educational Resources Information Center

Kirillova, Evgenia; Spindler, Karlheinz

2008-01-01

In this article we derive all salient properties of analytic functions, including the analytic version of the inverse function theorem, using only the most elementary convergence properties of series. Not even the notion of differentiability is required to do so. Instead, analytical arguments are replaced by combinatorial arguments exhibiting…

Culture-Sensitive Functional Analytic Psychotherapy

ERIC Educational Resources Information Center

Vandenberghe, L.

2008-01-01

Functional analytic psychotherapy (FAP) is defined as behavior-analytically conceptualized talk therapy. In contrast to the technique-oriented educational format of cognitive behavior therapy and the use of structural mediational models, FAP depends on the functional analysis of the moment-to-moment stream of interactions between client and…

A new approach to analytic, non-perturbative and gauge-invariant QCD

NASA Astrophysics Data System (ADS)

Fried, H. M.; Grandou, T.; Sheu, Y.-M.

2012-11-01

Following a previous calculation of quark scattering in eikonal approximation, this paper presents a new, analytic and rigorous approach to the calculation of QCD phenomena. In this formulation a basic distinction between the conventional "idealistic" description of QCD and a more "realistic" description is brought into focus by a non-perturbative, gauge-invariant evaluation of the Schwinger solution for the QCD generating functional in terms of the exact Fradkin representations of Green's functional G(x,y|A) and the vacuum functional L[A]. Because quarks exist asymptotically only in bound states, their transverse coordinates can never be measured with arbitrary precision; the non-perturbative neglect of this statement leads to obstructions that are easily corrected by invoking in the basic Lagrangian a probability amplitude which describes such transverse imprecision. The second result of this non-perturbative analysis is the appearance of a new and simplifying output called "Effective Locality", in which the interactions between quarks by the exchange of a "gluon bundle"-which "bundle" contains an infinite number of gluons, including cubic and quartic gluon interactions-display an exact locality property that reduces the several functional integrals of the formulation down to a set of ordinary integrals. It should be emphasized that "non-perturbative" here refers to the effective summation of all gluons between a pair of quark lines-which may be the same quark line, as in a self-energy graph-but does not (yet) include a summation over all closed-quark loops which are tied by gluon-bundle exchange to the rest of the "Bundle Diagram". As an example of the power of these methods we offer as a first analytic calculation the quark-antiquark binding potential of a pion, and the corresponding three-quark binding potential of a nucleon, obtained in a simple way from relevant eikonal scattering approximations. A second calculation, analytic, non-perturbative and gauge-invariant, of a nucleon-nucleon binding potential to form a model deuteron, will appear separately.

An analytical method for assessing the spatial and temporal variation of juvenile Atlantic salmon habitat in an upland Scottish river.

NASA Astrophysics Data System (ADS)

Buddendorf, B.; Fabris, L.; Malcolm, I.; Lazzaro, G.; Tetzlaff, D.; Botter, G.; Soulsby, C.

2016-12-01

Wild Atlantic salmon populations in Scottish rivers constitute an important economic and recreational resource, as well as being a key component of biodiversity. Salmon have specific habitat requirements at different life stages and their distribution is therefore strongly influenced by a complex suite of biological and physical controls. Stream hydrodynamics have a strong influence on habitat quality and affect the distribution and density of juvenile salmon. As stream hydrodynamics directly relate to stream flow variability and channel morphology, the effects of hydroclimatic drivers on the spatial and temporal variability of habitat suitability can be assessed. Critical Displacement Velocity (CDV), which describes the velocity at which fish can no longer hold station, is one potential approach for characterising habitat suitability. CDV is obtained using an empirical formula that depends on fish size and stream temperature. By characterising the proportion of a reach below CDV it is possible to assess the suitable area. We demonstrate that a generic analytical approach based on field survey and hydraulic modelling can provide insights on the interactions between flow regime and average suitable area (SA) for juvenile salmon that could be extended to other aquatic species. Analytical functions are used to model the pdf of stream flow p(q) and the relationship between flow and suitable area SA(q). Theoretically these functions can assume any form. Here we used a gamma distribution to model p(q) and a gamma function to model SA(q). Integrating the product of these functions we obtain an analytical expression of SA. Since parameters of p(q) can be estimated from meteorological and flow measurements, they can be used directly to predict the effect of flow regime on SA. We show the utility of the approach with reference to 6 electrofishing sites in a single river system where long term (50 years) data on spatially distributed juvenile salmon densities are available.

Homogeneous partial differential equations for superpositions of indeterminate functions of several variables

NASA Astrophysics Data System (ADS)

Asai, Kazuto

2009-02-01

We determine essentially all partial differential equations satisfied by superpositions of tree type and of a further special type. These equations represent necessary and sufficient conditions for an analytic function to be locally expressible as an analytic superposition of the type indicated. The representability of a real analytic function by a superposition of this type is independent of whether that superposition involves real-analytic functions or C^{\\rho}-functions, where the constant \\rho is determined by the structure of the superposition. We also prove that the function u defined by u^n=xu^a+yu^b+zu^c+1 is generally non-representable in any real (resp. complex) domain as f\\bigl(g(x,y),h(y,z)\\bigr) with twice differentiable f and differentiable g, h (resp. analytic f, g, h).

pySecDec: A toolbox for the numerical evaluation of multi-scale integrals

NASA Astrophysics Data System (ADS)

Borowka, S.; Heinrich, G.; Jahn, S.; Jones, S. P.; Kerner, M.; Schlenk, J.; Zirke, T.

2018-01-01

We present pySECDEC, a new version of the program SECDEC, which performs the factorization of dimensionally regulated poles in parametric integrals, and the subsequent numerical evaluation of the finite coefficients. The algebraic part of the program is now written in the form of python modules, which allow a very flexible usage. The optimization of the C++ code, generated using FORM, is improved, leading to a faster numerical convergence. The new version also creates a library of the integrand functions, such that it can be linked to user-specific codes for the evaluation of matrix elements in a way similar to analytic integral libraries.

"Living turned inside out": the musical expression of psychotic and schizoid experience in talking heads' Remain in light.

PubMed

Brog, Michael A

2002-06-01

The rock album form, advantageously suited for the artistic expression of intrapsychic experience, has been virtually ignored by analytic writers. Remain in Light by Talking Heads is presented as an example of an album that effectively utilizes the potentialities of this form to give powerful and disconcerning musical expression to a variety of psychotic and schizoid experiences, bringing to life the formulations for these phenomena of Bion, Winnicott, Guntrip, Ogden, Grotstein and others. The album suggests a variety of mechanisms by which sound and music may serve both defensive and compensatory functions in relation to these phenomena.

A New Closed Form Approximation for BER for Optical Wireless Systems in Weak Atmospheric Turbulence

NASA Astrophysics Data System (ADS)

Kaushik, Rahul; Khandelwal, Vineet; Jain, R. C.

2018-04-01

Weak atmospheric turbulence condition in an optical wireless communication (OWC) is captured by log-normal distribution. The analytical evaluation of average bit error rate (BER) of an OWC system under weak turbulence is intractable as it involves the statistical averaging of Gaussian Q-function over log-normal distribution. In this paper, a simple closed form approximation for BER of OWC system under weak turbulence is given. Computation of BER for various modulation schemes is carried out using proposed expression. The results obtained using proposed expression compare favorably with those obtained using Gauss-Hermite quadrature approximation and Monte Carlo Simulations.

Phase separation and the formation of cellular bodies

NASA Astrophysics Data System (ADS)

Xu, Bin; Broedersz, Chase P.; Meir, Yigal; Wingreen, Ned S.

Cellular bodies in eukaryotic cells spontaneously assemble to form cellular compartments. Among other functions, these bodies carry out essential biochemical reactions. Cellular bodies form micron-sized structures, which, unlike canonical cell organelles, are not surrounded by membranes. A recent in vitro experiment has shown that phase separation of polymers in solution can explain the formation of cellular bodies. We constructed a lattice-polymer model to capture the essential mechanism leading to this phase separation. We used both analytical and numerical tools to predict the phase diagram of a system of two interacting polymers, including the concentration of each polymer type in the condensed and dilute phase.

The Information Content of Discrete Functions and Their Application in Genetic Data Analysis

DOE PAGES

Sakhanenko, Nikita A.; Kunert-Graf, James; Galas, David J.

2017-10-13

The complex of central problems in data analysis consists of three components: (1) detecting the dependence of variables using quantitative measures, (2) defining the significance of these dependence measures, and (3) inferring the functional relationships among dependent variables. We have argued previously that an information theory approach allows separation of the detection problem from the inference of functional form problem. We approach here the third component of inferring functional forms based on information encoded in the functions. Here, we present here a direct method for classifying the functional forms of discrete functions of three variables represented in data sets. Discretemore » variables are frequently encountered in data analysis, both as the result of inherently categorical variables and from the binning of continuous numerical variables into discrete alphabets of values. The fundamental question of how much information is contained in a given function is answered for these discrete functions, and their surprisingly complex relationships are illustrated. The all-important effect of noise on the inference of function classes is found to be highly heterogeneous and reveals some unexpected patterns. We apply this classification approach to an important area of biological data analysis—that of inference of genetic interactions. Genetic analysis provides a rich source of real and complex biological data analysis problems, and our general methods provide an analytical basis and tools for characterizing genetic problems and for analyzing genetic data. Finally, we illustrate the functional description and the classes of a number of common genetic interaction modes and also show how different modes vary widely in their sensitivity to noise.« less

The Information Content of Discrete Functions and Their Application in Genetic Data Analysis

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

Sakhanenko, Nikita A.; Kunert-Graf, James; Galas, David J.

The complex of central problems in data analysis consists of three components: (1) detecting the dependence of variables using quantitative measures, (2) defining the significance of these dependence measures, and (3) inferring the functional relationships among dependent variables. We have argued previously that an information theory approach allows separation of the detection problem from the inference of functional form problem. We approach here the third component of inferring functional forms based on information encoded in the functions. Here, we present here a direct method for classifying the functional forms of discrete functions of three variables represented in data sets. Discretemore » variables are frequently encountered in data analysis, both as the result of inherently categorical variables and from the binning of continuous numerical variables into discrete alphabets of values. The fundamental question of how much information is contained in a given function is answered for these discrete functions, and their surprisingly complex relationships are illustrated. The all-important effect of noise on the inference of function classes is found to be highly heterogeneous and reveals some unexpected patterns. We apply this classification approach to an important area of biological data analysis—that of inference of genetic interactions. Genetic analysis provides a rich source of real and complex biological data analysis problems, and our general methods provide an analytical basis and tools for characterizing genetic problems and for analyzing genetic data. Finally, we illustrate the functional description and the classes of a number of common genetic interaction modes and also show how different modes vary widely in their sensitivity to noise.« less

The Information Content of Discrete Functions and Their Application in Genetic Data Analysis.

PubMed

Sakhanenko, Nikita A; Kunert-Graf, James; Galas, David J

2017-12-01

The complex of central problems in data analysis consists of three components: (1) detecting the dependence of variables using quantitative measures, (2) defining the significance of these dependence measures, and (3) inferring the functional relationships among dependent variables. We have argued previously that an information theory approach allows separation of the detection problem from the inference of functional form problem. We approach here the third component of inferring functional forms based on information encoded in the functions. We present here a direct method for classifying the functional forms of discrete functions of three variables represented in data sets. Discrete variables are frequently encountered in data analysis, both as the result of inherently categorical variables and from the binning of continuous numerical variables into discrete alphabets of values. The fundamental question of how much information is contained in a given function is answered for these discrete functions, and their surprisingly complex relationships are illustrated. The all-important effect of noise on the inference of function classes is found to be highly heterogeneous and reveals some unexpected patterns. We apply this classification approach to an important area of biological data analysis-that of inference of genetic interactions. Genetic analysis provides a rich source of real and complex biological data analysis problems, and our general methods provide an analytical basis and tools for characterizing genetic problems and for analyzing genetic data. We illustrate the functional description and the classes of a number of common genetic interaction modes and also show how different modes vary widely in their sensitivity to noise.

Spectroelectrochemical Sensors: New Polymer Films for Improved Sensitivity

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

Morris, Laura K.; Seliskar, Carl J.; Bryan, Samuel A.

2014-10-31

The selectivity of an optical sensor can be improved by combining optical detection with electrochemical oxidation or reduction of the target analyte to change its spectral properties. The changing signal can distinguish the analyte from interferences with similar spectral properties that would otherwise interfere. The analyte is detected by measuring the intensity of the electrochemically modulated signal. In one form this spectroelectrochemical sensor consists of an optically transparent electrode (OTE) coated with a film that preconcentrates the target analyte. The OTE functions as an optical waveguide for attenuated total reflectance (ATR) spectroscopy, which detects the analyte by absorption. Sensitivity reliesmore » in part on a large change in molar absorptivity between the two oxidation states used for electrochemical modulation of the optical signal. A critical part of the sensor is the ion selective film. It should preconcentrate the analyte and exclude some interferences. At the same time the film must not interfere with the electrochemistry or the optical detection. Therefore, since the debut of the sensor’s concept one major focus of our group has been developing appropriate films for different analytes. Here we report the development of a series of quaternized poly(vinylpyridine)-co-styrene (QPVP-co-S) anion exchange films for use in spectroelectrochemical sensors to enable sensitive detection of target anionic analytes in complex samples. The films were either 10% or 20% styrene and were prepared with varying degrees of quaternized pyridine groups, up to 70%. Films were characterized with respect to thickness with spectroscopic ellipsometry, degree of quaternization with FTIR, and electrochemically and spectroelectrochemically using the anions ferrocyanide and pertechnetate.« less

Differential Higgs production at N3LO beyond threshold

NASA Astrophysics Data System (ADS)

Dulat, Falko; Mistlberger, Bernhard; Pelloni, Andrea

2018-01-01

We present several key steps towards the computation of differential Higgs boson cross sections at N3LO in perturbative QCD. Specifically, we work in the framework of Higgs-differential cross sections that allows to compute precise predictions for realistic LHC observables. We demonstrate how to perform an expansion of the analytic N3LO coefficient functions around the production threshold of the Higgs boson. Our framework allows us to compute to arbitrarily high order in the threshold expansion and we explicitly obtain the first two expansion coefficients in analytic form. Furthermore, we assess the phenomenological viability of threshold expansions for differential distributions. We find that while a few terms in the threshold expansion are sufficient to approximate the exact rapidity distribution well, transverse momentum distributions require a signficantly higher number of terms in the expansion to be adequately described. We find that to improve state of the art predictions for the rapidity distribution beyond NNLO even more sub-leading terms in the threshold expansion than presented in this article are required. In addition, we report on an interesting obstacle for the computation of N3LO corrections with LHAPDF parton distribution functions and our solution. We provide files containing the analytic expressions for the partonic cross sections as supplementary material attached to this paper.

Differential Higgs production at N 3LO beyond threshold

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

Dulat, Falko; Mistlberger, Bernhard; Pelloni, Andrea

We present several key steps towards the computation of differential Higgs boson cross sections at N 3LO in perturbative QCD. Specifically, we work in the framework of Higgs-differential cross sections that allows to compute precise predictions for realistic LHC observables. We demonstrate how to perform an expansion of the analytic N 3LO coefficient functions around the production threshold of the Higgs boson. Our framework allows us to compute to arbitrarily high order in the threshold expansion and we explicitly obtain the first two expansion coefficients in analytic form. Furthermore, we assess the phenomenological viability of threshold expansions for differential distributions.more » We find that while a few terms in the threshold expansion are sufficient to approximate the exact rapidity distribution well, transverse momentum distributions require a signficantly higher number of terms in the expansion to be adequately described. We find that to improve state of the art predictions for the rapidity distribution beyond NNLO even more sub-leading terms in the threshold expansion than presented in this article are required. In addition, we report on an interesting obstacle for the computation of N 3LO corrections with LHAPDF parton distribution functions and our solution. We provide files containing the analytic expressions for the partonic cross sections as supplementary material attached to this paper.« less

Differential Higgs production at N 3LO beyond threshold

DOE PAGES

Dulat, Falko; Mistlberger, Bernhard; Pelloni, Andrea

2018-01-29

We present several key steps towards the computation of differential Higgs boson cross sections at N 3LO in perturbative QCD. Specifically, we work in the framework of Higgs-differential cross sections that allows to compute precise predictions for realistic LHC observables. We demonstrate how to perform an expansion of the analytic N 3LO coefficient functions around the production threshold of the Higgs boson. Our framework allows us to compute to arbitrarily high order in the threshold expansion and we explicitly obtain the first two expansion coefficients in analytic form. Furthermore, we assess the phenomenological viability of threshold expansions for differential distributions.more » We find that while a few terms in the threshold expansion are sufficient to approximate the exact rapidity distribution well, transverse momentum distributions require a signficantly higher number of terms in the expansion to be adequately described. We find that to improve state of the art predictions for the rapidity distribution beyond NNLO even more sub-leading terms in the threshold expansion than presented in this article are required. In addition, we report on an interesting obstacle for the computation of N 3LO corrections with LHAPDF parton distribution functions and our solution. We provide files containing the analytic expressions for the partonic cross sections as supplementary material attached to this paper.« less

Birkhoff Normal Form for Some Nonlinear PDEs

NASA Astrophysics Data System (ADS)

Bambusi, Dario

We consider the problem of extending to PDEs Birkhoff normal form theorem on Hamiltonian systems close to nonresonant elliptic equilibria. As a model problem we take the nonlinear wave equation with Dirichlet boundary conditions on [0,π] g is an analytic skewsymmetric function which vanishes for u=0 and is periodic with period 2π in the x variable. We prove, under a nonresonance condition which is fulfilled for most g's, that for any integer M there exists a canonical transformation that puts the Hamiltonian in Birkhoff normal form up to a reminder of order M. The canonical transformation is well defined in a neighbourhood of the origin of a Sobolev type phase space of sufficiently high order. Some dynamical consequences are obtained. The technique of proof is applicable to quite general semilinear equations in one space dimension.

Efficient Online Optimized Quantum Control for Adiabatic Quantum Computation

NASA Astrophysics Data System (ADS)

Quiroz, Gregory

Adiabatic quantum computation (AQC) relies on controlled adiabatic evolution to implement a quantum algorithm. While control evolution can take many forms, properly designed time-optimal control has been shown to be particularly advantageous for AQC. Grover's search algorithm is one such example where analytically-derived time-optimal control leads to improved scaling of the minimum energy gap between the ground state and first excited state and thus, the well-known quadratic quantum speedup. Analytical extensions beyond Grover's search algorithm present a daunting task that requires potentially intractable calculations of energy gaps and a significant degree of model certainty. Here, an in situ quantum control protocol is developed for AQC. The approach is shown to yield controls that approach the analytically-derived time-optimal controls for Grover's search algorithm. In addition, the protocol's convergence rate as a function of iteration number is shown to be essentially independent of system size. Thus, the approach is potentially scalable to many-qubit systems.

On the analytic and numeric optimisation of airplane trajectories under real atmospheric conditions

NASA Astrophysics Data System (ADS)

Gonzalo, J.; Domínguez, D.; López, D.

2014-12-01

From the beginning of aviation era, economic constraints have forced operators to continuously improve the planning of the flights. The revenue is proportional to the cost per flight and the airspace occupancy. Many methods, the first started in the middle of last century, have explore analytical, numerical and artificial intelligence resources to reach the optimal flight planning. In parallel, advances in meteorology and communications allow an almost real-time knowledge of the atmospheric conditions and a reliable, error-bounded forecast for the near future. Thus, apart from weather risks to be avoided, airplanes can dynamically adapt their trajectories to minimise their costs. International regulators are aware about these capabilities, so it is reasonable to envisage some changes to allow this dynamic planning negotiation to soon become operational. Moreover, current unmanned airplanes, very popular and often small, suffer the impact of winds and other weather conditions in form of dramatic changes in their performance. The present paper reviews analytic and numeric solutions for typical trajectory planning problems. Analytic methods are those trying to solve the problem using the Pontryagin principle, where influence parameters are added to state variables to form a split condition differential equation problem. The system can be solved numerically -indirect optimisation- or using parameterised functions -direct optimisation-. On the other hand, numerical methods are based on Bellman's dynamic programming (or Dijkstra algorithms), where the fact that two optimal trajectories can be concatenated to form a new optimal one if the joint point is demonstrated to belong to the final optimal solution. There is no a-priori conditions for the best method. Traditionally, analytic has been more employed for continuous problems whereas numeric for discrete ones. In the current problem, airplane behaviour is defined by continuous equations, while wind fields are given in a discrete grid at certain time intervals. The research demonstrates advantages and disadvantages of each method as well as performance figures of the solutions found for typical flight conditions under static and dynamic atmospheres. This provides significant parameters to be used in the selection of solvers for optimal trajectories.

Generalized time-dependent Schrödinger equation in two dimensions under constraints

NASA Astrophysics Data System (ADS)

Sandev, Trifce; Petreska, Irina; Lenzi, Ervin K.

2018-01-01

We investigate a generalized two-dimensional time-dependent Schrödinger equation on a comb with a memory kernel. A Dirac delta term is introduced in the Schrödinger equation so that the quantum motion along the x-direction is constrained at y = 0. The wave function is analyzed by using Green's function approach for several forms of the memory kernel, which are of particular interest. Closed form solutions for the cases of Dirac delta and power-law memory kernels in terms of Fox H-function, as well as for a distributed order memory kernel, are obtained. Further, a nonlocal term is also introduced and investigated analytically. It is shown that the solution for such a case can be represented in terms of infinite series in Fox H-functions. Green's functions for each of the considered cases are analyzed and plotted for the most representative ones. Anomalous diffusion signatures are evident from the presence of the power-law tails. The normalized Green's functions obtained in this work are of broader interest, as they are an important ingredient for further calculations and analyses of some interesting effects in the transport properties in low-dimensional heterogeneous media.

Attractor cosmology from nonminimally coupled gravity

NASA Astrophysics Data System (ADS)

Odintsov, S. D.; Oikonomou, V. K.

2018-03-01

By using a bottom-up reconstruction technique for nonminimally coupled scalar-tensor theories, we realize the Einstein frame attractor cosmologies in the Ω (ϕ )-Jordan frame. For our approach, what is needed for the reconstruction method to work is the functional form of the nonminimal coupling Ω (ϕ ) and of the scalar-to-tensor ratio, and also the assumption of the slow-roll inflation in the Ω (ϕ )-Jordan frame. By appropriately choosing the scalar-to-tensor ratio, we demonstrate that the observational indices of the attractor cosmologies can be realized directly in the Ω (ϕ )-Jordan frame. We investigate the special conditions that are required to hold true in for this realization to occur, and we provide the analytic form of the potential in the Ω (ϕ )-Jordan frame. Also, by performing a conformal transformation, we find the corresponding Einstein frame canonical scalar-tensor theory, and we calculate in detail the corresponding observational indices. The result indicates that although the spectral index of the primordial curvature perturbations is the same in the Jordan and Einstein frames, at leading order in the e -foldings number, the scalar-to-tensor ratio differs. We discuss the possible reasons behind this discrepancy, and we argue that the difference is due to some approximation we performed to the functional form of the potential in the Einstein frame, in order to obtain analytical results, and also due to the difference in the definition of the e -foldings number in the two frames, which is also pointed out in the related literature. Finally, we find the F (R ) gravity corresponding to the Einstein frame canonical scalar-tensor theory.

Exact solutions of kinetic equations in an autocatalytic growth model.

PubMed

Jędrak, Jakub

2013-02-01

Kinetic equations are introduced for the transition-metal nanocluster nucleation and growth mechanism, as proposed by Watzky and Finke [J. Am. Chem. Soc. 119, 10382 (1997)]. Equations of this type take the form of Smoluchowski coagulation equations supplemented with the terms responsible for the chemical reactions. In the absence of coagulation, we find complete analytical solutions of the model equations for the autocatalytic rate constant both proportional to the cluster mass, and the mass-independent one. In the former case, ξ(k)=s(k)(ξ(1))[proportionality]ξ(1)(k)/k was obtained, while in the latter, the functional form of s(k)(ξ(1)) is more complicated. In both cases, ξ(1)(t)=h(μ)(M(μ)(t)) is a function of the moments of the mass distribution. Both functions, s(k)(ξ(1)) and h(μ)(M(μ)), depend on the assumed mechanism of autocatalytic growth and monomer production, and not on other chemical reactions present in a system.

FAPRS Manual: Manual for the Functional Analytic Psychotherapy Rating Scale

ERIC Educational Resources Information Center

Callaghan, Glenn M.; Follette, William C.

2008-01-01

The Functional Analytic Psychotherapy Rating Scale (FAPRS) is behavioral coding system designed to capture those essential client and therapist behaviors that occur during Functional Analytic Psychotherapy (FAP). The FAPRS manual presents the purpose and rules for documenting essential aspects of FAP. The FAPRS codes are exclusive and exhaustive…

Nonlinear dynamics of mushy layers induced by external stochastic fluctuations.

PubMed

Alexandrov, Dmitri V; Bashkirtseva, Irina A; Ryashko, Lev B

2018-02-28

The time-dependent process of directional crystallization in the presence of a mushy layer is considered with allowance for arbitrary fluctuations in the atmospheric temperature and friction velocity. A nonlinear set of mushy layer equations and boundary conditions is solved analytically when the heat and mass fluxes at the boundary between the mushy layer and liquid phase are induced by turbulent motion in the liquid and, as a result, have the corresponding convective form. Namely, the 'solid phase-mushy layer' and 'mushy layer-liquid phase' phase transition boundaries as well as the solid fraction, temperature and concentration (salinity) distributions are found. If the atmospheric temperature and friction velocity are constant, the analytical solution takes a parametric form. In the more common case when they represent arbitrary functions of time, the analytical solution is given by means of the standard Cauchy problem. The deterministic and stochastic behaviour of the phase transition process is analysed on the basis of the obtained analytical solutions. In the case of stochastic fluctuations in the atmospheric temperature and friction velocity, the phase transition interfaces (mushy layer boundaries) move faster than in the deterministic case. A cumulative effect of these noise contributions is revealed as well. In other words, when the atmospheric temperature and friction velocity fluctuate simultaneously due to the influence of different external processes and phenomena, the phase transition boundaries move even faster. This article is part of the theme issue 'From atomistic interfaces to dendritic patterns'.This article is part of the theme issue 'From atomistic interfaces to dendritic patterns'. © 2018 The Author(s).

Analytical pyrolysis-based study on intra-skeletal organic matrices from Mediterranean corals.

PubMed

Adamiano, Alessio; Goffredo, Stefano; Dubinsky, Zvy; Levy, Oren; Fermani, Simona; Fabbri, Daniele; Falini, Giuseppe

2014-09-01

Off-line analytical pyrolysis combined with gas chromatography–mass spectroscopy (GC–MS), directly or after trimethylsilylation, along with infrared spectroscopy and amino acid analysis was applied for the first time to the characterization of the intra-skeletal organic matrix (OM) extracted from four Mediterranean hard corals. They were diverse in growth form and trophic strategy namely Balanophyllia europaea and Leptopsammia pruvoti—solitary corals, only the first having zooxanthelle—and Cladocora caespitosa and Astroides calycularis—colonial corals, only the first with zooxanthelle. Pyrolysis products evolved from OM could be assigned to lipid (e.g. fatty acids, fatty alcohols, monoacylglicerols), protein (e.g. 2,5-diketopiperazines, DKPs) and polysaccharide (e.g. anhydrosugars) precursors. Their quantitative distribution showed for all the species a low protein content with respect to lipids and polysaccharides. A chemometric approach using principal component analysis (PCA) and clustering analysis was applied on OM mean amino acidic compositions. The small compositional diversity across coral species was tentatively related with coral growth form. The presence of N-acetyl glucosamine markers suggested a functional link with other calcified tissues containing chitin. The protein fraction was further investigated using novel DKP markers tentatively identified from analytical pyrolysis of model polar linear dipeptides. Again, no correlation was observed in relation to coral ecology. These analytical results revealed that the bulk structure and composition of OMs among studied corals are similar, as it is the textural organization of the skeleton mineralized units. Therefore, they suggest that coral’s biomineralization is governed by similar macromolecules, and probably mechanisms, independently from their ecology.

Hill functions for stochastic gene regulatory networks from master equations with split nodes and time-scale separation

NASA Astrophysics Data System (ADS)

Lipan, Ovidiu; Ferwerda, Cameron

2018-02-01

The deterministic Hill function depends only on the average values of molecule numbers. To account for the fluctuations in the molecule numbers, the argument of the Hill function needs to contain the means, the standard deviations, and the correlations. Here we present a method that allows for stochastic Hill functions to be constructed from the dynamical evolution of stochastic biocircuits with specific topologies. These stochastic Hill functions are presented in a closed analytical form so that they can be easily incorporated in models for large genetic regulatory networks. Using a repressive biocircuit as an example, we show by Monte Carlo simulations that the traditional deterministic Hill function inaccurately predicts time of repression by an order of two magnitudes. However, the stochastic Hill function was able to capture the fluctuations and thus accurately predicted the time of repression.

Fluctuation-induced forces in confined ideal and imperfect Bose gases

NASA Astrophysics Data System (ADS)

Diehl, H. W.; Rutkevich, Sergei B.

2017-06-01

Fluctuation-induced ("Casimir") forces caused by thermal and quantum fluctuations are investigated for ideal and imperfect Bose gases confined to d -dimensional films of size ∞d -1×D under periodic (P), antiperiodic (A), Dirichlet-Dirichlet (DD), Neumann-Neumann (NN), and Robin (R) boundary conditions (BCs). The full scaling functions ΥdBC(xλ=D /λth ,xξ=D /ξ ) of the residual reduced grand potential per area φres,dBC(T ,μ ,D ) =D-(d -1 )ΥdBC(xλ,xξ) are determined for the ideal gas case with these BCs, where λth and ξ are the thermal de Broglie wavelength and the bulk correlation length, respectively. The associated limiting scaling functions ΘdBC(xξ) ≡ΥdBC(∞ ,xξ) describing the critical behavior at the bulk condensation transition are shown to agree with those previously determined from a massive free O (2 ) theory for BC=P,A,DD,DN,NN . For d =3 , they are expressed in closed analytical form in terms of polylogarithms. The analogous scaling functions ΥdBC(xλ,xξ,c1D ,c2D ) and ΘdR(xξ,c1D ,c2D ) under the RBCs (∂z-c1) ϕ |z=0=(∂z+c2) ϕ | z =D=0 with c1≥0 and c2≥0 are also determined. The corresponding scaling functions Υ∞,d P(xλ,xξ) and Θ∞,d P(xξ) for the imperfect Bose gas are shown to agree with those of the interacting Bose gas with n internal degrees of freedom in the limit n →∞ . Hence, for d =3 , Θ∞,d P(xξ) is known exactly in closed analytic form. To account for the breakdown of translation invariance in the direction perpendicular to the boundary planes implied by free BCs such as DDBCs, a modified imperfect Bose gas model is introduced that corresponds to the limit n →∞ of this interacting Bose gas. Numerically and analytically exact results for the scaling function Θ∞,3 DD(xξ) therefore follow from those of the O (2 n ) ϕ4 model for n →∞ .

Fluctuation-induced forces in confined ideal and imperfect Bose gases.

PubMed

Diehl, H W; Rutkevich, Sergei B

2017-06-01

Fluctuation-induced ("Casimir") forces caused by thermal and quantum fluctuations are investigated for ideal and imperfect Bose gases confined to d-dimensional films of size ∞^{d-1}×D under periodic (P), antiperiodic (A), Dirichlet-Dirichlet (DD), Neumann-Neumann (NN), and Robin (R) boundary conditions (BCs). The full scaling functions Υ_{d}^{BC}(x_{λ}=D/λ_{th},x_{ξ}=D/ξ) of the residual reduced grand potential per area φ_{res,d}^{BC}(T,μ,D)=D^{-(d-1)}Υ_{d}^{BC}(x_{λ},x_{ξ}) are determined for the ideal gas case with these BCs, where λ_{th} and ξ are the thermal de Broglie wavelength and the bulk correlation length, respectively. The associated limiting scaling functions Θ_{d}^{BC}(x_{ξ})≡Υ_{d}^{BC}(∞,x_{ξ}) describing the critical behavior at the bulk condensation transition are shown to agree with those previously determined from a massive free O(2) theory for BC=P,A,DD,DN,NN. For d=3, they are expressed in closed analytical form in terms of polylogarithms. The analogous scaling functions Υ_{d}^{BC}(x_{λ},x_{ξ},c_{1}D,c_{2}D) and Θ_{d}^{R}(x_{ξ},c_{1}D,c_{2}D) under the RBCs (∂_{z}-c_{1})ϕ|_{z=0}=(∂_{z}+c_{2})ϕ|_{z=D}=0 with c_{1}≥0 and c_{2}≥0 are also determined. The corresponding scaling functions Υ_{∞,d}^{P}(x_{λ},x_{ξ}) and Θ_{∞,d}^{P}(x_{ξ}) for the imperfect Bose gas are shown to agree with those of the interacting Bose gas with n internal degrees of freedom in the limit n→∞. Hence, for d=3, Θ_{∞,d}^{P}(x_{ξ}) is known exactly in closed analytic form. To account for the breakdown of translation invariance in the direction perpendicular to the boundary planes implied by free BCs such as DDBCs, a modified imperfect Bose gas model is introduced that corresponds to the limit n→∞ of this interacting Bose gas. Numerically and analytically exact results for the scaling function Θ_{∞,3}^{DD}(x_{ξ}) therefore follow from those of the O(2n)ϕ^{4} model for n→∞.

The analytical representation of viscoelastic material properties using optimization techniques

NASA Technical Reports Server (NTRS)

Hill, S. A.

1993-01-01

This report presents a technique to model viscoelastic material properties with a function of the form of the Prony series. Generally, the method employed to determine the function constants requires assuming values for the exponential constants of the function and then resolving the remaining constants through linear least-squares techniques. The technique presented here allows all the constants to be analytically determined through optimization techniques. This technique is employed in a computer program named PRONY and makes use of commercially available optimization tool developed by VMA Engineering, Inc. The PRONY program was utilized to compare the technique against previously determined models for solid rocket motor TP-H1148 propellant and V747-75 Viton fluoroelastomer. In both cases, the optimization technique generated functions that modeled the test data with at least an order of magnitude better correlation. This technique has demonstrated the capability to use small or large data sets and to use data sets that have uniformly or nonuniformly spaced data pairs. The reduction of experimental data to accurate mathematical models is a vital part of most scientific and engineering research. This technique of regression through optimization can be applied to other mathematical models that are difficult to fit to experimental data through traditional regression techniques.

Relay-aided free-space optical communications using α - μ distribution over atmospheric turbulence channels with misalignment errors

NASA Astrophysics Data System (ADS)

Upadhya, Abhijeet; Dwivedi, Vivek K.; Singh, G.

2018-06-01

In this paper, we have analyzed the performance of dual hop radio frequency (RF)/free-space optical (FSO) fixed gain relay environment confined by atmospheric turbulence induced fading channel over FSO link and modeled using α - μ distribution. The RF hop of the amplify-and-forward scheme undergoes the Rayleigh fading and the proposed system model also considers the pointing error effect on the FSO link. A novel and accurate mathematical expression of the probability density function for a FSO link experiencing α - μ distributed atmospheric turbulence in the presence of pointing error is derived. Further, we have presented analytical expressions of outage probability and bit error rate in terms of Meijer-G function. In addition to this, a useful and mathematically tractable closed-form expression for the end-to-end ergodic capacity of the dual hop scheme in terms of bivariate Fox's H function is derived. The atmospheric turbulence, misalignment errors and various binary modulation schemes for intensity modulation on optical wireless link are considered to yield the results. Finally, we have analyzed each of the three performance metrics for high SNR in order to represent them in terms of elementary functions and the achieved analytical results are supported by computer-based simulations.

Reliability analysis of composite structures

NASA Technical Reports Server (NTRS)

Kan, Han-Pin

1992-01-01

A probabilistic static stress analysis methodology has been developed to estimate the reliability of a composite structure. Closed form stress analysis methods are the primary analytical tools used in this methodology. These structural mechanics methods are used to identify independent variables whose variations significantly affect the performance of the structure. Once these variables are identified, scatter in their values is evaluated and statistically characterized. The scatter in applied loads and the structural parameters are then fitted to appropriate probabilistic distribution functions. Numerical integration techniques are applied to compute the structural reliability. The predicted reliability accounts for scatter due to variability in material strength, applied load, fabrication and assembly processes. The influence of structural geometry and mode of failure are also considerations in the evaluation. Example problems are given to illustrate various levels of analytical complexity.

Approximate Analytical Time-Dependent Solutions to Describe Large-Amplitude Local Calcium Transients in the Presence of Buffers

PubMed Central

Mironova, Lidia A.; Mironov, Sergej L.

2008-01-01

Local Ca2+ signaling controls many neuronal functions, which is often achieved through spatial localization of Ca2+ signals. These nanodomains are formed due to combined effects of Ca2+ diffusion and binding to the cytoplasmic buffers. In this article we derived simple analytical expressions to describe Ca2+ diffusion in the presence of mobile and immobile buffers. A nonlinear character of the reaction-diffusion problem was circumvented by introducing a logarithmic approximation of the concentration term. The obtained formulas reproduce free Ca2+ levels up to 50 μM and their changes in the millisecond range. Derived equations can be useful to predict spatiotemporal profiles of large-amplitude [Ca2+] transients, which participate in various physiological processes. PMID:17872951

An analytical approach to the rise velocity of periodic bubble trains in non-Newtonian fluids.

PubMed

Frank, X; Li, H Z; Funfschilling, D

2005-01-01

The present study aims at providing insight into the acceleration mechanism of a bubble chain rising in shear-thinning viscoelastic fluids. The experimental investigation by the Particle Image Velocimetry (PIV), birefringence visualisation and rheological simulation shows that two aspects are central to bubble interactions in such media: the stress creation by the passage of bubbles, and their relaxation due to the fluid's memory forming an evanescent corridor of reduced viscosity. Interactions between bubbles were taken into account mainly through a linear superposition of the stress evolution behind each bubble. An analytical approach together with the rheological consideration was developed to compute the rise velocity of a bubble chain in function of the injection period and bubble volume. The model predictions compare satisfactorily with the experimental investigation.

Riccati parameterized self-similar waves in two-dimensional graded-index waveguide

NASA Astrophysics Data System (ADS)

Kumar De, Kanchan; Goyal, Amit; Raju, Thokala Soloman; Kumar, C. N.; Panigrahi, Prasanta K.

2015-04-01

An analytical method based on gauge-similarity transformation technique has been employed for mapping a (2+1)- dimensional variable coefficient coupled nonlinear Schrödinger equations (vc-CNLSE) with dispersion, nonlinearity and gain to standard NLSE. Under certain functional relations we construct a large family of self-similar waves in the form of bright similaritons, Akhmediev breathers and rogue waves. We report the effect of dispersion on the intensity of the solitary waves. Further, we illustrate the procedure to amplify the intensity of self-similar waves using isospectral Hamiltonian approach. This approach provides an efficient mechanism to generate analytically a wide class of tapering profiles and widths by exploiting the Riccati parameter. Equivalently, it enables one to control efficiently the self-similar wave structures and hence their evolution.

Neoclassical transport including collisional nonlinearity.

PubMed

Candy, J; Belli, E A

2011-06-10

In the standard δf theory of neoclassical transport, the zeroth-order (Maxwellian) solution is obtained analytically via the solution of a nonlinear equation. The first-order correction δf is subsequently computed as the solution of a linear, inhomogeneous equation that includes the linearized Fokker-Planck collision operator. This equation admits analytic solutions only in extreme asymptotic limits (banana, plateau, Pfirsch-Schlüter), and so must be solved numerically for realistic plasma parameters. Recently, numerical codes have appeared which attempt to compute the total distribution f more accurately than in the standard ordering by retaining some nonlinear terms related to finite-orbit width, while simultaneously reusing some form of the linearized collision operator. In this work we show that higher-order corrections to the distribution function may be unphysical if collisional nonlinearities are ignored.

A Research Program on the Asymptotic Description of Electromagnetic Pulse Propagation in Spatially Inhomogeneous Temporally Dispersive, Attenuative Media

DTIC Science & Technology

2007-09-01

the right- half of the complex wo- plane . The Sommerfeld precursor then describes the signal front which arrives at 0 = 1 with...resonance Lorentz model dielectric [18], the complex phase function qO(w, 0) is analytic in the w- plane formed by the two branch cuts in the lower half of... the w,- plane symmetrically located about the imaginary axis. In the right half plane , the branch

Vibration analysis of partially cracked plate submerged in fluid

NASA Astrophysics Data System (ADS)

Soni, Shashank; Jain, N. K.; Joshi, P. V.

2018-01-01

The present work proposes an analytical model for vibration analysis of partially cracked rectangular plates coupled with fluid medium. The governing equation of motion for the isotropic plate based on the classical plate theory is modified to accommodate a part through continuous line crack according to simplified line spring model. The influence of surrounding fluid medium is incorporated in the governing equation in the form of inertia effects based on velocity potential function and Bernoulli's equations. Both partially and totally submerged plate configurations are considered. The governing equation also considers the in-plane stretching due to lateral deflection in the form of in-plane forces which introduces geometric non-linearity into the system. The fundamental frequencies are evaluated by expressing the lateral deflection in terms of modal functions. The assessment of the present results is carried out for intact submerged plate as to the best of the author's knowledge the literature lacks in analytical results for submerged cracked plates. New results for fundamental frequencies are presented as affected by crack length, fluid level, fluid density and immersed depth of plate. By employing the method of multiple scales, the frequency response and peak amplitude of the cracked structure is analyzed. The non-linear frequency response curves show the phenomenon of bending hardening or softening and the effect of fluid dynamic pressure on the response of the cracked plate.

A Functional Analytic Approach to Group Psychotherapy

ERIC Educational Resources Information Center

Vandenberghe, Luc

2009-01-01

This article provides a particular view on the use of Functional Analytical Psychotherapy (FAP) in a group therapy format. This view is based on the author's experiences as a supervisor of Functional Analytical Psychotherapy Groups, including groups for women with depression and groups for chronic pain patients. The contexts in which this approach…

Superhydrophobic Analyte Concentration Utilizing Colloid-Pillar Array SERS Substrates

DOE PAGES

Wallace, Ryan A.; Charlton, Jennifer J.; Kirchner, Teresa B.; ...

2014-11-04

In order to detect a few molecules present in a large sample it is important to know the trace components in the medicinal and environmental sample. Surface enhanced Raman spectroscopy (SERS) is a technique that can be utilized to detect molecules at very low absolute numbers. However, detection at trace concentration levels in real samples requires properly designed delivery and detection systems. Moreover, the following work involves superhydrophobic surfaces that includes silicon pillar arrays formed by lithographic and dewetting protocols. In order to generate the necessary plasmonic substrate for SERS detection, simple and flow stable Ag colloid was added tomore » the functionalized pillar array system via soaking. The pillars are used native and with hydrophobic modification. The pillars provide a means to concentrate analyte via superhydrophobic droplet evaporation effects. A 100-fold concentration of analyte was estimated, with a limit of detection of 2.9 10-12 M for mitoxantrone dihydrochloride. Additionally, analytes were delivered to the surface via a multiplex approach in order to demonstrate an ability to control droplet size and placement for scaled-up applications in real world applications. Finally, a concentration process involving transport and sequestration based on surface treatment selective wicking is demonstrated.« less

Control of the Intrinsic Sensor Response to Volatile Organic Compounds with Fringing Electric Fields.

PubMed

Henning, Alex; Swaminathan, Nandhini; Vaknin, Yonathan; Jurca, Titel; Shimanovich, Klimentiy; Shalev, Gil; Rosenwaks, Yossi

2018-01-26

The ability to control surface-analyte interaction allows tailoring chemical sensor sensitivity to specific target molecules. By adjusting the bias of the shallow p-n junctions in the electrostatically formed nanowire (EFN) chemical sensor, a multiple gate transistor with an exposed top dielectric layer allows tuning of the fringing electric field strength (from 0.5 × 10 7 to 2.5 × 10 7 V/m) above the EFN surface. Herein, we report that the magnitude and distribution of this fringing electric field correlate with the intrinsic sensor response to volatile organic compounds. The local variations of the surface electric field influence the analyte-surface interaction affecting the work function of the sensor surface, assessed by Kelvin probe force microscopy on the nanometer scale. We show that the sensitivity to fixed vapor analyte concentrations can be nullified and even reversed by varying the fringing field strength, and demonstrate selectivity between ethanol and n-butylamine at room temperature using a single transistor without any extrinsic chemical modification of the exposed SiO 2 surface. The results imply an electric-field-controlled analyte reaction with a dielectric surface extremely compelling for sensitivity and selectivity enhancement in chemical sensors.

Superhydrophobic Analyte Concentration Utilizing Colloid-Pillar Array SERS Substrates

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

Wallace, Ryan A.; Charlton, Jennifer J.; Kirchner, Teresa B.

In order to detect a few molecules present in a large sample it is important to know the trace components in the medicinal and environmental sample. Surface enhanced Raman spectroscopy (SERS) is a technique that can be utilized to detect molecules at very low absolute numbers. However, detection at trace concentration levels in real samples requires properly designed delivery and detection systems. Moreover, the following work involves superhydrophobic surfaces that includes silicon pillar arrays formed by lithographic and dewetting protocols. In order to generate the necessary plasmonic substrate for SERS detection, simple and flow stable Ag colloid was added tomore » the functionalized pillar array system via soaking. The pillars are used native and with hydrophobic modification. The pillars provide a means to concentrate analyte via superhydrophobic droplet evaporation effects. A 100-fold concentration of analyte was estimated, with a limit of detection of 2.9 10-12 M for mitoxantrone dihydrochloride. Additionally, analytes were delivered to the surface via a multiplex approach in order to demonstrate an ability to control droplet size and placement for scaled-up applications in real world applications. Finally, a concentration process involving transport and sequestration based on surface treatment selective wicking is demonstrated.« less

When can a single-species, density-dependent model capture the dynamics of a consumer-resource system?

PubMed

Reynolds, Sara A; Brassil, Chad E

2013-12-21

Single-species population models often include density-dependence phenomenologically in order to approximate higher order mechanisms. Here we consider the common scenario in which density-dependence acts via depletion of a renewed resource. When the response of the resource is very quick relative to that of the consumer, the consumer dynamics can be captured by a single-species, density-dependent model. Time scale separation is used to show analytically how the shape of the density-dependent relationship depends on the type of resource and the form of the functional response. Resource types of abiotic, biotic, and biotic with migration are considered, in combination with linear and saturating functional responses. In some cases, we derive familiar forms of single-species models, adding to the justification for their use. In other scenarios novel forms of density-dependence are derived, for example an abiotic resource and a saturating functional response can result in a nonlinear density-dependent relationship in the associated single-species model of the consumer. In this case, the per capita relationship has both concave-up and concave-down sections. © 2013 Published by Elsevier Ltd. All rights reserved.

Generalized moment analysis of magnetic field correlations for accumulations of spherical and cylindrical magnetic pertubers

NASA Astrophysics Data System (ADS)

Kurz, Felix; Kampf, Thomas; Buschle, Lukas; Schlemmer, Heinz-Peter; Bendszus, Martin; Heiland, Sabine; Ziener, Christian

2016-12-01

In biological tissue, an accumulation of similarly shaped objects with a susceptibility difference to the surrounding tissue generates a local distortion of the external magnetic field in magnetic resonance imaging. It induces stochastic field fluctuations that characteristically influence proton spin diffusion in the vicinity of these magnetic perturbers. The magnetic field correlation that is associated with such local magnetic field inhomogeneities can be expressed in the form of a dynamic frequency autocorrelation function that is related to the time evolution of the measured magnetization. Here, an eigenfunction expansion for two simple magnetic perturber shapes, that of spheres and cylinders, is considered for restricted spin diffusion in a simple model geometry. Then, the concept of generalized moment analysis, an approximation technique that is applied in the study of (non-)reactive processes that involve Brownian motion, allows to provide analytical expressions for the correlation function for different exponential decay forms. Results for the biexponential decay for both spherical and cylindrical magnetized objects are derived and compared with the frequently used (less accurate) monoexponential decay forms. They are in asymptotic agreement with the numerically exact value of the correlation function for long and short times.

On the distribution of local dissipation scales in turbulent flows

NASA Astrophysics Data System (ADS)

May, Ian; Morshed, Khandakar; Venayagamoorthy, Karan; Dasi, Lakshmi

2014-11-01

Universality of dissipation scales in turbulence relies on self-similar scaling and large scale independence. We show that the probability density function of dissipation scales, Q (η) , is analytically defined by the two-point correlation function, and the Reynolds number (Re). We also present a new analytical form for the two-point correlation function for the dissipation scales through a generalized definition of a directional Taylor microscale. Comparison of Q (η) predicted within this framework and published DNS data shows excellent agreement. It is shown that for finite Re no single similarity law exists even for the case of homogeneous isotropic turbulence. Instead a family of scaling is presented, defined by Re and a dimensionless local inhomogeneity parameter based on the spatial gradient of the rms velocity. For moderate Re inhomogeneous flows, we note a strong directional dependence of Q (η) dictated by the principal Reynolds stresses. It is shown that the mode of the distribution Q (η) significantly shifts to sub-Kolmogorov scales along the inhomogeneous directions, as in wall bounded turbulence. This work extends the classical Kolmogorov's theory to finite Re homogeneous isotropic turbulence as well as the case of inhomogeneous anisotropic turbulence.

Two-particle correlation function and dihadron correlation approach

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

Vechernin, V. V., E-mail: v.vechernin@spbu.ru; Ivanov, K. O.; Neverov, D. I.

It is shown that, in the case of asymmetric nuclear interactions, the application of the traditional dihadron correlation approach to determining a two-particle correlation function C may lead to a form distorted in relation to the canonical pair correlation function {sub C}{sup 2}. This result was obtained both by means of exact analytic calculations of correlation functions within a simple string model for proton–nucleus and deuteron–nucleus collisions and by means of Monte Carlo simulations based on employing the HIJING event generator. It is also shown that the method based on studying multiplicity correlations in two narrow observation windows separated inmore » rapidity makes it possible to determine correctly the canonical pair correlation function C{sub 2} for all cases, including the case where the rapidity distribution of product particles is not uniform.« less

YORP torque as the function of shape harmonics

NASA Astrophysics Data System (ADS)

Breiter, Sławomir; Michalska, Hanna

2008-08-01

The second-order analytical approximation of the mean Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) torque components is given as an explicit function of the shape spherical harmonics coefficients for a sufficiently regular minor body. The results are based upon a new expression for the insolation function, significantly simpler than in previous works. Linearized plane-parallel model of the temperature distribution derived from the insolation function allows us to take into account a non-zero conductivity. Final expressions for the three average components of the YORP torque related with rotation period, obliquity and precession are given in a form of the Legendre series of the cosine of obliquity. The series have good numerical properties and can be easily truncated according to the degree of the Legendre polynomials or associated functions, with first two terms playing the principal role.

Chemical Functionalization of Graphene Family Members

NASA Astrophysics Data System (ADS)

Vacchi, Isabella Anna; Ménard-Moyon, Cécilia; Bianco, Alberto

2017-01-01

Thanks to their outstanding physicochemical properties, graphene and its derivatives are interesting nanomaterials with a high potential in several fields. Graphene, graphene oxide, and reduced graphene oxide, however, differ partially in their characteristics due to their diverse surface composition. Those differences influence the chemical reactivity of these materials. In the following chapter the reactivity and main functionalization reactions performed on graphene, graphene oxide, and reduced graphene oxide are discussed. A part is also dedicated to the main analytical techniques used for characterization of these materials. Functionalization of graphene and its derivatives is highly important to modulate their characteristics and design graphene-based conjugates with novel properties. Functionalization can be covalent by forming strong and stable bonds with the graphene surface, or non-covalent via π-π, electrostatic, hydrophobic, and/or van der Waals interactions. Both types of functionalization are currently exploited.

Equivalent-circuit models for electret-based vibration energy harvesters

NASA Astrophysics Data System (ADS)

Phu Le, Cuong; Halvorsen, Einar

2017-08-01

This paper presents a complete analysis to build a tool for modelling electret-based vibration energy harvesters. The calculational approach includes all possible effects of fringing fields that may have significant impact on output power. The transducer configuration consists of two sets of metal strip electrodes on a top substrate that faces electret strips deposited on a bottom movable substrate functioning as a proof mass. Charge distribution on each metal strip is expressed by series expansion using Chebyshev polynomials multiplied by a reciprocal square-root form. The Galerkin method is then applied to extract all charge induction coefficients. The approach is validated by finite element calculations. From the analytic tool, a variety of connection schemes for power extraction in slot-effect and cross-wafer configurations can be lumped to a standard equivalent circuit with inclusion of parasitic capacitance. Fast calculation of the coefficients is also obtained by a proposed closed-form solution based on leading terms of the series expansions. The achieved analytical result is an important step for further optimisation of the transducer geometry and maximising harvester performance.

Solid phase extraction for the speciation and preconcentration of inorganic selenium in water samples: a review.

PubMed

Herrero Latorre, C; Barciela García, J; García Martín, S; Peña Crecente, R M

2013-12-04

Selenium is an essential element for the normal cellular function of living organisms. However, selenium is toxic at concentrations of only three to five times higher than the essential concentration. The inorganic forms (mainly selenite and selenate) present in environmental water generally exhibit higher toxicity (up to 40 times) than organic forms. Therefore, the determination of low levels of different inorganic selenium species in water is an analytical challenge. Solid-phase extraction has been used as a separation and/or preconcentration technique prior to the determination of selenium species due to the need for accurate measurements for Se species in water at extremely low levels. The present paper provides a critical review of the published methods for inorganic selenium speciation in water samples using solid phase extraction as a preconcentration procedure. On the basis of more than 75 references, the different speciation strategies used for this task have been highlighted and classified. The solid-phase extraction sorbents and the performance and analytical characteristics of the developed methods for Se speciation are also discussed. Copyright © 2013 Elsevier B.V. All rights reserved.

Systematic and simulation-free coarse graining of homopolymer melts: a relative-entropy-based study.

PubMed

Yang, Delian; Wang, Qiang

2015-09-28

We applied the systematic and simulation-free strategy proposed in our previous work (D. Yang and Q. Wang, J. Chem. Phys., 2015, 142, 054905) to the relative-entropy-based (RE-based) coarse graining of homopolymer melts. RE-based coarse graining provides a quantitative measure of the coarse-graining performance and can be used to select the appropriate analytic functional forms of the pair potentials between coarse-grained (CG) segments, which are more convenient to use than the tabulated (numerical) CG potentials obtained from structure-based coarse graining. In our general coarse-graining strategy for homopolymer melts using the RE framework proposed here, the bonding and non-bonded CG potentials are coupled and need to be solved simultaneously. Taking the hard-core Gaussian thread model (K. S. Schweizer and J. G. Curro, Chem. Phys., 1990, 149, 105) as the original system, we performed RE-based coarse graining using the polymer reference interaction site model theory under the assumption that the intrachain segment pair correlation functions of CG systems are the same as those in the original system, which de-couples the bonding and non-bonded CG potentials and simplifies our calculations (that is, we only calculated the latter). We compared the performance of various analytic functional forms of non-bonded CG pair potential and closures for CG systems in RE-based coarse graining, as well as the structural and thermodynamic properties of original and CG systems at various coarse-graining levels. Our results obtained from RE-based coarse graining are also compared with those from structure-based coarse graining.

"Analytical" vector-functions I

NASA Astrophysics Data System (ADS)

Todorov, Vladimir Todorov

2017-12-01

In this note we try to give a new (or different) approach to the investigation of analytical vector functions. More precisely a notion of a power xn; n ∈ ℕ+ of a vector x ∈ ℝ3 is introduced which allows to define an "analytical" function f : ℝ3 → ℝ3. Let furthermore f (ξ )= ∑n =0 ∞ anξn be an analytical function of the real variable ξ. Here we replace the power ξn of the number ξ with the power of a vector x ∈ ℝ3 to obtain a vector "power series" f (x )= ∑n =0 ∞ anxn . We research some properties of the vector series as well as some applications of this idea. Note that an "analytical" vector function does not depend of any basis, which may be used in research into some problems in physics.

Models for randomly distributed nanoscopic domains on spherical vesicles

NASA Astrophysics Data System (ADS)

Anghel, Vinicius N. P.; Bolmatov, Dima; Katsaras, John

2018-06-01

The existence of lipid domains in the plasma membrane of biological systems has proven controversial, primarily due to their nanoscopic size—a length scale difficult to interrogate with most commonly used experimental techniques. Scattering techniques have recently proven capable of studying nanoscopic lipid domains populating spherical vesicles. However, the development of analytical methods able of predicting and analyzing domain pair correlations from such experiments has not kept pace. Here, we developed models for the random distribution of monodisperse, circular nanoscopic domains averaged on the surface of a spherical vesicle. Specifically, the models take into account (i) intradomain correlations corresponding to form factors and interdomain correlations corresponding to pair distribution functions, and (ii) the analytical computation of interdomain correlations for cases of two and three domains on a spherical vesicle. In the case of more than three domains, these correlations are treated either by Monte Carlo simulations or by spherical analogs of the Ornstein-Zernike and Percus-Yevick (PY) equations. Importantly, the spherical analog of the PY equation works best in the case of nanoscopic size domains, a length scale that is mostly inaccessible by experimental approaches such as, for example, fluorescent techniques and optical microscopies. The analytical form factors and structure factors of nanoscopic domains populating a spherical vesicle provide a new and important framework for the quantitative analysis of experimental data from commonly studied phase-separated vesicles used in a wide range of biophysical studies.

Analysis of the strong coupling form factors of ΣbNB and ΣcND in QCD sum rules

NASA Astrophysics Data System (ADS)

Yu, Guo-Liang; Wang, Zhi-Gang; Li, Zhen-Yu

2017-08-01

In this article, we study the strong interaction of the vertices Σ b NB and Σ c ND using the three-point QCD sum rules under two different Dirac structures. Considering the contributions of the vacuum condensates up to dimension 5 in the operation product expansion, the form factors of these vertices are calculated. Then, we fit the form factors into analytical functions and extrapolate them into time-like regions, which gives the coupling constants. Our analysis indicates that the coupling constants for these two vertices are G ΣbNB = 0.43±0.01 GeV-1 and G ΣcND = 3.76±0.05 GeV-1. Supported by Fundamental Research Funds for the Central Universities (2016MS133)

Fame and obsolescence: Disentangling growth and aging dynamics of patent citations.

PubMed

Higham, K W; Governale, M; Jaffe, A B; Zülicke, U

2017-04-01

We present an analysis of citations accrued over time by patents granted by the United States Patent and Trademark Office in 1998. In contrast to previous studies, a disaggregation by technology category is performed, and exogenously caused citation-number growth is controlled for. Our approach reveals an intrinsic citation rate that clearly separates into an-in the long run, exponentially time-dependent-aging function and a completely time-independent preferential-attachment-type growth kernel. For the general case of such a separable citation rate, we obtain the time-dependent citation distribution analytically in a form that is valid for any functional form of its aging and growth parts. Good agreement between theory and long-time characteristics of patent-citation data establishes our work as a useful framework for addressing still open questions about knowledge-propagation dynamics, such as the observed excess of citations at short times.

An analytic method to account for drag in the Vinti Satellite theory

NASA Technical Reports Server (NTRS)

Watson, J. S.; Mistretta, G. D.; Bonavito, N. L.

1974-01-01

To retain separability in the Vinti theory of earth satellite motion when a nonconservative force such as air drag is considered, a set of variational equations for the orbital elements are introduced, and expressed as functions of the transverse, radial, and normal components of the nonconservative forces acting on the system. In this approach, the Hamiltonian is preserved in form, and remains the total energy, but the initial or boundary conditions and hence the Jacobi constants of the motion advance with time through the variational equations. In particular, the atmospheric density profile is written as a fitted exponential function of the eccentric anomaly, which adheres to tabular data at all altitudes and simultaneously reduced the variational equations to indefinite integrals with closed form evaluations. The values of the limits for any arbitrary time interval are obtained from the Vinti program.

Fame and obsolescence: Disentangling growth and aging dynamics of patent citations

NASA Astrophysics Data System (ADS)

Higham, K. W.; Governale, M.; Jaffe, A. B.; Zülicke, U.

2017-04-01

We present an analysis of citations accrued over time by patents granted by the United States Patent and Trademark Office in 1998. In contrast to previous studies, a disaggregation by technology category is performed, and exogenously caused citation-number growth is controlled for. Our approach reveals an intrinsic citation rate that clearly separates into an—in the long run, exponentially time-dependent—aging function and a completely time-independent preferential-attachment-type growth kernel. For the general case of such a separable citation rate, we obtain the time-dependent citation distribution analytically in a form that is valid for any functional form of its aging and growth parts. Good agreement between theory and long-time characteristics of patent-citation data establishes our work as a useful framework for addressing still open questions about knowledge-propagation dynamics, such as the observed excess of citations at short times.

Path-integral approach to the Wigner-Kirkwood expansion.

PubMed

Jizba, Petr; Zatloukal, Václav

2014-01-01

We study the high-temperature behavior of quantum-mechanical path integrals. Starting from the Feynman-Kac formula, we derive a functional representation of the Wigner-Kirkwood perturbation expansion for quantum Boltzmann densities. As shown by its applications to different potentials, the presented expansion turns out to be quite efficient in generating analytic form of the higher-order expansion coefficients. To put some flesh on the bare bones, we apply the expansion to obtain basic thermodynamic functions of the one-dimensional anharmonic oscillator. Further salient issues, such as generalization to the Bloch density matrix and comparison with the more customary world-line formulation, are discussed.

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

NASA Astrophysics Data System (ADS)

Sulyok, G.

2017-07-01

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

Spacing distribution functions for the one-dimensional point-island model with irreversible attachment

NASA Astrophysics Data System (ADS)

González, Diego Luis; Pimpinelli, Alberto; Einstein, T. L.

2011-07-01

We study the configurational structure of the point-island model for epitaxial growth in one dimension. In particular, we calculate the island gap and capture zone distributions. Our model is based on an approximate description of nucleation inside the gaps. Nucleation is described by the joint probability density pnXY(x,y), which represents the probability density to have nucleation at position x within a gap of size y. Our proposed functional form for pnXY(x,y) describes excellently the statistical behavior of the system. We compare our analytical model with extensive numerical simulations. Our model retains the most relevant physical properties of the system.

On the Analytical and Numerical Properties of the Truncated Laplace Transform

DTIC Science & Technology

2014-05-01

classical study of the truncated Fourier trans- form. The resulting algorithms are applicable to all environments likely to be encountered in applications...other words, (((La,b)∗ ◦ La,b) (un)) (t) = ∫ b a 1 t+ s un(s)ds = α 2 nun (t). (2.69) Observation 2.22. Similarly, La,b ◦ (La,b)∗ of a function g ∈ L2(0...3.20)) are even and odd functions in the regular sense: Un(s) = (Cγ(un)) (s) = (−1) nUn (−s). (3.25) In particular, at the point s = 0, we have: U2j+1(0

The Modified Hartmann Potential Effects on γ-rigid Bohr Hamiltonian

NASA Astrophysics Data System (ADS)

Suparmi, A.; Cari, C.; Nur Pratiwi, Beta

2018-04-01

In this paper, we present the solution of Bohr Hamiltonian in the case of γ-rigid for the modified Hartmann potential. The modified Hartmann potential was formed from the original Hartmann potential, consists of β function and θ function. By using the separation method, the three-dimensional Bohr Hamiltonian equation was reduced into three one-dimensional Schrodinger-like equation which was solved analytically. The results for the wavefunction were shown in mathematically, while for the binding energy was solved numerically. The numerical binding energy for the presence of the modified Hartmann potential is lower than the binding energy value in the absence of modified Hartmann potential effect.

Eulerian Mapping Closure Approach for Probability Density Function of Concentration in Shear Flows

NASA Technical Reports Server (NTRS)

He, Guowei; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

The Eulerian mapping closure approach is developed for uncertainty propagation in computational fluid mechanics. The approach is used to study the Probability Density Function (PDF) for the concentration of species advected by a random shear flow. An analytical argument shows that fluctuation of the concentration field at one point in space is non-Gaussian and exhibits stretched exponential form. An Eulerian mapping approach provides an appropriate approximation to both convection and diffusion terms and leads to a closed mapping equation. The results obtained describe the evolution of the initial Gaussian field, which is in agreement with direct numerical simulations.

Mass functions from the excursion set model

NASA Astrophysics Data System (ADS)

Hiotelis, Nicos; Del Popolo, Antonino

2017-11-01

Aims: We aim to study the stochastic evolution of the smoothed overdensity δ at scale S of the form δ(S) = ∫0S K(S,u)dW(u), where K is a kernel and dW is the usual Wiener process. Methods: For a Gaussian density field, smoothed by the top-hat filter, in real space, we used a simple kernel that gives the correct correlation between scales. A Monte Carlo procedure was used to construct random walks and to calculate first crossing distributions and consequently mass functions for a constant barrier. Results: We show that the evolution considered here improves the agreement with the results of N-body simulations relative to analytical approximations which have been proposed from the same problem by other authors. In fact, we show that an evolution which is fully consistent with the ideas of the excursion set model, describes accurately the mass function of dark matter haloes for values of ν ≤ 1 and underestimates the number of larger haloes. Finally, we show that a constant threshold of collapse, lower than it is usually used, it is able to produce a mass function which approximates the results of N-body simulations for a variety of redshifts and for a wide range of masses. Conclusions: A mass function in good agreement with N-body simulations can be obtained analytically using a lower than usual constant collapse threshold.

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

Choun, Yoon Seok, E-mail: ychoun@gmail.com

The Heun function generalizes all well-known special functions such as Spheroidal Wave, Lame, Mathieu, and hypergeometric {sub 2}F{sub 1}, {sub 1}F{sub 1} and {sub 0}F{sub 1} functions. Heun functions are applicable to diverse areas such as theory of black holes, lattice systems in statistical mechanics, solution of the Schrödinger equation of quantum mechanics, and addition of three quantum spins. In this paper I will apply three term recurrence formula (Y.S. Choun, (arXiv:1303.0806), 2013) to the power series expansion in closed forms of Heun function (infinite series and polynomial) including all higher terms of A{sub n}’s. Section 3 contains my analysismore » on applying the power series expansions of Heun function to a recent paper (R.S. Maier, Math. Comp. 33 (2007) 811–843). Due to space restriction final equations for the 192 Heun functions are not included in the paper, but feel free to contact me for the final solutions. Section 4 contains two additional examples using the power series expansions of Heun function. This paper is 3rd out of 10 in series “Special functions and three term recurrence formula (3TRF)”. See Section 5 for all the papers in the series. The previous paper in series deals with three term recurrence formula (3TRF). The next paper in the series describes the integral forms of Heun function and its asymptotic behaviors analytically. -- Highlights: •Power series expansion for infinite series of Heun function using 3 term rec. form. •Power series for polynomial which makes B{sub n} term terminated of Heun function. •Applicable to areas such as the Teukolsky equation in Kerr–Newman–de Sitter geometries.« less

Bounded extremum seeking with discontinuous dithers

DOE PAGES

Scheinker, Alexander; Scheinker, David

2016-03-21

The analysis of discontinuous extremum seeking (ES) controllers, e.g. those applicable to digital systems, has historically been more complicated than that of continuous controllers. We establish a simple and general extension of a recently developed bounded form of ES to a general class of oscillatory functions, including functions discontinuous with respect to time, such as triangle or square waves with dead time. We establish our main results by combining a novel idea for oscillatory control with an extension of functional analytic techniques originally utilized by Kurzweil, Jarnik, Sussmann, and Liu in the late 80s and early 90s and recently studiedmore » by Durr et al. Lastly, we demonstrate the value of the result with an application to inverter switching control.« less

Simulation Of Wave Function And Probability Density Of Modified Poschl Teller Potential Derived Using Supersymmetric Quantum Mechanics

NASA Astrophysics Data System (ADS)

Angraini, Lily Maysari; Suparmi, Variani, Viska Inda

2010-12-01

SUSY quantum mechanics can be applied to solve Schrodinger equation for high dimensional system that can be reduced into one dimensional system and represented in lowering and raising operators. Lowering and raising operators can be obtained using relationship between original Hamiltonian equation and the (super) potential equation. In this paper SUSY quantum mechanics is used as a method to obtain the wave function and the energy level of the Modified Poschl Teller potential. The graph of wave function equation and probability density is simulated by using Delphi 7.0 programming language. Finally, the expectation value of quantum mechanics operator could be calculated analytically using integral form or probability density graph resulted by the programming.

Cosmic reionization on computers: The faint end of the galaxy luminosity function

DOE PAGES

Gnedin, Nickolay Y.

2016-07-01

Using numerical cosmological simulations completed under the “Cosmic Reionization On Computers” project, I explore theoretical predictions for the faint end of the galaxy UV luminosity functions atmore » $$z\\gtrsim 6$$. A commonly used Schechter function approximation with the magnitude cut at $${M}_{{\\rm{cut}}}\\sim -13$$ provides a reasonable fit to the actual luminosity function of simulated galaxies. When the Schechter functional form is forced on the luminosity functions from the simulations, the magnitude cut $${M}_{{\\rm{cut}}}$$ is found to vary between -12 and -14 with a mild redshift dependence. Here, an analytical model of reionization from Madau et al., as used by Robertson et al., provides a good description of the simulated results, which can be improved even further by adding two physically motivated modifications to the original Madau et al. equation.« less

Cosmic reionization on computers: The faint end of the galaxy luminosity function

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

Gnedin, Nickolay Y.

Using numerical cosmological simulations completed under the “Cosmic Reionization On Computers” project, I explore theoretical predictions for the faint end of the galaxy UV luminosity functions atmore » $$z\\gtrsim 6$$. A commonly used Schechter function approximation with the magnitude cut at $${M}_{{\\rm{cut}}}\\sim -13$$ provides a reasonable fit to the actual luminosity function of simulated galaxies. When the Schechter functional form is forced on the luminosity functions from the simulations, the magnitude cut $${M}_{{\\rm{cut}}}$$ is found to vary between -12 and -14 with a mild redshift dependence. Here, an analytical model of reionization from Madau et al., as used by Robertson et al., provides a good description of the simulated results, which can be improved even further by adding two physically motivated modifications to the original Madau et al. equation.« less

SU-E-I-16: Scan Length Dependency of the Radial Dose Distribution in a Long Polyethylene Cylinder

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

Bakalyar, D; McKenney, S; Feng, W

Purpose: The area-averaged dose in the central plane of a long cylinder following a CT scan depends upon the radial dose distribution and the length of the scan. The ICRU/TG200 phantom, a polyethylene cylinder 30 cm in diameter and 60 cm long, was the subject of this study. The purpose was to develop an analytic function that could determine the dose for a scan length L at any point in the central plane of this phantom. Methods: Monte Carlo calculations were performed on a simulated ICRU/TG200 phantom under conditions of cylindrically symmetric conditions of irradiation. Thus, the radial dose distributionmore » function must be an even function that accounts for two competing effects: The direct beam makes its weakest contribution at the center while the scatter begins abruptly at the outer radius and grows as the center is approached. The scatter contribution also increases with scan length with the increase approaching its limiting value at the periphery faster than along the central axis. An analytic function was developed that fit the data and possessed these features. Results: Symmetry and continuity dictate a local extremum at the center which is a minimum for the ICRU/TG200 phantom. The relative depth of the minimum decreases as the scan length grows and an absolute maximum can occur between the center and outer edge of the cylinders. As the scan length grows, the relative dip in the center decreases so that for very long scan lengths, the dose profile is relatively flat. Conclusion: An analytic function characterizes the radial and scan length dependency of dose for long cylindrical phantoms. The function can be integrated with the results expressed in closed form. One use for this is to help determine average dose distribution over the central cylinder plane for any scan length.« less

Development of an analytical solution for thermal single-well injection-withdrawal tests in horizontally fractured reservoirs

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

Jung, Yoojin

In this study, we have developed an analytical solution for thermal single-well injection-withdrawal tests in horizontally fractured reservoirs where fluid flow through the fracture is radial. The dimensionless forms of the governing equations and the initial and boundary conditions in the radial flow system can be written in a form identical to those in the linear flow system developed by Jung and Pruess [Jung, Y., and K. Pruess (2012), A Closed-Form Analytical Solution for Thermal Single-Well Injection-Withdrawal Tests, Water Resour. Res., 48, W03504, doi:10.1029/2011WR010979], and therefore the analytical solutions developed in Jung and Pruess (2012) can be applied to computemore » the time dependence of temperature recovery at the injection/withdrawal well in a horizontally oriented fracture with radial flow.« less

Structural changes of TasA in biofilm formation of Bacillus subtilis.

PubMed

Diehl, Anne; Roske, Yvette; Ball, Linda; Chowdhury, Anup; Hiller, Matthias; Molière, Noel; Kramer, Regina; Stöppler, Daniel; Worth, Catherine L; Schlegel, Brigitte; Leidert, Martina; Cremer, Nils; Erdmann, Natalja; Lopez, Daniel; Stephanowitz, Heike; Krause, Eberhard; van Rossum, Barth-Jan; Schmieder, Peter; Heinemann, Udo; Turgay, Kürşad; Akbey, Ümit; Oschkinat, Hartmut

2018-03-27

Microorganisms form surface-attached communities, termed biofilms, which can serve as protection against host immune reactions or antibiotics. Bacillus subtilis biofilms contain TasA as major proteinaceous component in addition to exopolysaccharides. In stark contrast to the initially unfolded biofilm proteins of other bacteria, TasA is a soluble, stably folded monomer, whose structure we have determined by X-ray crystallography. Subsequently, we characterized in vitro different oligomeric forms of TasA by NMR, EM, X-ray diffraction, and analytical ultracentrifugation (AUC) experiments. However, by magic-angle spinning (MAS) NMR on live biofilms, a swift structural change toward only one of these forms, consisting of homogeneous and protease-resistant, β-sheet-rich fibrils, was observed in vivo. Thereby, we characterize a structural change from a globular state to a fibrillar form in a functional prokaryotic system on the molecular level. Copyright © 2018 the Author(s). Published by PNAS.

Structural changes of TasA in biofilm formation of Bacillus subtilis

PubMed Central

Diehl, Anne; Roske, Yvette; Ball, Linda; Chowdhury, Anup; Hiller, Matthias; Molière, Noel; Kramer, Regina; Stöppler, Daniel; Worth, Catherine L.; Schlegel, Brigitte; Leidert, Martina; Cremer, Nils; Erdmann, Natalja; Lopez, Daniel; Stephanowitz, Heike; Krause, Eberhard; Schmieder, Peter; Akbey, Ümit; Oschkinat, Hartmut

2018-01-01

Microorganisms form surface-attached communities, termed biofilms, which can serve as protection against host immune reactions or antibiotics. Bacillus subtilis biofilms contain TasA as major proteinaceous component in addition to exopolysaccharides. In stark contrast to the initially unfolded biofilm proteins of other bacteria, TasA is a soluble, stably folded monomer, whose structure we have determined by X-ray crystallography. Subsequently, we characterized in vitro different oligomeric forms of TasA by NMR, EM, X-ray diffraction, and analytical ultracentrifugation (AUC) experiments. However, by magic-angle spinning (MAS) NMR on live biofilms, a swift structural change toward only one of these forms, consisting of homogeneous and protease-resistant, β-sheet–rich fibrils, was observed in vivo. Thereby, we characterize a structural change from a globular state to a fibrillar form in a functional prokaryotic system on the molecular level. PMID:29531041

[The questions of improving the information-analytical component in the reform of the health care system in Ukraine].

PubMed

Беликова, Инна В; Руденко, Леся А

2016-01-01

A priority task of the development strategy of the Ukrainian health care system is the saving and improving of public health. With the development of new economic relations, health care restructuring, the introduction of new financing mechanisms to policy-makers have an important task of the organization of operational management on the basis of timely quality information. According to many authors, the ability to improve the quality of the received information is possible due to the intercalation of information technologies. The main aim of our study is to determine the main directions of modernization of information-analytical component during the health care reform. The medical institutions reporting forms (f.20, f.12, f.17, f.47) were analyzed to achieve the goal, were conducted a survey of primary care physicians. The survey was attended by 265 family doctors, 80 of whom are family doctors of family medicine clinic of the regional center, 185 - medical centers of primary health care district centers. The analysis of the sociological research indicates that the work of the family doctor is accompanied by filling a large number of records, so according to the survey, an average of doctors per day filled about 15.74 +2.2 registration forms, on average per month 333,7+ 30 a month. The necessity of reform of the information-analytical component of the health care system have noted by 94% 1.4. Do not have a automated workstation 34.5% + 5.3 physicians of the regional center and 68% + 3.4 countryside. Possession of the computer at user level observed by 92% + 1.6, which is a good basis for the introduction of information in healthcare system. The data of the sociological survey confirm the necession of structural-functional procuring of the system of information-analytical supporting of the healthcare system of Ukraine. Annual health statistics reports are still relevant, but they need to improve and adapt to the new conditions of functioning of healthcare system and should be subject to automated processing of data at all levels.

The Framework of Intervention Engine Based on Learning Analytics

ERIC Educational Resources Information Center

Sahin, Muhittin; Yurdugül, Halil

2017-01-01

Learning analytics primarily deals with the optimization of learning environments and the ultimate goal of learning analytics is to improve learning and teaching efficiency. Studies on learning analytics seem to have been made in the form of adaptation engine and intervention engine. Adaptation engine studies are quite widespread, but intervention…

The Spectral Shift Function and Spectral Flow

NASA Astrophysics Data System (ADS)

Azamov, N. A.; Carey, A. L.; Sukochev, F. A.

2007-11-01

At the 1974 International Congress, I. M. Singer proposed that eta invariants and hence spectral flow should be thought of as the integral of a one form. In the intervening years this idea has lead to many interesting developments in the study of both eta invariants and spectral flow. Using ideas of [24] Singer’s proposal was brought to an advanced level in [16] where a very general formula for spectral flow as the integral of a one form was produced in the framework of noncommutative geometry. This formula can be used for computing spectral flow in a general semifinite von Neumann algebra as described and reviewed in [5]. In the present paper we take the analytic approach to spectral flow much further by giving a large family of formulae for spectral flow between a pair of unbounded self-adjoint operators D and D + V with D having compact resolvent belonging to a general semifinite von Neumann algebra {mathcal{N}} and the perturbation V in {mathcal{N}} . In noncommutative geometry terms we remove summability hypotheses. This level of generality is made possible by introducing a new idea from [3]. There it was observed that M. G. Krein’s spectral shift function (in certain restricted cases with V trace class) computes spectral flow. The present paper extends Krein’s theory to the setting of semifinite spectral triples where D has compact resolvent belonging to {mathcal{N}} and V is any bounded self-adjoint operator in {mathcal{N}} . We give a definition of the spectral shift function under these hypotheses and show that it computes spectral flow. This is made possible by the understanding discovered in the present paper of the interplay between spectral shift function theory and the analytic theory of spectral flow. It is this interplay that enables us to take Singer’s idea much further to create a large class of one forms whose integrals calculate spectral flow. These advances depend critically on a new approach to the calculus of functions of non-commuting operators discovered in [3] which generalizes the double operator integral formalism of [8-10]. One surprising conclusion that follows from our results is that the Krein spectral shift function is computed, in certain circumstances, by the Atiyah-Patodi-Singer index theorem [2].

Current limit diagrams for dendrite formation in solid-state electrolytes for Li-ion batteries

NASA Astrophysics Data System (ADS)

Raj, R.; Wolfenstine, J.

2017-03-01

We build upon the concept that nucleation of lithium dendrites at the lithium anode-solid state electrolyte interface is instigated by the higher resistance of grain boundaries that raises the local electro-chemical potential of lithium, near the lithium-electrode. This excess electro-chemo-mechanical potential, however, is reduced by the mechanical back stress generated when the dendrite is formed within the electrolyte. These parameters are coalesced into an analytical model that prescribes a specific criterion for dendrite formation. The results are presented in the form of current limit diagrams that show the "safe" and "fail" regimes for battery function. A higher conductivity of the electrolyte can reduce dendrite formation.

Nonlocal Symmetries, Consistent Riccati Expansion, and Analytical Solutions of the Variant Boussinesq System

NASA Astrophysics Data System (ADS)

Feng, Lian-Li; Tian, Shou-Fu; Zhang, Tian-Tian; Zhou, Jun

2017-07-01

Under investigation in this paper is the variant Boussinesq system, which describes the propagation of surface long wave towards two directions in a certain deep trough. With the help of the truncated Painlevé expansion, we construct its nonlocal symmetry, Bäcklund transformation, and Schwarzian form, respectively. The nonlocal symmetries can be localised to provide the corresponding nonlocal group, and finite symmetry transformations and similarity reductions are computed. Furthermore, we verify that the variant Boussinesq system is solvable via the consistent Riccati expansion (CRE). By considering the consistent tan-function expansion (CTE), which is a special form of CRE, the interaction solutions between soliton and cnoidal periodic wave are explicitly studied.

Steady-state and dynamic analysis of a jet engine, gas lubricated shaft seal

NASA Technical Reports Server (NTRS)

Shapiro, W.; Colsher, R.

1974-01-01

Dynamic response of a gas-lubricated, jet-engine main shaft seal was analytically established as a function of collar misalignment and secondary seal friction. Response was obtained by a forward integration-in-time (time-transient) scheme, which traces a time history of seal motions in all its degrees of freedom. Results were summarized in the form of a seal tracking map which indicated regions of acceptable collar misalignments and secondary seal friction. Methodology, results and interpretations are comprehensively described.

Quantum corrections to quasi-periodic solution of Sine-Gordon model and periodic solution of phi4 model

NASA Astrophysics Data System (ADS)

Kwiatkowski, G.; Leble, S.

2014-03-01

Analytical form of quantum corrections to quasi-periodic solution of Sine-Gordon model and periodic solution of phi4 model is obtained through zeta function regularisation with account of all rest variables of a d-dimensional theory. Qualitative dependence of quantum corrections on parameters of the classical systems is also evaluated for a much broader class of potentials u(x) = b2f(bx) + C with b and C as arbitrary real constants.

Approximate bound-state solutions of the Dirac equation for the generalized yukawa potential plus the generalized tensor interaction

NASA Astrophysics Data System (ADS)

Ikot, Akpan N.; Maghsoodi, Elham; Hassanabadi, Hassan; Obu, Joseph A.

2014-05-01

In this paper, we obtain the approximate analytical bound-state solutions of the Dirac particle with the generalized Yukawa potential within the framework of spin and pseudospin symmetries for the arbitrary к state with a generalized tensor interaction. The generalized parametric Nikiforov-Uvarov method is used to obtain the energy eigenvalues and the corresponding wave functions in closed form. We also report some numerical results and present figures to show the effect of the tensor interaction.

On one solution of Volterra integral equations of second kind

NASA Astrophysics Data System (ADS)

Myrhorod, V.; Hvozdeva, I.

2016-10-01

A solution of Volterra integral equations of the second kind with separable and difference kernels based on solutions of corresponding equations linking the kernel and resolvent is suggested. On the basis of a discrete functions class, the equations linking the kernel and resolvent are obtained and the methods of their analytical solutions are proposed. A mathematical model of the gas-turbine engine state modification processes in the form of Volterra integral equation of the second kind with separable kernel is offered.

Enhancing robustness and immunization in geographical networks

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

Huang Liang; Department of Physics, Lanzhou University, Lanzhou 730000; Yang Kongqing

2007-03-15

We find that different geographical structures of networks lead to varied percolation thresholds, although these networks may have similar abstract topological structures. Thus, strategies for enhancing robustness and immunization of a geographical network are proposed. Using the generating function formalism, we obtain an explicit form of the percolation threshold q{sub c} for networks containing arbitrary order cycles. For three-cycles, the dependence of q{sub c} on the clustering coefficients is ascertained. The analysis substantiates the validity of the strategies with analytical evidence.

Wind tunnel investigation of a 14 foot vertical axis windmill

NASA Technical Reports Server (NTRS)

Muraca, R. J.; Guillotte, R. J.

1976-01-01

A full scale wind tunnel investigation was made to determine the performance characteristics of a 14 ft diameter vertical axis windmill. The parameters measured were wind velocity, shaft torque, shaft rotation rate, along with the drag and yawing moment. A velocity survey of the flow field downstream of the windmill was also made. The results of these tests along with some analytically predicted data are presented in the form of generalized data as a function of tip speed ratio.

Reactant conversion in homogeneous turbulence - Mathematical modeling, computational validations, and practical applications

NASA Technical Reports Server (NTRS)

Madnia, C. K.; Frankel, S. H.; Givi, P.

1992-01-01

The presently obtained closed-form analytical expressions, which predict the limiting rate of mean reactant conversion in homogeneous turbulent flows under the influence of a binary reaction, are derived via the single-point pdf method based on amplitude mapping closure. With this model, the maximum rate of the mean reactant's decay can be conveniently expressed in terms of definite integrals of the parabolic cylinder functions. The results obtained are shown to be in good agreement with data generated by direct numerical simulations.

Smart Phase Tuning in Microwave Photonic Integrated Circuits Toward Automated Frequency Multiplication by Design

NASA Astrophysics Data System (ADS)

Nabavi, N.

2018-07-01

The author investigates the monitoring methods for fine adjustment of the previously proposed on-chip architecture for frequency multiplication and translation of harmonics by design. Digital signal processing (DSP) algorithms are utilized to create an optimized microwave photonic integrated circuit functionality toward automated frequency multiplication. The implemented DSP algorithms are formed on discrete Fourier transform and optimization-based algorithms (Greedy and gradient-based algorithms), which are analytically derived and numerically compared based on the accuracy and speed of convergence criteria.

Gauge-independent decoherence models for solids in external fields

NASA Astrophysics Data System (ADS)

Wismer, Michael S.; Yakovlev, Vladislav S.

2018-04-01

We demonstrate gauge-invariant modeling of an open system of electrons in a periodic potential interacting with an optical field. For this purpose, we adapt the covariant derivative to the case of mixed states and put forward a decoherence model that has simple analytical forms in the length and velocity gauges. We demonstrate our methods by calculating harmonic spectra in the strong-field regime and numerically verifying the equivalence of the deterministic master equation to the stochastic Monte Carlo wave-function method.

Electron scattering from excited states of hydrogen: Implications for the ionization threshold law

NASA Astrophysics Data System (ADS)

Temkin, A.; Shertzer, J.

2013-05-01

The elastic scattering wave function for electrons scattered from the Nth excited state of hydrogen is the final state of the matrix element for excitation of that state. This paper deals with the solution of that problem primarily in the context of the Temkin-Poet (TP) model [A. Temkin, Phys. Rev.PHRVAO0031-899X10.1103/PhysRev.126.130 126, 130 (1962); R. Poet, J. Phys. BJPAPEH0022-370010.1088/0022-3700/11/17/019 11, 3081 (1978)], wherein only the radial parts of the interaction are included. The relevant potential for the outer electron is dominated by the Hartree potential, VNH(r). In the first part of the paper, VNH(r) is approximated by a potential WN(r), for which the scattering equation can be analytically solved. The results allow formal analytical continuation of N into the continuum, so that the ionization threshold law can be deduced. Because the analytic continuation involves going from N to an imaginary function of the momentum of the inner electron, the threshold law turns out to be an exponentially damped function of the available energy E, in qualitative accord with the result of Macek and Ihra [J. H. Macek and W. Ihra, Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.55.2024 55, 2024 (1997)] for the TP model. Thereafter, the scattering equation for the Hartree potential VNH(r) is solved numerically. The numerical aspects of these calculations have proven to be challenging and required several developments for the difficulties to be overcome. The results for VNH(r) show only a simple energy-dependent shift from the approximate potential WN(r), which therefore does not change the analytic continuation and the form of the threshold law. It is concluded that the relevant optical potential must be included in order to compare directly with the analytic result of Macek and Ihra. The paper concludes with discussions of (a) a quantum mechanical interpretation of the result, and (b) the outlook of this approach for the complete problem.

Using Extreme Tropical Precipitation Statistics to Constrain Future Climate States

NASA Astrophysics Data System (ADS)

Igel, M.; Biello, J. A.

2017-12-01

Tropical precipitation is characterized by a rapid growth in mean intensity as the column humidity increases. This behavior is examined in both a cloud resolving model and with high-resolution observations of precipitation and column humidity from CloudSat and AIRS, respectively. The model and the observations exhibit remarkable consistency and suggest a new paradigm for extreme precipitation. We show that the total precipitation can be decomposed into a product of contributions from a mean intensity, a probability of precipitation, and a global PDF of column humidity values. We use the modeling and observational results to suggest simple, analytic forms for each of these functions. The analytic representations are then used to construct a simple expression for the global accumulated precipitation as a function of the parameters of each of the component functions. As the climate warms, extreme precipitation intensity and global precipitation are expected to increase, though at different rates. When these predictions are incorporated into the new analytic expression for total precipitation, predictions for changes due to global warming to the probability of precipitation and the PDF of column humidity can be made. We show that strong constraints can be imposed on the future shape of the PDF of column humidity but that only weak constraints can be set on the probability of precipitation. These are largely imposed by the intensification of extreme precipitation. This result suggests that understanding precisely how extreme precipitation responds to climate warming is critical to predicting other impactful properties of global hydrology. The new framework can also be used to confirm and discount existing theories for shifting precipitation.

Incremental viscosity by non-equilibrium molecular dynamics and the Eyring model

NASA Astrophysics Data System (ADS)

Heyes, D. M.; Dini, D.; Smith, E. R.

2018-05-01

The viscoelastic behavior of sheared fluids is calculated by Non-Equilibrium Molecular Dynamics (NEMD) simulation, and complementary analytic solutions of a time-dependent extension of Eyring's model (EM) for shear thinning are derived. It is argued that an "incremental viscosity," ηi, or IV which is the derivative of the steady state stress with respect to the shear rate is a better measure of the physical state of the system than the conventional definition of the shear rate dependent viscosity (i.e., the shear stress divided by the strain rate). The stress relaxation function, Ci(t), associated with ηi is consistent with Boltzmann's superposition principle and is computed by NEMD and the EM. The IV of the Eyring model is shown to be a special case of the Carreau formula for shear thinning. An analytic solution for the transient time correlation function for the EM is derived. An extension of the EM to allow for significant local shear stress fluctuations on a molecular level, represented by a gaussian distribution, is shown to have the same analytic form as the original EM but with the EM stress replaced by its time and spatial average. Even at high shear rates and on small scales, the probability distribution function is almost gaussian (apart from in the wings) with the peak shifted by the shear. The Eyring formula approximately satisfies the Fluctuation Theorem, which may in part explain its success in representing the shear thinning curves of a wide range of different types of chemical systems.

Number series of atoms, interatomic bonds and interface bonds defining zinc-blende nanocrystals as function of size, shape and surface orientation: Analytic tools to interpret solid state spectroscopy data

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

König, Dirk, E-mail: dirk.koenig@unsw.edu.au

2016-08-15

Semiconductor nanocrystals (NCs) experience stress and charge transfer by embedding materials or ligands and impurity atoms. In return, the environment of NCs experiences a NC stress response which may lead to matrix deformation and propagated strain. Up to now, there is no universal gauge to evaluate the stress impact on NCs and their response as a function of NC size d{sub NC}. I deduce geometrical number series as analytical tools to obtain the number of NC atoms N{sub NC}(d{sub NC}[i]), bonds between NC atoms N{sub bnd}(d{sub NC}[i]) and interface bonds N{sub IF}(d{sub NC}[i]) for seven high symmetry zinc-blende (zb) NCsmore » with low-index faceting: {001} cubes, {111} octahedra, {110} dodecahedra, {001}-{111} pyramids, {111} tetrahedra, {111}-{001} quatrodecahedra and {001}-{111} quadrodecahedra. The fundamental insights into NC structures revealed here allow for major advancements in data interpretation and understanding of zb- and diamond-lattice based nanomaterials. The analytical number series can serve as a standard procedure for stress evaluation in solid state spectroscopy due to their deterministic nature, easy use and general applicability over a wide range of spectroscopy methods as well as NC sizes, forms and materials.« less

How Do Gut Feelings Feature in Tutorial Dialogues on Diagnostic Reasoning in GP Traineeship?

ERIC Educational Resources Information Center

Stolper, C. F.; Van de Wiel, M. W. J.; Hendriks, R. H. M.; Van Royen, P.; Van Bokhoven, M. A.; Van der Weijden, T.; Dinant, G. J.

2015-01-01

Diagnostic reasoning is considered to be based on the interaction between analytical and non-analytical cognitive processes. Gut feelings, a specific form of non-analytical reasoning, play a substantial role in diagnostic reasoning by general practitioners (GPs) and may activate analytical reasoning. In GP traineeships in the Netherlands, trainees…

Nonlinearity of the forward-backward correlation function in the model with string fusion

NASA Astrophysics Data System (ADS)

Vechernin, Vladimir

2017-12-01

The behavior of the forward-backward correlation functions and the corresponding correlation coefficients between multiplicities and transverse momenta of particles produced in high energy hadronic interactions is analyzed by analytical and MC calculations in the models with and without string fusion. The string fusion is taking into account in simplified form by introducing the lattice in the transverse plane. The results obtained with two alternative definitions of the forward-backward correlation coefficient are compared. It is shown that the nonlinearity of correlation functions increases with the width of observation windows, leading at small string density to a strong dependence of correlation coefficient value on the definition. The results of the modeling enable qualitatively to explain the experimentally observed features in the behavior of the correlation functions between multiplicities and mean transverse momenta at small and large multiplicities.

Trajectory phase transitions and dynamical Lee-Yang zeros of the Glauber-Ising chain.

PubMed

Hickey, James M; Flindt, Christian; Garrahan, Juan P

2013-07-01

We examine the generating function of the time-integrated energy for the one-dimensional Glauber-Ising model. At long times, the generating function takes on a large-deviation form and the associated cumulant generating function has singularities corresponding to continuous trajectory (or "space-time") phase transitions between paramagnetic trajectories and ferromagnetically or antiferromagnetically ordered trajectories. In the thermodynamic limit, the singularities make up a whole curve of critical points in the complex plane of the counting field. We evaluate analytically the generating function by mapping the generator of the biased dynamics to a non-Hermitian Hamiltonian of an associated quantum spin chain. We relate the trajectory phase transitions to the high-order cumulants of the time-integrated energy which we use to extract the dynamical Lee-Yang zeros of the generating function. This approach offers the possibility to detect continuous trajectory phase transitions from the finite-time behavior of measurable quantities.

An analytical study of physical models with inherited temporal and spatial memory

NASA Astrophysics Data System (ADS)

Jaradat, Imad; Alquran, Marwan; Al-Khaled, Kamel

2018-04-01

Du et al. (Sci. Reb. 3, 3431 (2013)) demonstrated that the fractional derivative order can be physically interpreted as a memory index by fitting the test data of memory phenomena. The aim of this work is to study analytically the joint effect of the memory index on time and space coordinates simultaneously. For this purpose, we introduce a novel bivariate fractional power series expansion that is accompanied by twofold fractional derivatives ordering α, β\\in(0,1]. Further, some convergence criteria concerning our expansion are presented and an analog of the well-known bivariate Taylor's formula in the sense of mixed fractional derivatives is obtained. Finally, in order to show the functionality and efficiency of this expansion, we employ the corresponding Taylor's series method to obtain closed-form solutions of various physical models with inherited time and space memory.

Discontinuous model with semi analytical sheath interface for radio frequency plasma

NASA Astrophysics Data System (ADS)

Miyashita, Masaru

2016-09-01

Sumitomo Heavy Industries, Ltd. provide many products utilizing plasma. In this study, we focus on the Radio Frequency (RF) plasma source by interior antenna. The plasma source is expected to be high density and low metal contamination. However, the sputtering the antenna cover by high energy ion from sheath voltage still have been problematic. We have developed the new model which can calculate sheath voltage wave form in the RF plasma source for realistic calculation time. This model is discontinuous that electronic fluid equation in plasma connect to usual passion equation in antenna cover and chamber with semi analytical sheath interface. We estimate the sputtering distribution based on calculated sheath voltage waveform by this model, sputtering yield and ion energy distribution function (IEDF) model. The estimated sputtering distribution reproduce the tendency of experimental results.

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.

Electrostatic shock structures in dissipative multi-ion dusty plasmas

NASA Astrophysics Data System (ADS)

Elkamash, I. S.; Kourakis, I.

2018-06-01

A comprehensive analytical model is introduced for shock excitations in dusty bi-ion plasma mixtures, taking into account collisionality and kinematic (fluid) viscosity. A multicomponent plasma configuration is considered, consisting of positive ions, negative ions, electrons, and a massive charged component in the background (dust). The ionic dynamical scale is focused upon; thus, electrons are assumed to be thermalized, while the dust is stationary. A dissipative hybrid Korteweg-de Vries/Burgers equation is derived. An analytical solution is obtained, in the form of a shock structure (a step-shaped function for the electrostatic potential, or an electric field pulse) whose maximum amplitude in the far downstream region decays in time. The effect of relevant plasma configuration parameters, in addition to dissipation, is investigated. Our work extends earlier studies of ion-acoustic type shock waves in pure (two-component) bi-ion plasma mixtures.

Multiple Scattering Effects on Pulse Propagation in Optically Turbid Media.

NASA Astrophysics Data System (ADS)

Joelson, Bradley David

The effects of multiple scattering in a optically turbid media is examined for an impulse solution to the radiative transfer equation for a variety of geometries and phase functions. In regions where the complexities of the phase function proved too cumbersome for analytic methods Monte Carlo techniques were developed to describe the entire scalar radiance distribution. The determination of a general spread function is strongly dependent on geometry and particular regions where limits can be placed on the variables of the problem. Hence, the general spread function is first simplified by considering optical regions which reduce the complexity of the variable dependence. First, in the small-angle limit we calculate some contracted spread functions along with their moments and then use Monte Carlo techniques to establish the limitations imposed by the small-angle approximation in planar geometry. The point spread function (PSF) for a spherical geometry is calculated for the full angular spread in the forward direction of ocean waters using Monte Carlo methods in the optically thin and moderate depths and analytic methods in the diffusion domain. The angular dependence of the PSF for various ocean waters is examined for a range of optical parameters. The analytic method used in the diffusion calculation is justified by examining the angular dependence of the radiance of a impulse solution in a planar geometry for a prolongated Henyey-Greenstein phase function of asymmetry factor approximately equal to that of the ocean phase functions. The Legendre moments of the radiance are examined in order to examine the viability of the diffusion approximation which assumes a linearly anisotropic angular distribution for the radiance. A realistic lidar calculation is performed for a variety of ocean waters to determine the effects of multiple scattering on the determination of the speed of sound by using the range gated frequency spectrum of the lidar signal. It is shown that the optical properties of the ocean help to ensure single scatter form for the frequency spectra of the lidar signal. This spectra can then be used to compute the speed of sound and backscatter probability.

A Cameron-Storvick Theorem for Analytic Feynman Integrals on Product Abstract Wiener Space and Applications

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

Choi, Jae Gil, E-mail: jgchoi@dankook.ac.kr; Chang, Seung Jun, E-mail: sejchang@dankook.ac.kr

In this paper we derive a Cameron-Storvick theorem for the analytic Feynman integral of functionals on product abstract Wiener space B{sup 2}. We then apply our result to obtain an evaluation formula for the analytic Feynman integral of unbounded functionals on B{sup 2}. We also present meaningful examples involving functionals which arise naturally in quantum mechanics.

Functionalized magnetic nanoparticle analyte sensor

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

Yantasee, Wassana; Warner, Maryin G; Warner, Cynthia L

2014-03-25

A method and system for simply and efficiently determining quantities of a preselected material in a particular solution by the placement of at least one superparamagnetic nanoparticle having a specified functionalized organic material connected thereto into a particular sample solution, wherein preselected analytes attach to the functionalized organic groups, these superparamagnetic nanoparticles are then collected at a collection site and analyzed for the presence of a particular analyte.

Two-dimensional analytic weighting functions for limb scattering

NASA Astrophysics Data System (ADS)

Zawada, D. J.; Bourassa, A. E.; Degenstein, D. A.

2017-10-01

Through the inversion of limb scatter measurements it is possible to obtain vertical profiles of trace species in the atmosphere. Many of these inversion methods require what is often referred to as weighting functions, or derivatives of the radiance with respect to concentrations of trace species in the atmosphere. Several radiative transfer models have implemented analytic methods to calculate weighting functions, alleviating the computational burden of traditional numerical perturbation methods. Here we describe the implementation of analytic two-dimensional weighting functions, where derivatives are calculated relative to atmospheric constituents in a two-dimensional grid of altitude and angle along the line of sight direction, in the SASKTRAN-HR radiative transfer model. Two-dimensional weighting functions are required for two-dimensional inversions of limb scatter measurements. Examples are presented where the analytic two-dimensional weighting functions are calculated with an underlying one-dimensional atmosphere. It is shown that the analytic weighting functions are more accurate than ones calculated with a single scatter approximation, and are orders of magnitude faster than a typical perturbation method. Evidence is presented that weighting functions for stratospheric aerosols calculated under a single scatter approximation may not be suitable for use in retrieval algorithms under solar backscatter conditions.

Closed-form solution for the Wigner phase-space distribution function for diffuse reflection and small-angle scattering in a random medium.

PubMed

Yura, H T; Thrane, L; Andersen, P E

2000-12-01

Within the paraxial approximation, a closed-form solution for the Wigner phase-space distribution function is derived for diffuse reflection and small-angle scattering in a random medium. This solution is based on the extended Huygens-Fresnel principle for the optical field, which is widely used in studies of wave propagation through random media. The results are general in that they apply to both an arbitrary small-angle volume scattering function, and arbitrary (real) ABCD optical systems. Furthermore, they are valid in both the single- and multiple-scattering regimes. Some general features of the Wigner phase-space distribution function are discussed, and analytic results are obtained for various types of scattering functions in the asymptotic limit s > 1, where s is the optical depth. In particular, explicit results are presented for optical coherence tomography (OCT) systems. On this basis, a novel way of creating OCT images based on measurements of the momentum width of the Wigner phase-space distribution is suggested, and the advantage over conventional OCT images is discussed. Because all previous published studies regarding the Wigner function are carried out in the transmission geometry, it is important to note that the extended Huygens-Fresnel principle and the ABCD matrix formalism may be used successfully to describe this geometry (within the paraxial approximation). Therefore for completeness we present in an appendix the general closed-form solution for the Wigner phase-space distribution function in ABCD paraxial optical systems for direct propagation through random media, and in a second appendix absorption effects are included.

A positive-definite form of bounce-averaged quasilinear velocity diffusion for the parallel inhomogeneity in a tokamak

NASA Astrophysics Data System (ADS)

Lee, Jungpyo; Smithe, David; Wright, John; Bonoli, Paul

2018-02-01

In this paper, the analytical form of the quasilinear diffusion coefficients is modified from the Kennel-Engelmann diffusion coefficients to guarantee the positive definiteness of its bounce average in a toroidal geometry. By evaluating the parallel inhomogeneity of plasmas and magnetic fields in the trajectory integral, we can ensure the positive definiteness and help illuminate some non-resonant toroidal effects in the quasilinear diffusion. When the correlation length of the plasma-wave interaction is comparable to the magnetic field variation length, the variation becomes important and the parabolic variation at the outer-midplane, the inner-midplane, and trapping tips can be evaluated by Airy functions. The new form allows the coefficients to include both resonant and non-resonant contributions, and the correlations between the consecutive resonances and in many poloidal periods. The positive-definite form is implemented in a wave code TORIC and we present an example for ITER using this form.

Effects of Vibrations on Metal Forming Process: Analytical Approach and Finite Element Simulations

NASA Astrophysics Data System (ADS)

Armaghan, Khan; Christophe, Giraud-Audine; Gabriel, Abba; Régis, Bigot

2011-01-01

Vibration assisted forming is one of the most recent and beneficial technique used to improve forming process. Effects of vibration on metal forming processes can be attributed to two causes. First, the volume effect links lowering of yield stress with the influence of vibration on the dislocation movement. Second, the surface effect explains lowering of the effective coefficient of friction by periodic reduction contact area. This work is related to vibration assisted forming process in viscoplastic domain. Impact of change in vibration waveform has been analyzed. For this purpose, two analytical models have been developed for two different types of vibration waveforms (sinusoidal and triangular). These models were developed on the basis of Slice method that is used to find out the required forming force for the process. Final relationships show that application of triangular waveform in forming process is more beneficial as compare to sinusoidal vibrations in terms of reduced forming force. Finite Element Method (FEM) based simulations were performed using Forge2008®and these confirmed the results of analytical models. The ratio of vibration speed to upper die speed is a critical factor in the reduction of the forming force.

Wigner distribution function of Hermite-cosine-Gaussian beams through an apertured optical system.

PubMed

Sun, Dong; Zhao, Daomu

2005-08-01

By introducing the hard-aperture function into a finite sum of complex Gaussian functions, the approximate analytical expressions of the Wigner distribution function for Hermite-cosine-Gaussian beams passing through an apertured paraxial ABCD optical system are obtained. The analytical results are compared with the numerically integrated ones, and the absolute errors are also given. It is shown that the analytical results are proper and that the calculation speed for them is much faster than for the numerical results.

On the Gibbs phenomenon 1: Recovering exponential accuracy from the Fourier partial sum of a non-periodic analytic function

NASA Technical Reports Server (NTRS)

Gottlieb, David; Shu, Chi-Wang; Solomonoff, Alex; Vandeven, Herve

1992-01-01

It is well known that the Fourier series of an analytic or periodic function, truncated after 2N+1 terms, converges exponentially with N, even in the maximum norm, although the function is still analytic. This is known as the Gibbs phenomenon. Here, we show that the first 2N+1 Fourier coefficients contain enough information about the function, so that an exponentially convergent approximation (in the maximum norm) can be constructed.

Some elements of a theory of multidimensional complex variables. I - General theory. II - Expansions of analytic functions and application to fluid flows

NASA Technical Reports Server (NTRS)

Martin, E. Dale

1989-01-01

The paper introduces a new theory of N-dimensional complex variables and analytic functions which, for N greater than 2, is both a direct generalization and a close analog of the theory of ordinary complex variables. The algebra in the present theory is a commutative ring, not a field. Functions of a three-dimensional variable were defined and the definition of the derivative then led to analytic functions.

Quick and Easy Rate Equations for Multistep Reactions

ERIC Educational Resources Information Center

Savage, Phillip E.

2008-01-01

Students rarely see closed-form analytical rate equations derived from underlying chemical mechanisms that contain more than a few steps unless restrictive simplifying assumptions (e.g., existence of a rate-determining step) are made. Yet, work published decades ago allows closed-form analytical rate equations to be written quickly and easily for…

Analyte species and concentration identification using differentially functionalized microcantilever arrays and artificial neural networks

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

Senesac, Larry R; Datskos, Panos G; Sepaniak, Michael J

2006-01-01

In the present work, we have performed analyte species and concentration identification using an array of ten differentially functionalized microcantilevers coupled with a back-propagation artificial neural network pattern recognition algorithm. The array consists of ten nanostructured silicon microcantilevers functionalized by polymeric and gas chromatography phases and macrocyclic receptors as spatially dense, differentially responding sensing layers for identification and quantitation of individual analyte(s) and their binary mixtures. The array response (i.e. cantilever bending) to analyte vapor was measured by an optical readout scheme and the responses were recorded for a selection of individual analytes as well as several binary mixtures. Anmore » artificial neural network (ANN) was designed and trained to recognize not only the individual analytes and binary mixtures, but also to determine the concentration of individual components in a mixture. To the best of our knowledge, ANNs have not been applied to microcantilever array responses previously to determine concentrations of individual analytes. The trained ANN correctly identified the eleven test analyte(s) as individual components, most with probabilities greater than 97%, whereas it did not misidentify an unknown (untrained) analyte. Demonstrated unique aspects of this work include an ability to measure binary mixtures and provide both qualitative (identification) and quantitative (concentration) information with array-ANN-based sensor methodologies.« less

Construction Method of Analytical Solutions to the Mathematical Physics Boundary Problems for Non-Canonical Domains

NASA Astrophysics Data System (ADS)

Mobarakeh, Pouyan Shakeri; Grinchenko, Victor T.

2015-06-01

The majority of practical cases of acoustics problems requires solving the boundary problems in non-canonical domains. Therefore construction of analytical solutions of mathematical physics boundary problems for non-canonical domains is both lucrative from the academic viewpoint, and very instrumental for elaboration of efficient algorithms of quantitative estimation of the field characteristics under study. One of the main solving ideologies for such problems is based on the superposition method that allows one to analyze a wide class of specific problems with domains which can be constructed as the union of canonically-shaped subdomains. It is also assumed that an analytical solution (or quasi-solution) can be constructed for each subdomain in one form or another. However, this case implies some difficulties in the construction of calculation algorithms, insofar as the boundary conditions are incompletely defined in the intervals, where the functions appearing in the general solution are orthogonal to each other. We discuss several typical examples of problems with such difficulties, we study their nature and identify the optimal methods to overcome them.

Dynamic imaging model and parameter optimization for a star tracker.

PubMed

Yan, Jinyun; Jiang, Jie; Zhang, Guangjun

2016-03-21

Under dynamic conditions, star spots move across the image plane of a star tracker and form a smeared star image. This smearing effect increases errors in star position estimation and degrades attitude accuracy. First, an analytical energy distribution model of a smeared star spot is established based on a line segment spread function because the dynamic imaging process of a star tracker is equivalent to the static imaging process of linear light sources. The proposed model, which has a clear physical meaning, explicitly reflects the key parameters of the imaging process, including incident flux, exposure time, velocity of a star spot in an image plane, and Gaussian radius. Furthermore, an analytical expression of the centroiding error of the smeared star spot is derived using the proposed model. An accurate and comprehensive evaluation of centroiding accuracy is obtained based on the expression. Moreover, analytical solutions of the optimal parameters are derived to achieve the best performance in centroid estimation. Finally, we perform numerical simulations and a night sky experiment to validate the correctness of the dynamic imaging model, the centroiding error expression, and the optimal parameters.

Training analysis and reanalysis in the development of the psychoanalyst.

PubMed

Meyer, Jon K

2007-01-01

A psychoanalyst faces the extraordinary demand of becoming instrumental in the psychoanalytic process. In the candidate's attempt to rise to that expectation, the first step is the training analysis. As the center-piece of psychoanalytic education, it is no ordinary analysis and bears special burdens intrinsic to its multiple functions and institutionalization. Recognizing the difficulties of both analytic education and analytic practice, Freud suggested that the analyst be periodically reanalyzed; for many, reanalysis is integral to their analytic development. Indeed, an analyst is actually never "made" but is always "in the making," developing and maturing in life and in practice. Reanalysis serves to focus elements of transference and resistance, rework defenses, facilitate more extensive regression in the service of the ego, deepen emotional integration, rework those elements of psychoanalysis itself that have been incorporated into defensive structure, and further the maturation of the analyzing instrument. If analysis is our most powerful mode of initial education, reanalysis is the most powerful form of continuing education. That remarkably little attention has been paid to reanalysis is testimony to the infantile fantasies that remain invested in our personal analyses.

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

DOE PAGES

Gao, Xujiao; Huang, Andy; Kerr, Bert

2017-10-25

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

Sound Emission of Rotor Induced Deformations of Generator Casings

NASA Technical Reports Server (NTRS)

Polifke, W.; Mueller, B.; Yee, H. C.; Mansour, Nagi (Technical Monitor)

2001-01-01

The casing of large electrical generators can be deformed slightly by the rotor's magnetic field. The sound emission produced by these periodic deformations, which could possibly exceed guaranteed noise emission limits, is analysed analytically and numerically. From the deformation of the casing, the normal velocity of the generator's surface is computed. Taking into account the corresponding symmetry, an analytical solution for the acoustic pressure outside the generator is round in terms of the Hankel function of second order. The normal velocity or the generator surface provides the required boundary condition for the acoustic pressure and determines the magnitude of pressure oscillations. For the numerical simulation, the nonlinear 2D Euler equations are formulated In a perturbation form for low Mach number Computational Aeroacoustics (CAA). The spatial derivatives are discretized by the classical sixth-order central interior scheme and a third-order boundary scheme. Spurious high frequency oscillations are damped by a characteristic-based artificial compression method (ACM) filter. The time derivatives are approximated by the classical 4th-order Runge-Kutta method. The numerical results are In excellent agreement with the analytical solution.

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

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

Gao, Xujiao; Huang, Andy; Kerr, Bert

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

Simple Analytic Model for Nanowire Array Polarizers

NASA Astrophysics Data System (ADS)

Pelletier, Vincent; Asakawa, Koji; Wu, Mingshaw; Register, Richard; Chaikin, Paul

2006-03-01

Cylinder-forming diblock copolymers can be used to pattern nanowire arrays on a transparent substrate to be used as a polarizer, as described by Koji Asakawa in a complementary talk at this meeting. With a 33nm period, these wire arrays can polarize UV radiation, which is of great interest in lithography, astronomy and other areas. One can gain an analytical understanding of such an array made of non-perfectly conducting material of finite thickness using a model with an appropriately averaged complex dielectric function in an infinite wavelength approximation. This analysis predicts that the grid can go from an E-polarizer to an H-polarizer as the wavelength decreases below a cross-over wavelength, and experimental data confirm this cross-over. The overall response of the polarizing grid depends primarily on the plasma frequency of the metal used and the volume fraction of the nanowires, as well as the grid thickness. A numerical approach is also used to confirm the analytical model and assess departure from infinite wavelength effects. For our array dimensions, the polarization is only slightly different from this approximation for wavelengths down to 150nm.

Bessel function expansion to reduce the calculation time and memory usage for cylindrical computer-generated holograms.

PubMed

Sando, Yusuke; Barada, Daisuke; Jackin, Boaz Jessie; Yatagai, Toyohiko

2017-07-10

This study proposes a method to reduce the calculation time and memory usage required for calculating cylindrical computer-generated holograms. The wavefront on the cylindrical observation surface is represented as a convolution integral in the 3D Fourier domain. The Fourier transformation of the kernel function involving this convolution integral is analytically performed using a Bessel function expansion. The analytical solution can drastically reduce the calculation time and the memory usage without any cost, compared with the numerical method using fast Fourier transform to Fourier transform the kernel function. In this study, we present the analytical derivation, the efficient calculation of Bessel function series, and a numerical simulation. Furthermore, we demonstrate the effectiveness of the analytical solution through comparisons of calculation time and memory usage.

Spatiotemporal and geometric optimization of sensor arrays for detecting analytes fluids

DOEpatents

Lewis, Nathan S.; Freund, Michael S.; Briglin, Shawn M.; Tokumaru, Phil; Martin, Charles R.; Mitchell, David T.

2006-10-17

Sensor arrays and sensor array systems for detecting analytes in fluids. Sensors configured to generate a response upon introduction of a fluid containing one or more analytes can be located on one or more surfaces relative to one or more fluid channels in an array. Fluid channels can take the form of pores or holes in a substrate material. Fluid channels can be formed between one or more substrate plates. Sensor can be fabricated with substantially optimized sensor volumes to generate a response having a substantially maximized signal to noise ratio upon introduction of a fluid containing one or more target analytes. Methods of fabricating and using such sensor arrays and systems are also disclosed.

Spatiotemporal and geometric optimization of sensor arrays for detecting analytes in fluids

DOEpatents

Lewis, Nathan S [La Canada, CA; Freund, Michael S [Winnipeg, CA; Briglin, Shawn S [Chittenango, NY; Tokumaru, Phillip [Moorpark, CA; Martin, Charles R [Gainesville, FL; Mitchell, David [Newtown, PA

2009-09-29

Sensor arrays and sensor array systems for detecting analytes in fluids. Sensors configured to generate a response upon introduction of a fluid containing one or more analytes can be located on one or more surfaces relative to one or more fluid channels in an array. Fluid channels can take the form of pores or holes in a substrate material. Fluid channels can be formed between one or more substrate plates. Sensor can be fabricated with substantially optimized sensor volumes to generate a response having a substantially maximized signal to noise ratio upon introduction of a fluid containing one or more target analytes. Methods of fabricating and using such sensor arrays and systems are also disclosed.

Direct-Potential (dpf) Analysis for the a 3Π1-X 1Σ+ System of I35/37Cl.

NASA Astrophysics Data System (ADS)

Kobayashi, Shinji; Nishimiya, Nobuo; Yukiya, Tokio; Suzuki, Masao; Le Roy, Robert J.

2016-06-01

The goal of this research is to obtain an optimal, portable, global description of, and summary of the dynamical properties of, the A 3Π1 and X 1Σ+ states of I35/37Cl, by using `direct potential fits' (DPFs) to all of the available spectroscopic data for this system to determine optimal analytic potential energy functions for these two states that represent all of those data (on average), within the experimental uncertainties. The DPF method compares observed spectroscopic data with synthetic data generated by solving the radial Schrödinger equation for the upper and lower level of every observed transition for some parameterized analytic potential function(s), and using least-squares fits to the data to optimize those parameters. The present work uses the Morse/Long-Range (MLR) potential function form because it is very flexible, can incorporate the correct theoretically known inverse-power-sum long-range behaviour, is everywhere continuous and differentiable to all orders, and has robust extrapolation properties at both large and small distances. The DPF approach also tends to require fewer fitting parameters than do traditional Dunham analyses, as well as having much more robust extrapolation properties in both the v and J domains. The present work combines the data for the A 3Π1 and X 1Σ+ states obtained in 1980 by Coxon et al. using UV and near-infrared grating spectrometers, with our measurements in the 0.7-0.8μm region, obtained using a CW Ti:Sapphire Ring Laser. The results of this study and our new fully analytic potential energy functions for the A 3Π1 and X 1Σ+ states of ICl will be presented. J.A. Coxon, R.M. Gordon and M.A. Wickramaaratchi, J. Mol. Spectrosc. 79 (1980) 363 and 380. T.Yukiya, N. Nishimiya and M. Suzuki, J. Mol. Spectrosc. 269 (2011) 193.

CONSTRUCTING AND DERIVING RECIPROCAL TRIGONOMETRIC RELATIONS: A FUNCTIONAL ANALYTIC APPROACH

PubMed Central

Ninness, Chris; Dixon, Mark; Barnes-Holmes, Dermot; Rehfeldt, Ruth Anne; Rumph, Robin; McCuller, Glen; Holland, James; Smith, Ronald; Ninness, Sharon K; McGinty, Jennifer

2009-01-01

Participants were pretrained and tested on mutually entailed trigonometric relations and combinatorially entailed relations as they pertained to positive and negative forms of sine, cosine, secant, and cosecant. Experiment 1 focused on training and testing transformations of these mathematical functions in terms of amplitude and frequency followed by tests of novel relations. Experiment 2 addressed training in accordance with frames of coordination (same as) and frames of opposition (reciprocal of) followed by more tests of novel relations. All assessments of derived and novel formula-to-graph relations, including reciprocal functions with diversified amplitude and frequency transformations, indicated that all 4 participants demonstrated substantial improvement in their ability to identify increasingly complex trigonometric formula-to-graph relations pertaining to same as and reciprocal of to establish mathematically complex repertoires. PMID:19949509

Constructing and deriving reciprocal trigonometric relations: a functional analytic approach.

PubMed

Ninness, Chris; Dixon, Mark; Barnes-Holmes, Dermot; Rehfeldt, Ruth Anne; Rumph, Robin; McCuller, Glen; Holland, James; Smith, Ronald; Ninness, Sharon K; McGinty, Jennifer

2009-01-01

Participants were pretrained and tested on mutually entailed trigonometric relations and combinatorially entailed relations as they pertained to positive and negative forms of sine, cosine, secant, and cosecant. Experiment 1 focused on training and testing transformations of these mathematical functions in terms of amplitude and frequency followed by tests of novel relations. Experiment 2 addressed training in accordance with frames of coordination (same as) and frames of opposition (reciprocal of) followed by more tests of novel relations. All assessments of derived and novel formula-to-graph relations, including reciprocal functions with diversified amplitude and frequency transformations, indicated that all 4 participants demonstrated substantial improvement in their ability to identify increasingly complex trigonometric formula-to-graph relations pertaining to same as and reciprocal of to establish mathematically complex repertoires.

Basic analytical investigation of plasma-chemically modified carbon fibers1

NASA Astrophysics Data System (ADS)

Bubert, H.; Ai, X.; Haiber, S.; Heintze, M.; Brüser, V.; Pasch, E.; Brandl, W.; Marginean, G.

2002-10-01

The background of the present investigation is to enhance the overall adherence of vapor grown carbon fibers (VGCF) to the surrounding polymer matrix in different applications by forming polar groups at their surfaces and by modifying the surface morphology. This has been done by plasma treatments using a low-pressure plasma with different gases, flow rates, pressures and powers. Two different types of carbon fibers were investigated: carbon microfibers and carbon nanofibers. The characterization of fiber surfaces was achieved by photoelectron spectroscopy (XPS), contact angle measurements and titration. These investigations were accompanied by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). The oxygen plasma treatment of the fibers changes the surfaces by forming a layer with a thickness of the order of one nanometer mainly consisting of functional groups like hydroxyl, carbonyl and carboxyl. After functionalization of the complete surface, a further plasma treatment does not enhance the superficial oxygen content but changes slightly the portions of the functional groups. A comparison of the methods applied provides a largely consistent image of the effect of plasma treatment.

Spatiotemporal optical pulse transformation by a resonant diffraction grating

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

Golovastikov, N. V.; Bykov, D. A., E-mail: bykovd@gmail.com; Doskolovich, L. L., E-mail: leonid@smr.ru

The diffraction of a spatiotemporal optical pulse by a resonant diffraction grating is considered. The pulse diffraction is described in terms of the signal (the spatiotemporal incident pulse envelope) passage through a linear system. An analytic approximation in the form of a rational function of two variables corresponding to the angular and spatial frequencies has been obtained for the transfer function of the system. A hyperbolic partial differential equation describing the general form of the incident pulse envelope transformation upon diffraction by a resonant diffraction grating has been derived from the transfer function. A solution of this equation has beenmore » obtained for the case of normal incidence of a pulse with a central frequency lying near the guided-mode resonance of a diffraction structure. The presented results of numerical simulations of pulse diffraction by a resonant grating show profound changes in the pulse envelope shape that closely correspond to the proposed theoretical description. The results of the paper can be applied in creating new devices for optical pulse shape transformation, in optical information processing problems, and analog optical computations.« less

A study on some urban bus transport networks

NASA Astrophysics Data System (ADS)

Chen, Yong-Zhou; Li, Nan; He, Da-Ren

2007-03-01

In this paper, we present the empirical investigation results on the urban bus transport networks (BTNs) of four major cities in China. In BTN, nodes are bus stops. Two nodes are connected by an edge when the stops are serviced by a common bus route. The empirical results show that the degree distributions of BTNs take exponential function forms. Other two statistical properties of BTNs are also considered, and they are suggested as the distributions of so-called “the number of stops in a bus route” (represented by S) and “the number of bus routes a stop joins” (by R). The distributions of R also show exponential function forms, while the distributions of S follow asymmetric, unimodal functions. To explain these empirical results and attempt to simulate a possible evolution process of BTN, we introduce a model by which the analytic and numerical result obtained agrees well with the empirical facts. Finally, we also discuss some other possible evolution cases, where the degree distribution shows a power law or an interpolation between the power law and the exponential decay.

A mathematical solution for the parameters of three interfering resonances

NASA Astrophysics Data System (ADS)

Han, X.; Shen, C. P.

2018-04-01

The multiple-solution problem in determining the parameters of three interfering resonances from a fit to an experimentally measured distribution is considered from a mathematical viewpoint. It is shown that there are four numerical solutions for a fit with three coherent Breit-Wigner functions. Although explicit analytical formulae cannot be derived in this case, we provide some constraint equations between the four solutions. For the cases of nonrelativistic and relativistic Breit-Wigner forms of amplitude functions, a numerical method is provided to derive the other solutions from that already obtained, based on the obtained constraint equations. In real experimental measurements with more complicated amplitude forms similar to Breit-Wigner functions, the same method can be deduced and performed to get numerical solutions. The good agreement between the solutions found using this mathematical method and those directly from the fit verifies the correctness of the constraint equations and mathematical methodology used. Supported by National Natural Science Foundation of China (NSFC) (11575017, 11761141009), the Ministry of Science and Technology of China (2015CB856701) and the CAS Center for Excellence in Particle Physics (CCEPP)

Response of a rigid aircraft to nonstationary atmospheric turbulence.

NASA Technical Reports Server (NTRS)

Verdon, J. M.; Steiner, R.

1973-01-01

The plunging response of an aircraft to a type of nonstationary turbulent excitation is considered. The latter consists of stationary Gaussian noise modulated by a well-defined envelope function. The intent of the investigation is to model the excitation experienced by an airplane flying through turbulence of varying intensity and to examine the influence of intensity variations on exceedance frequencies of the gust velocity and the airplane's plunging velocity and acceleration. One analytical advantage of the proposed model is that the Gaussian assumption for the gust excitation is retained. The analysis described herein is developed in terms of an envelope function of arbitrary form; however, numerical calculations are limited to the case of harmonic modulation.

Pelvic form and locomotor adaptation in strepsirrhine primates.

PubMed

Lewton, Kristi L

2015-01-01

The pelvic girdle is a complex structure with a critical role in locomotion, but efforts to model the mechanical effects of locomotion on its shape remain difficult. Traditional approaches to understanding form and function include univariate adaptive hypothesis-testing derived from mechanical models. Geometric morphometric (GM) methods can yield novel insight into overall three-dimensional shape similarities and differences across groups, although the utility of GM in assessing functional differences has been questioned. This study evaluates the contributions of both univariate and GM approaches to unraveling the trait-function associations between pelvic form and locomotion. Three-dimensional landmarks were collected on a phylogenetically-broad sample of 180 pelves from nine primate taxa. Euclidean interlandmark distances were calculated to facilitate testing of biomechanical hypotheses, and a principal components (PC) analysis was performed on Procrustes coordinates to examine overall shape differences. Both linear dimensions and PC scores were subjected to phylogenetic ANOVA. Many of the null hypotheses relating linear dimensions to locomotor loading were not rejected. Although both analytical approaches suggest that ilium width and robusticity differ among locomotor groups, the GM analysis also suggests that ischiopubic shape differentiates groups. Although GM provides additional quantitative results beyond the univariate analyses, this study highlights the need for new GM methods to more specifically address functional shape differences among species. Until these methods are developed, it would be prudent to accompany tests of directional biomechanical hypotheses with current GM methods for a more nuanced understanding of shape and function. © 2014 Wiley Periodicals, Inc.

Feature Detection and Curve Fitting Using Fast Walsh Transforms for Shock Tracking: Applications

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.

2017-01-01

Walsh functions form an orthonormal basis set consisting of square waves. Square waves make the system well suited for detecting and representing functions with discontinuities. Given a uniform distribution of 2p cells on a one-dimensional element, it has been proven that the inner product of the Walsh Root function for group p with every polynomial of degree < or = (p - 1) across the element is identically zero. It has also been proven that the magnitude and location of a discontinuous jump, as represented by a Heaviside function, are explicitly identified by its Fast Walsh Transform (FWT) coefficients. These two proofs enable an algorithm that quickly provides a Weighted Least Squares fit to distributions across the element that include a discontinuity. The detection of a discontinuity enables analytic relations to locally describe its evolution and provide increased accuracy. Time accurate examples are provided for advection, Burgers equation, and Riemann problems (diaphragm burst) in closed tubes and de Laval nozzles. New algorithms to detect up to two C0 and/or C1 discontinuities within a single element are developed for application to the Riemann problem, in which a contact discontinuity and shock wave form after the diaphragm bursts.

Closed-form eigensolutions of nonviscously, nonproportionally damped systems based on continuous damping sensitivity

NASA Astrophysics Data System (ADS)

Lázaro, Mario

2018-01-01

In this paper, nonviscous, nonproportional, vibrating structures are considered. Nonviscously damped systems are characterized by dissipative mechanisms which depend on the history of the response velocities via hereditary kernel functions. Solutions of the free motion equation lead to a nonlinear eigenvalue problem involving mass, stiffness and damping matrices. Viscoelasticity leads to a frequency dependence of this latter. In this work, a novel closed-form expression to estimate complex eigenvalues is derived. The key point is to consider the damping model as perturbed by a continuous fictitious parameter. Assuming then the eigensolutions as function of this parameter, the computation of the eigenvalues sensitivity leads to an ordinary differential equation, from whose solution arises the proposed analytical formula. The resulting expression explicitly depends on the viscoelasticity (frequency derivatives of the damping function), the nonproportionality (influence of the modal damping matrix off-diagonal terms). Eigenvectors are obtained using existing methods requiring only the corresponding eigenvalue. The method is validated using a numerical example which compares proposed with exact ones and with those determined from the linear first order approximation in terms of the damping matrix. Frequency response functions are also plotted showing that the proposed approach is valid even for moderately or highly damped systems.

Magnetic fields for transporting charged beams

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

Parzen, G.

1976-01-01

The transport of charged particle beams requires magnetic fields that must be shaped correctly and very accurately. During the last 20 years or so, many studies have been made, both analytically and through the use of computer programs, of various magnetic shapes that have proved to be useful. Many of the results for magnetic field shapes can be applied equally well to electric field shapes. A report is given which gathers together the results that have more general significance and would be useful in designing a configuration to produce a desired magnetic field shape. The field shapes studied include themore » fields in dipoles, quadrupoles, sextupoles, octupoles, septum magnets, combined-function magnets, and electrostatic septums. Where possible, empirical formulas are proposed, based on computer and analytical studies and on magnetic field measurements. These empirical formulas are often easier to use than analytical formulas and often include effects that are difficult to compute analytically. In addition, results given in the form of tables and graphs serve as illustrative examples. The field shapes studied include uniform fields produced by window-frame magnets, C-magnets, H-magnets, and cosine magnets; linear fields produced by various types of quadrupoles; quadratic and cubic fields produced by sextupoles and octupoles; combinations of uniform and linear fields; and septum fields with sharp boundaries.« less

Superhydrophobic analyte concentration utilizing colloid-pillar array SERS substrates.

PubMed

Wallace, Ryan A; Charlton, Jennifer J; Kirchner, Teresa B; Lavrik, Nickolay V; Datskos, Panos G; Sepaniak, Michael J

2014-12-02

The ability to detect a few molecules present in a large sample is of great interest for the detection of trace components in both medicinal and environmental samples. Surface enhanced Raman spectroscopy (SERS) is a technique that can be utilized to detect molecules at very low absolute numbers. However, detection at trace concentration levels in real samples requires properly designed delivery and detection systems. The following work involves superhydrophobic surfaces that have as a framework deterministic or stochastic silicon pillar arrays formed by lithographic or metal dewetting protocols, respectively. In order to generate the necessary plasmonic substrate for SERS detection, simple and flow stable Ag colloid was added to the functionalized pillar array system via soaking. Native pillars and pillars with hydrophobic modification are used. The pillars provide a means to concentrate analyte via superhydrophobic droplet evaporation effects. A ≥ 100-fold concentration of analyte was estimated, with a limit of detection of 2.9 × 10(-12) M for mitoxantrone dihydrochloride. Additionally, analytes were delivered to the surface via a multiplex approach in order to demonstrate an ability to control droplet size and placement for scaled-up uses in real world applications. Finally, a concentration process involving transport and sequestration based on surface treatment selective wicking is demonstrated.

Firing-rate response of linear and nonlinear integrate-and-fire neurons to modulated current-based and conductance-based synaptic drive.

PubMed

Richardson, Magnus J E

2007-08-01

Integrate-and-fire models are mainstays of the study of single-neuron response properties and emergent states of recurrent networks of spiking neurons. They also provide an analytical base for perturbative approaches that treat important biological details, such as synaptic filtering, synaptic conductance increase, and voltage-activated currents. Steady-state firing rates of both linear and nonlinear integrate-and-fire models, receiving fluctuating synaptic drive, can be calculated from the time-independent Fokker-Planck equation. The dynamic firing-rate response is less easy to extract, even at the first-order level of a weak modulation of the model parameters, but is an important determinant of neuronal response and network stability. For the linear integrate-and-fire model the response to modulations of current-based synaptic drive can be written in terms of hypergeometric functions. For the nonlinear exponential and quadratic models no such analytical forms for the response are available. Here it is demonstrated that a rather simple numerical method can be used to obtain the steady-state and dynamic response for both linear and nonlinear models to parameter modulation in the presence of current-based or conductance-based synaptic fluctuations. To complement the full numerical solution, generalized analytical forms for the high-frequency response are provided. A special case is also identified--time-constant modulation--for which the response to an arbitrarily strong modulation can be calculated exactly.

A Radical-Mediated Pathway for the Formation of [M + H](+) in Dielectric Barrier Discharge Ionization.

PubMed

Wolf, Jan-Christoph; Gyr, Luzia; Mirabelli, Mario F; Schaer, Martin; Siegenthaler, Peter; Zenobi, Renato

2016-09-01

Active capillary plasma ionization is a highly efficient ambient ionization method. Its general principle of ion formation is closely related to atmospheric pressure chemical ionization (APCI). The method is based on dielectric barrier discharge ionization (DBDI), and can be constructed in the form of a direct flow-through interface to a mass spectrometer. Protonated species ([M + H](+)) are predominantly formed, although in some cases radical cations are also observed. We investigated the underlying ionization mechanisms and reaction pathways for the formation of protonated analyte ([M + H](+)). We found that ionization occurs in the presence and in the absence of water vapor. Therefore, the mechanism cannot exclusively rely on hydronium clusters, as generally accepted for APCI. Based on isotope labeling experiments, protons were shown to originate from various solvents (other than water) and, to a minor extent, from gaseous impurities and/or self-protonation. By using CO2 instead of air or N2 as plasma gas, additional species like [M + OH](+) and [M - H](+) were observed. These gas-phase reaction products of CO2 with the analyte (tertiary amines) indicate the presence of a radical-mediated ionization pathway, which proceeds by direct reaction of the ionized plasma gas with the analyte. The proposed reaction pathway is supported with density functional theory (DFT) calculations. These findings add a new ionization pathway leading to the protonated species to those currently known for APCI. Graphical Abstract ᅟ.

EARL: Exoplanet Analytic Reflected Lightcurves package

NASA Astrophysics Data System (ADS)

Haggard, Hal M.; Cowan, Nicolas B.

2018-05-01

EARL (Exoplanet Analytic Reflected Lightcurves) computes the analytic form of a reflected lightcurve, given a spherical harmonic decomposition of the planet albedo map and the viewing and orbital geometries. The EARL Mathematica notebook allows rapid computation of reflected lightcurves, thus making lightcurve numerical experiments accessible.

Analytic representations of mK , FK, mη, and Fη in two loop S U (3 ) chiral perturbation theory

NASA Astrophysics Data System (ADS)

Ananthanarayan, B.; Bijnens, Johan; Friot, Samuel; Ghosh, Shayan

2018-06-01

In this work, we consider expressions for the masses and decay constants of the pseudoscalar mesons in S U (3 ) chiral perturbation theory. These involve sunset diagrams and their derivatives evaluated at p2=mP2 (P =π , K , η ). Recalling that there are three mass scales in this theory, mπ, mK and mη, there are instances when the finite part of the sunset diagrams do not admit an expression in terms of elementary functions, and have therefore been evaluated numerically in the past. In a recent publication, an expansion in the external momentum was performed to obtain approximate analytic expressions for mπ and Fπ, the pion mass and decay constant. We provide fully analytic exact expressions for mK and mη, the kaon and eta masses, and FK and Fη, the kaon and eta decay constants. These expressions, calculated using Mellin-Barnes methods, are in the form of double series in terms of two mass ratios. A numerical analysis of the results to evaluate the relative size of contributions coming from loops, chiral logarithms as well as phenomenological low-energy constants is presented. We also present a set of approximate analytic expressions for mK, FK, mη and Fη that facilitate comparisons with lattice results. Finally, we show how exact analytic expressions for mπ and Fπ may be obtained, the latter having been used in conjunction with the results for FK to produce a recently published analytic representation of FK/Fπ.

Generalized model of electromigration with 1:1 (analyte:selector) complexation stoichiometry: part II. Application to dual systems and experimental verification.

PubMed

Müllerová, Ludmila; Dubský, Pavel; Gaš, Bohuslav

2015-03-06

Interactions among analyte forms that undergo simultaneous dissociation/protonation and complexation with multiple selectors take the shape of a highly interconnected multi-equilibrium scheme. This makes it difficult to express the effective mobility of the analyte in these systems, which are often encountered in electrophoretical separations, unless a generalized model is introduced. In the first part of this series, we presented the theory of electromigration of a multivalent weakly acidic/basic/amphoteric analyte undergoing complexation with a mixture of an arbitrary number of selectors. In this work we demonstrate the validity of this concept experimentally. The theory leads to three useful perspectives, each of which is closely related to the one originally formulated for simpler systems. If pH, IS and the selector mixture composition are all kept constant, the system is treated as if only a single analyte form interacted with a single selector. If the pH changes at constant IS and mixture composition, the already well-established models of a weakly acidic/basic analyte interacting with a single selector can be employed. Varying the mixture composition at constant IS and pH leads to a situation where virtually a single analyte form interacts with a mixture of selectors. We show how to switch between the three perspectives in practice and confirm that they can be employed interchangeably according to the specific needs by measurements performed in single- and dual-selector systems at a pH where the analyte is fully dissociated, partly dissociated or fully protonated. Weak monoprotic analyte (R-flurbiprofen) and two selectors (native β-cyclodextrin and monovalent positively charged 6-monodeoxy-6-monoamino-β-cyclodextrin) serve as a model system. Copyright © 2015 Elsevier B.V. All rights reserved.

Ion yields in UV-MALDI mass spectrometry as a function of excitation laser wavelength and optical and physico-chemical properties of classical and halogen-substituted MALDI matrixes.

PubMed

Soltwisch, Jens; Jaskolla, Thorsten W; Hillenkamp, Franz; Karas, Michael; Dreisewerd, Klaus

2012-08-07

The laser wavelength constitutes a key parameter in ultraviolet-matrix-assisted laser desorption ionization-mass spectrometry (UV-MALDI-MS). Optimal analytical results are only achieved at laser wavelengths that correspond to a high optical absorption of the matrix. In the presented work, the wavelength dependence and the contribution of matrix proton affinity to the MALDI process were investigated. A tunable dye laser was used to examine the wavelength range between 280 and 355 nm. The peptide and matrix ion signals recorded as a function of these irradiation parameters are displayed in the form of heat maps, a data representation that furnishes multidimensional data interpretation. Matrixes with a range of proton affinities from 809 to 866 kJ/mol were investigated. Among those selected are the standard matrixes 2,5-dihydroxybenzoic acid (DHB) and α-cyano-4-hydroxycinnamic acid (HCCA) as well as five halogen-substituted cinnamic acid derivatives, including the recently introduced 4-chloro-α-cyanocinnamic acid (ClCCA) and α-cyano-2,4-difluorocinnamic acid (DiFCCA) matrixes. With the exception of DHB, the highest analyte ion signals were obtained toward the red side of the peak optical absorption in the solid state. A stronger decline of the molecular analyte ion signals generated from the matrixes was consistently observed at the low wavelength side of the peak absorption. This effect is mainly the result of increased fragmentation of both analyte and matrix ions. Optimal use of multiply halogenated matrixes requires adjustment of the excitation wavelength to values below that of the standard MALDI lasers emitting at 355 (Nd:YAG) or 337 nm (N(2) laser). The combined data provide new insights into the UV-MALDI desorption/ionization processes and indicate ways to improve the analytical sensitivity.

Closed-form solutions and scaling laws for Kerr frequency combs

PubMed Central

Renninger, William H.; Rakich, Peter T.

2016-01-01

A single closed-form analytical solution of the driven nonlinear Schrödinger equation is developed, reproducing a large class of the behaviors in Kerr-comb systems, including bright-solitons, dark-solitons, and a large class of periodic wavetrains. From this analytical framework, a Kerr-comb area theorem and a pump-detuning relation are developed, providing new insights into soliton- and wavetrain-based combs along with concrete design guidelines for both. This new area theorem reveals significant deviation from the conventional soliton area theorem, which is crucial to understanding cavity solitons in certain limits. Moreover, these closed-form solutions represent the first step towards an analytical framework for wavetrain formation, and reveal new parameter regimes for enhanced Kerr-comb performance. PMID:27108810

Quantitative Analysis of Fullerene Nanomaterials in Environmental Systems: A Critical Review

PubMed Central

Isaacson, Carl W.; Kleber, Markus; Field, Jennifer A.

2009-01-01

The increasing production and use of fullerene nanomaterials has led to calls for more information regarding the potential impacts that releases of these materials may have on human and environmental health. Fullerene nanomaterials, which are comprised of both fullerenes and surface-functionalized fullerenes, are used in electronic, optic, medical and cosmetic applications. Measuring fullerene nanomaterial concentrations in natural environments is difficult because they exhibit a duality of physical and chemical characteristics as they transition from hydrophobic to polar forms upon exposure to water. In aqueous environments, this is expressed as their tendency to initially (i) self assemble into aggregates of appreciable size and hydrophobicity, and subsequently (ii) interact with the surrounding water molecules and other chemical constituents in natural environments thereby acquiring negative surface charge. Fullerene nanomaterials may therefore deceive the application of any single analytical method that is applied with the assumption that fullerenes have but one defining characteristic (e.g., hydrophobicity). [1] We find that analytical procedures are needed to account for the potentially transitory nature of fullerenes in natural environments through the use of approaches that provide chemically-explicit information including molecular weight and the number and identity of surface functional groups. [2] We suggest that sensitive and mass-selective detection, such as that offered by mass spectrometry when combined with optimized extraction procedures, offers the greatest potential to achieve this goal. [3] With this review, we show that significant improvements in analytical rigor would result from an increased availability of well characterized authentic standards, reference materials, and isotopically-labeled internal standards. Finally, the benefits of quantitative and validated analytical methods for advancing the knowledge on fullerene occurrence, fate, and behavior are indicated. PMID:19764203

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.

Analytical solutions for avalanche-breakdown voltages of single-diffused Gaussian junctions

NASA Astrophysics Data System (ADS)

Shenai, K.; Lin, H. C.

1983-03-01

Closed-form solutions of the potential difference between the two edges of the depletion layer of a single diffused Gaussian p-n junction are obtained by integrating Poisson's equation and equating the magnitudes of the positive and negative charges in the depletion layer. By using the closed form solution of the static Poisson's equation and Fulop's average ionization coefficient, the ionization integral in the depletion layer is computed, which yields the correct values of avalanche breakdown voltage, depletion layer thickness at breakdown, and the peak electric field as a function of junction depth. Newton's method is used for rapid convergence. A flowchart to perform the calculations with a programmable hand-held calculator, such as the TI-59, is shown.

Analytical model for effect of temperature variation on PSF consistency in wavefront coding infrared imaging system

NASA Astrophysics Data System (ADS)

Feng, Bin; Shi, Zelin; Zhang, Chengshuo; Xu, Baoshu; Zhang, Xiaodong

2016-05-01

The point spread function (PSF) inconsistency caused by temperature variation leads to artifacts in decoded images of a wavefront coding infrared imaging system. Therefore, this paper proposes an analytical model for the effect of temperature variation on the PSF consistency. In the proposed model, a formula for the thermal deformation of an optical phase mask is derived. This formula indicates that a cubic optical phase mask (CPM) is still cubic after thermal deformation. A proposed equivalent cubic phase mask (E-CPM) is a virtual and room-temperature lens which characterizes the optical effect of temperature variation on the CPM. Additionally, a calculating method for PSF consistency after temperature variation is presented. Numerical simulation illustrates the validity of the proposed model and some significant conclusions are drawn. Given the form parameter, the PSF consistency achieved by a Ge-material CPM is better than the PSF consistency by a ZnSe-material CPM. The effect of the optical phase mask on PSF inconsistency is much slighter than that of the auxiliary lens group. A large form parameter of the CPM will introduce large defocus-insensitive aberrations, which improves the PSF consistency but degrades the room-temperature MTF.

Fast and Analytical EAP Approximation from a 4th-Order Tensor.

PubMed

Ghosh, Aurobrata; Deriche, Rachid

2012-01-01

Generalized diffusion tensor imaging (GDTI) was developed to model complex apparent diffusivity coefficient (ADC) using higher-order tensors (HOTs) and to overcome the inherent single-peak shortcoming of DTI. However, the geometry of a complex ADC profile does not correspond to the underlying structure of fibers. This tissue geometry can be inferred from the shape of the ensemble average propagator (EAP). Though interesting methods for estimating a positive ADC using 4th-order diffusion tensors were developed, GDTI in general was overtaken by other approaches, for example, the orientation distribution function (ODF), since it is considerably difficult to recuperate the EAP from a HOT model of the ADC in GDTI. In this paper, we present a novel closed-form approximation of the EAP using Hermite polynomials from a modified HOT model of the original GDTI-ADC. Since the solution is analytical, it is fast, differentiable, and the approximation converges well to the true EAP. This method also makes the effort of computing a positive ADC worthwhile, since now both the ADC and the EAP can be used and have closed forms. We demonstrate our approach with 4th-order tensors on synthetic data and in vivo human data.

Fast and Analytical EAP Approximation from a 4th-Order Tensor

PubMed Central

Ghosh, Aurobrata; Deriche, Rachid

2012-01-01

Generalized diffusion tensor imaging (GDTI) was developed to model complex apparent diffusivity coefficient (ADC) using higher-order tensors (HOTs) and to overcome the inherent single-peak shortcoming of DTI. However, the geometry of a complex ADC profile does not correspond to the underlying structure of fibers. This tissue geometry can be inferred from the shape of the ensemble average propagator (EAP). Though interesting methods for estimating a positive ADC using 4th-order diffusion tensors were developed, GDTI in general was overtaken by other approaches, for example, the orientation distribution function (ODF), since it is considerably difficult to recuperate the EAP from a HOT model of the ADC in GDTI. In this paper, we present a novel closed-form approximation of the EAP using Hermite polynomials from a modified HOT model of the original GDTI-ADC. Since the solution is analytical, it is fast, differentiable, and the approximation converges well to the true EAP. This method also makes the effort of computing a positive ADC worthwhile, since now both the ADC and the EAP can be used and have closed forms. We demonstrate our approach with 4th-order tensors on synthetic data and in vivo human data. PMID:23365552

DEMONSTRATION OF THE ANALYTIC ELEMENT METHOD FOR WELLHEAD PROTECTION

EPA Science Inventory

A new computer program has been developed to determine time-of-travel capture zones in relatively simple geohydrological settings. The WhAEM package contains an analytic element model that uses superposition of (many) closed form analytical solutions to generate a ground-water fl...

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

ERIC Educational Resources Information Center

Follette, William C.; Bonow, Jordan T.

2009-01-01

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

Executive Function and Reading Comprehension: A Meta-Analytic Review

ERIC Educational Resources Information Center

Follmer, D. Jake

2018-01-01

This article presents a meta-analytic review of the relation between executive function and reading comprehension. Results (N = 6,673) supported a moderate positive association between executive function and reading comprehension (r = 0.36). Moderator analyses suggested that correlations between executive function and reading comprehension did not…

Maximum likelihood solution for inclination-only data in paleomagnetism

NASA Astrophysics Data System (ADS)

Arason, P.; Levi, S.

2010-08-01

We have developed a new robust maximum likelihood method for estimating the unbiased mean inclination from inclination-only data. In paleomagnetic analysis, the arithmetic mean of inclination-only data is known to introduce a shallowing bias. Several methods have been introduced to estimate the unbiased mean inclination of inclination-only data together with measures of the dispersion. Some inclination-only methods were designed to maximize the likelihood function of the marginal Fisher distribution. However, the exact analytical form of the maximum likelihood function is fairly complicated, and all the methods require various assumptions and approximations that are often inappropriate. For some steep and dispersed data sets, these methods provide estimates that are significantly displaced from the peak of the likelihood function to systematically shallower inclination. The problem locating the maximum of the likelihood function is partly due to difficulties in accurately evaluating the function for all values of interest, because some elements of the likelihood function increase exponentially as precision parameters increase, leading to numerical instabilities. In this study, we succeeded in analytically cancelling exponential elements from the log-likelihood function, and we are now able to calculate its value anywhere in the parameter space and for any inclination-only data set. Furthermore, we can now calculate the partial derivatives of the log-likelihood function with desired accuracy, and locate the maximum likelihood without the assumptions required by previous methods. To assess the reliability and accuracy of our method, we generated large numbers of random Fisher-distributed data sets, for which we calculated mean inclinations and precision parameters. The comparisons show that our new robust Arason-Levi maximum likelihood method is the most reliable, and the mean inclination estimates are the least biased towards shallow values.

Solution of D dimensional Dirac equation for hyperbolic tangent potential using NU method and its application in material properties

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

Suparmi, A., E-mail: soeparmi@staff.uns.ac.id; Cari, C., E-mail: cari@staff.uns.ac.id; Pratiwi, B. N., E-mail: namakubetanurpratiwi@gmail.com

2016-02-08

The analytical solution of D-dimensional Dirac equation for hyperbolic tangent potential is investigated using Nikiforov-Uvarov method. In the case of spin symmetry the D dimensional Dirac equation reduces to the D dimensional Schrodinger equation. The D dimensional relativistic energy spectra are obtained from D dimensional relativistic energy eigen value equation by using Mat Lab software. The corresponding D dimensional radial wave functions are formulated in the form of generalized Jacobi polynomials. The thermodynamically properties of materials are generated from the non-relativistic energy eigen-values in the classical limit. In the non-relativistic limit, the relativistic energy equation reduces to the non-relativistic energy.more » The thermal quantities of the system, partition function and specific heat, are expressed in terms of error function and imaginary error function which are numerically calculated using Mat Lab software.« less

Secular Orbit Evolution in Systems with a Strong External Perturber—A Simple and Accurate Model

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

Andrade-Ines, Eduardo; Eggl, Siegfried, E-mail: eandrade.ines@gmail.com, E-mail: siegfried.eggl@jpl.nasa.gov

We present a semi-analytical correction to the seminal solution for the secular motion of a planet’s orbit under gravitational influence of an external perturber derived by Heppenheimer. A comparison between analytical predictions and numerical simulations allows us to determine corrective factors for the secular frequency and forced eccentricity in the coplanar restricted three-body problem. The correction is given in the form of a polynomial function of the system’s parameters that can be applied to first-order forced eccentricity and secular frequency estimates. The resulting secular equations are simple, straight forward to use, and improve the fidelity of Heppenheimers solution well beyond higher-ordermore » models. The quality and convergence of the corrected secular equations are tested for a wide range of parameters and limits of its applicability are given.« less

Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial differential equations

NASA Astrophysics Data System (ADS)

Arqub, Omar Abu; El-Ajou, Ahmad; Momani, Shaher

2015-07-01

Building fractional mathematical models for specific phenomena and developing numerical or analytical solutions for these fractional mathematical models are crucial issues in mathematics, physics, and engineering. In this work, a new analytical technique for constructing and predicting solitary pattern solutions of time-fractional dispersive partial differential equations is proposed based on the generalized Taylor series formula and residual error function. The new approach provides solutions in the form of a rapidly convergent series with easily computable components using symbolic computation software. For method evaluation and validation, the proposed technique was applied to three different models and compared with some of the well-known methods. The resultant simulations clearly demonstrate the superiority and potentiality of the proposed technique in terms of the quality performance and accuracy of substructure preservation in the construct, as well as the prediction of solitary pattern solutions for time-fractional dispersive partial differential equations.

Mapping Systemic Risk: Critical Degree and Failures Distribution in Financial Networks.

PubMed

Smerlak, Matteo; Stoll, Brady; Gupta, Agam; Magdanz, James S

2015-01-01

The financial crisis illustrated the need for a functional understanding of systemic risk in strongly interconnected financial structures. Dynamic processes on complex networks being intrinsically difficult to model analytically, most recent studies of this problem have relied on numerical simulations. Here we report analytical results in a network model of interbank lending based on directly relevant financial parameters, such as interest rates and leverage ratios. We obtain a closed-form formula for the "critical degree" (the number of creditors per bank below which an individual shock can propagate throughout the network), and relate failures distributions to network topologies, in particular scalefree ones. Our criterion for the onset of contagion turns out to be isomorphic to the condition for cooperation to evolve on graphs and social networks, as recently formulated in evolutionary game theory. This remarkable connection supports recent calls for a methodological rapprochement between finance and ecology.

Comment on atomic independent-particle models

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

Doda, D.D.; Gravey, R.H.; Green, A.E.S.

1975-08-01

The Hartree-Fock-Slater (HFS) independent-particle model in the form developed by Hermann and Skillman (HS) and the Green, Sellin, and Zachor (GSZ) analytic independent-particle model are being used for many types of applications of atomic theory to avoid cumbersome, albeit more rigorous, many-body calculations. The single-electron eigenvalues obtained with these models are examined and it is found that the GSZ model is capable of yielding energy eigenvalues for valence electrons which are substantially closer to experimental values than are the results of HS-HFS calculations. With the aid of an analytic representation of the equivalent HS-HFS screening function, the difficulty with thismore » model is identified as a weakness of the potential in the neighborhood of the valence shell. Accurate representations of valence states are important in most atomic applications of the independent-particle model. (auth)« less

Structural mechanics and helical geometry of thin elastic composites.

PubMed

Wada, Hirofumi

2016-09-21

Helices are ubiquitous in nature, and helical shape transition is often observed in residually stressed bodies, such as composites, wherein materials with different mechanical properties are glued firmly together to form a whole body. Inspired by a variety of biological examples, the basic physical mechanism responsible for the emergence of twisting and bending in such thin composite structures has been extensively studied. Here, we propose a simplified analytical model wherein a slender membrane tube undergoes a helical transition driven by the contraction of an elastic ribbon bound to the membrane surface. We analytically predict the curvature and twist of an emergent helix as functions of differential strains and elastic moduli, which are confirmed by our numerical simulations. Our results may help understand shapes observed in different biological systems, such as spiral bacteria, and could be applied to novel designs of soft machines and robots.

Self ordering threshold and superradiant backscattering to slow a fast gas beam in a ring cavity with counter propagating pump

NASA Astrophysics Data System (ADS)

Maes, C.; Asbóth, J. K.; Ritsch, H.

2007-05-01

We study the dynamics of a fast gaseous beam in a high Q ring cavity counter propagating a strong pump laser with large detuning from any particle optical resonance. As spontaneous emission is strongly suppressed the particles can be treated as polarizable point masses forming a dynamic moving mirror. Above a threshold intensity the particles exhibit spatial periodic ordering enhancing collective coherent backscattering which decelerates the beam. Based on a linear stability analysis in their accelerated rest frame we derive analytic bounds for the intensity threshold of this selforganization as a function of particle number, average velocity, kinetic temperature, pump detuning and resonator linewidth. The analytical results agree well with time dependent simulations of the N-particle motion including field damping and spontaneous emission noise. Our results give conditions which may be easily evaluated for stopping and cooling a fast molecular beam.

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)

Self ordering threshold and superradiant backscattering to slow a fast gas beam in a ring cavity with counter propagating pump.

PubMed

Maes, C; Asbóth, J K; Ritsch, H

2007-05-14

We study the dynamics of a fast gaseous beam in a high Q ring cavity counter propagating a strong pump laser with large detuning from any particle optical resonance. As spontaneous emission is strongly suppressed the particles can be treated as polarizable point masses forming a dynamic moving mirror. Above a threshold intensity the particles exhibit spatial periodic ordering enhancing collective coherent backscattering which decelerates the beam. Based on a linear stability analysis in their accelerated rest frame we derive analytic bounds for the intensity threshold of this selforganization as a function of particle number, average velocity, kinetic temperature, pump detuning and resonator linewidth. The analytical results agree well with time dependent simulations of the N-particle motion including field damping and spontaneous emission noise. Our results give conditions which may be easily evaluated for stopping and cooling a fast molecular beam.

Quantum criticality of one-dimensional multicomponent Fermi gas with strongly attractive interaction

NASA Astrophysics Data System (ADS)

He, Peng; Jiang, Yuzhu; Guan, Xiwen; He, Jinyu

2015-01-01

Quantum criticality of strongly attractive Fermi gas with SU(3) symmetry in one dimension is studied via the thermodynamic Bethe ansatz (TBA) equations. The phase transitions driven by the chemical potential μ , effective magnetic field H1, H2 (chemical potential biases) are analyzed at the quantum criticality. The phase diagram and critical fields are analytically determined by the TBA equations in the zero temperature limit. High accurate equations of state, scaling functions are also obtained analytically for the strong interacting gases. The dynamic exponent z=2 and correlation length exponent ν =1/2 read off the universal scaling form. It turns out that the quantum criticality of the three-component gases involves a sudden change of density of states of one cluster state, two or three cluster states. In general, this method can be adapted to deal with the quantum criticality of multicomponent Fermi gases with SU(N) symmetry.

Classical Dynamics of Fullerenes

NASA Astrophysics Data System (ADS)

Sławianowski, Jan J.; Kotowski, Romuald K.

2017-06-01

The classical mechanics of large molecules and fullerenes is studied. The approach is based on the model of collective motion of these objects. The mixed Lagrangian (material) and Eulerian (space) description of motion is used. In particular, the Green and Cauchy deformation tensors are geometrically defined. The important issue is the group-theoretical approach to describing the affine deformations of the body. The Hamiltonian description of motion based on the Poisson brackets methodology is used. The Lagrange and Hamilton approaches allow us to formulate the mechanics in the canonical form. The method of discretization in analytical continuum theory and in classical dynamics of large molecules and fullerenes enable us to formulate their dynamics in terms of the polynomial expansions of configurations. Another approach is based on the theory of analytical functions and on their approximations by finite-order polynomials. We concentrate on the extremely simplified model of affine deformations or on their higher-order polynomial perturbations.

Analytic-continuation approach to the resummation of divergent series in Rayleigh-Schrödinger perturbation theory

NASA Astrophysics Data System (ADS)

Mihálka, Zsuzsanna É.; Surján, Péter R.

2017-12-01

The method of analytic continuation is applied to estimate eigenvalues of linear operators from finite order results of perturbation theory even in cases when the latter is divergent. Given a finite number of terms E(k ),k =1 ,2 ,⋯M resulting from a Rayleigh-Schrödinger perturbation calculation, scaling these numbers by μk (μ being the perturbation parameter) we form the sum E (μ ) =∑kμkE(k ) for small μ values for which the finite series is convergent to a certain numerical accuracy. Extrapolating the function E (μ ) to μ =1 yields an estimation of the exact solution of the problem. For divergent series, this procedure may serve as resummation tool provided the perturbation problem has a nonzero radius of convergence. As illustrations, we treat the anharmonic (quartic) oscillator and an example from the many-electron correlation problem.

An Analytic Approximation to Very High Specific Impulse and Specific Power Interplanetary Space Mission Analysis

NASA Technical Reports Server (NTRS)

Williams, Craig Hamilton

1995-01-01

A simple, analytic approximation is derived to calculate trip time and performance for propulsion systems of very high specific impulse (50,000 to 200,000 seconds) and very high specific power (10 to 1000 kW/kg) for human interplanetary space missions. The approach assumed field-free space, constant thrust/constant specific power, and near straight line (radial) trajectories between the planets. Closed form, one dimensional equations of motion for two-burn rendezvous and four-burn round trip missions are derived as a function of specific impulse, specific power, and propellant mass ratio. The equations are coupled to an optimizing parameter that maximizes performance and minimizes trip time. Data generated for hypothetical one-way and round trip human missions to Jupiter were found to be within 1% and 6% accuracy of integrated solutions respectively, verifying that for these systems, credible analysis does not require computationally intensive numerical techniques.

Mapping Systemic Risk: Critical Degree and Failures Distribution in Financial Networks

PubMed Central

Smerlak, Matteo; Stoll, Brady; Gupta, Agam; Magdanz, James S.

2015-01-01

The financial crisis illustrated the need for a functional understanding of systemic risk in strongly interconnected financial structures. Dynamic processes on complex networks being intrinsically difficult to model analytically, most recent studies of this problem have relied on numerical simulations. Here we report analytical results in a network model of interbank lending based on directly relevant financial parameters, such as interest rates and leverage ratios. We obtain a closed-form formula for the “critical degree” (the number of creditors per bank below which an individual shock can propagate throughout the network), and relate failures distributions to network topologies, in particular scalefree ones. Our criterion for the onset of contagion turns out to be isomorphic to the condition for cooperation to evolve on graphs and social networks, as recently formulated in evolutionary game theory. This remarkable connection supports recent calls for a methodological rapprochement between finance and ecology. PMID:26207631

A new method for constructing analytic elements for groundwater flow.

NASA Astrophysics Data System (ADS)

Strack, O. D.

2007-12-01

The analytic element method is based upon the superposition of analytic functions that are defined throughout the infinite domain, and can be used to meet a variety of boundary conditions. Analytic elements have been use successfully for a number of problems, mainly dealing with the Poisson equation (see, e.g., Theory and Applications of the Analytic Element Method, Reviews of Geophysics, 41,2/1005 2003 by O.D.L. Strack). The majority of these analytic elements consists of functions that exhibit jumps along lines or curves. Such linear analytic elements have been developed also for other partial differential equations, e.g., the modified Helmholz equation and the heat equation, and were constructed by integrating elementary solutions, the point sink and the point doublet, along a line. This approach is limiting for two reasons. First, the existence is required of the elementary solutions, and, second, the integration tends to limit the range of solutions that can be obtained. We present a procedure for generating analytic elements that requires merely the existence of a harmonic function with the desired properties; such functions exist in abundance. The procedure to be presented is used to generalize this harmonic function in such a way that the resulting expression satisfies the applicable differential equation. The approach will be applied, along with numerical examples, for the modified Helmholz equation and for the heat equation, while it is noted that the method is in no way restricted to these equations. The procedure is carried out entirely in terms of complex variables, using Wirtinger calculus.

GENERAL: The Analytic Solution of Schrödinger Equation with Potential Function Superposed by Six Terms with Positive-power and Inverse-power Potentials

NASA Astrophysics Data System (ADS)

Hu, Xian-Quan; Luo, Guang; Cui, Li-Peng; Li, Fang-Yu; Niu, Lian-Bin

2009-03-01

The analytic solution of the radial Schrödinger equation is studied by using the tight coupling condition of several positive-power and inverse-power potential functions in this article. Furthermore, the precisely analytic solutions and the conditions that decide the existence of analytic solution have been searched when the potential of the radial Schrödinger equation is V(r) = α1r8 + α2r3 + α3r2 + β3r-1 + β2r-3 + β1r-4. Generally speaking, there is only an approximate solution, but not analytic solution for Schrödinger equation with several potentials' superposition. However, the conditions that decide the existence of analytic solution have been found and the analytic solution and its energy level structure are obtained for the Schrödinger equation with the potential which is motioned above in this paper. According to the single-value, finite and continuous standard of wave function in a quantum system, the authors firstly solve the asymptotic solution through the radial coordinate r → and r → 0; secondly, they make the asymptotic solutions combining with the series solutions nearby the neighborhood of irregular singularities; and then they compare the power series coefficients, deduce a series of analytic solutions of the stationary state wave function and corresponding energy level structure by tight coupling among the coefficients of potential functions for the radial Schrödinger equation; and lastly, they discuss the solutions and make conclusions.

DEMONSTRATION OF THE ANALYTIC ELEMENT METHOD FOR WELLHEAD PROJECTION - PROJECT SUMMARY

EPA Science Inventory

A new computer program has been developed to determine time-of-travel capture zones in relatively simple geohydrological settings. The WhAEM package contains an analytic element model that uses superposition of (many) closed form analytical solutions to generate a ground-water fl...

Nontrivial thermodynamics in 't Hooft's large-N limit

NASA Astrophysics Data System (ADS)

Cubero, Axel Cortés

2015-05-01

We study the finite volume/temperature correlation functions of the (1 +1 )-dimensional SU (N ) principal chiral sigma model in the planar limit. The exact S-matrix of the sigma model is known to simplify drastically at large N , and this leads to trivial thermodynamic Bethe ansatz (TBA) equations. The partition function, if derived using the TBA, can be shown to be that of free particles. We show that the correlation functions and expectation values of operators at finite volume/temperature are not those of the free theory, and that the TBA does not give enough information to calculate them. Our analysis is done using the Leclair-Mussardo formula for finite-volume correlators, and knowledge of the exact infinite-volume form factors. We present analytical results for the one-point function of the energy-momentum tensor, and the two-point function of the renormalized field operator. The results for the energy-momentum tensor can be used to define a nontrivial partition function.

The intrinsic fluorescence of FAD and its application in analytical chemistry: a review

NASA Astrophysics Data System (ADS)

Galbán, Javier; Sanz-Vicente, Isabel; Navarro, Jesús; de Marcos, Susana

2016-12-01

This review (with 106 references) mainly deals with the analytical applications of flavin-adenine dinucleotide (FAD) fluorescence. In the first section, the spectroscopic properties of this compound are reviewed at the light of his different acid-base, oxidation and structural forms; the chemical and spectroscopic properties of flavin mononucleotide (FMN) and other flavins will be also briefly discussed. The second section discusses how the properties of FAD fluorescence changes in flavoenzymes (FvEs), again considering the different chemical and structural forms; the glucose oxidase (GOx) and the choline oxidase (ChOx) cases will be commented. Since almost certainly the most reported analytical application of FAD fluorescence is as an auto-indicator in enzymatic methods catalysed by FvE oxidoreductases, it is important to know how the concentrations of the different forms of FAD changes along the reaction and, consequently, the fluorescence and the analytical signals. An approach to do this will be presented in section 3. The fourth part of the paper compiles the analytical applications which have been reported until now based in these fluorescence properties. Finally, some suggestions about tentative future research are also given.

The intrinsic fluorescence of FAD and its application in analytical chemistry: a review.

PubMed

Galbán, Javier; Sanz-Vicente, Isabel; Navarro, Jesús; de Marcos, Susana

2016-12-19

This review (with 106 references) mainly deals with the analytical applications of flavin-adenine dinucleotide (FAD) fluorescence. In the first section, the spectroscopic properties of this compound are reviewed at the light of his different acid-base, oxidation and structural forms; the chemical and spectroscopic properties of flavin mononucleotide (FMN) and other flavins will be also briefly discussed. The second section discusses how the properties of FAD fluorescence changes in flavoenzymes (FvEs), again considering the different chemical and structural forms; the glucose oxidase (GOx) and the choline oxidase (ChOx) cases will be commented. Since almost certainly the most reported analytical application of FAD fluorescence is as an auto-indicator in enzymatic methods catalysed by FvE oxidoreductases, it is important to know how the concentrations of the different forms of FAD changes along the reaction and, consequently, the fluorescence and the analytical signals. An approach to do this will be presented in section 3. The fourth part of the paper compiles the analytical applications which have been reported until now based in these fluorescence properties. Finally, some suggestions about tentative future research are also given.

Mapping copy number variation by population-scale genome sequencing.

PubMed

Mills, Ryan E; Walter, Klaudia; Stewart, Chip; Handsaker, Robert E; Chen, Ken; Alkan, Can; Abyzov, Alexej; Yoon, Seungtai Chris; Ye, Kai; Cheetham, R Keira; Chinwalla, Asif; Conrad, Donald F; Fu, Yutao; Grubert, Fabian; Hajirasouliha, Iman; Hormozdiari, Fereydoun; Iakoucheva, Lilia M; Iqbal, Zamin; Kang, Shuli; Kidd, Jeffrey M; Konkel, Miriam K; Korn, Joshua; Khurana, Ekta; Kural, Deniz; Lam, Hugo Y K; Leng, Jing; Li, Ruiqiang; Li, Yingrui; Lin, Chang-Yun; Luo, Ruibang; Mu, Xinmeng Jasmine; Nemesh, James; Peckham, Heather E; Rausch, Tobias; Scally, Aylwyn; Shi, Xinghua; Stromberg, Michael P; Stütz, Adrian M; Urban, Alexander Eckehart; Walker, Jerilyn A; Wu, Jiantao; Zhang, Yujun; Zhang, Zhengdong D; Batzer, Mark A; Ding, Li; Marth, Gabor T; McVean, Gil; Sebat, Jonathan; Snyder, Michael; Wang, Jun; Ye, Kenny; Eichler, Evan E; Gerstein, Mark B; Hurles, Matthew E; Lee, Charles; McCarroll, Steven A; Korbel, Jan O

2011-02-03

Genomic structural variants (SVs) are abundant in humans, differing from other forms of variation in extent, origin and functional impact. Despite progress in SV characterization, the nucleotide resolution architecture of most SVs remains unknown. We constructed a map of unbalanced SVs (that is, copy number variants) based on whole genome DNA sequencing data from 185 human genomes, integrating evidence from complementary SV discovery approaches with extensive experimental validations. Our map encompassed 22,025 deletions and 6,000 additional SVs, including insertions and tandem duplications. Most SVs (53%) were mapped to nucleotide resolution, which facilitated analysing their origin and functional impact. We examined numerous whole and partial gene deletions with a genotyping approach and observed a depletion of gene disruptions amongst high frequency deletions. Furthermore, we observed differences in the size spectra of SVs originating from distinct formation mechanisms, and constructed a map of SV hotspots formed by common mechanisms. Our analytical framework and SV map serves as a resource for sequencing-based association studies.

Isotope and Chemical Methods in Support of the U.S. Geological Survey Science Strategy, 2003-2008

USGS Publications Warehouse

Rye, R.O.; Johnson, C.A.; Landis, G.P.; Hofstra, A.H.; Emsbo, P.; Stricker, C.A.; Hunt, A.G.; Rusk, B.G.

2008-01-01

Principal functions of the Mineral Resources Program are providing information to decision-makers related to mineral deposits on federal lands and predicting the environmental consequences of the mining or natural weathering of those deposits. Performing these functions requires that predictions be made of the likelihood of undiscovered deposits. The predictions are based on geologic and geoenvironmental models that are constructed for the various types of mineral deposits from detailed descriptions of actual deposits and detailed understanding of the processes that formed them. Over the past three decades the understanding of ore-forming processes has benefitted greatly from the integration of laboratory-based geochemical tools with field observations and other data sources. Under the aegis of the Evolution of Ore Deposits and Technology Transfer Project (EODTTP), a five-year effort that terminated in 2008, the Mineral Resources Program provided state-of-the-art analytical capabilities to support applications of several related geochemical tools.

Atomic and molecular far-infrared lines from high redshift galaxies

NASA Astrophysics Data System (ADS)

Vallini, L.

2015-03-01

The advent of Atacama Large Millimeter-submillimeter Array (ALMA), with its unprecedented sensitivity, makes it possible the detection of far-infrared (FIR) metal cooling and molecular lines from the first galaxies that formed after the Big Bang. These lines represent a powerful tool to shed light on the physical properties of the interstellar medium (ISM) in high-redshift sources. In what follows we show the potential of a physically motivated theoretical approach that we developed to predict the ISM properties of high redshift galaxies. The model allows to infer, as a function of the metallicity, the luminosities of various FIR lines observable with ALMA. It is based on high resolution cosmological simulations of star-forming galaxies at the end of the Epoch of Reionization (z˜eq6) , further implemented with sub-grid physics describing the cooling and the heating processes that take place in the neutral diffuse ISM. Finally we show how a different approach based on semi-analytical calculations can allow to predict the CO flux function at z>6.

Aerodynamic response of an airfoil with thickness to a longitudinal and transverse periodic gust

NASA Technical Reports Server (NTRS)

Hamad, G.; Atassi, H.

1980-01-01

The unsteady lift of an airfoil with thickness subject to a two-dimensional periodic gust is analyzed using the recent theory of Goldstein and Atassi. It is found that to properly account for the coupling between the steady potential flow and the unsteady vortical flow, one has to consider the contribution of order alpha-squared (when alpha is steady state disturbance) to the potential flowfield. A closed form analytical formula is then derived for the lift function. The results show strong dependence on the wave members of the gust.

From non-trivial geometries to power spectra and vice versa

NASA Astrophysics Data System (ADS)

Brooker, D. J.; Tsamis, N. C.; Woodard, R. P.

2018-04-01

We review a recent formalism which derives the functional forms of the primordial—tensor and scalar—power spectra of scalar potential inflationary models. The formalism incorporates the case of geometries with non-constant first slow-roll parameter. Analytic expressions for the power spectra are given that explicitly display the dependence on the geometric properties of the background. Moreover, we present the full algorithm for using our formalism, to reconstruct the model from the observed power spectra. Our techniques are applied to models possessing "features" in their potential with excellent agreement.

Evaluation of the optical axis tilt of zinc oxide films via noncollinear second harmonic generation

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

Bovino, F. A.; Larciprete, M. C.; Belardini, A.

2009-06-22

We investigated noncollinear second harmonic generation form zinc oxide films, grown on glass substrates by dual ion beam sputtering technique. At a fixed incidence angle, the generated signal is investigated by scanning the polarization state of both fundamental beams. We show that the map of the generated signal as a function of polarization states of both pump beams, together with the analytical curves, allows to retrieve the orientation of the optical axis and eventually, its angular tilt, with respect to the surface normal.

Lump and lump-soliton solutions to the (2+1) -dimensional Ito equation

NASA Astrophysics Data System (ADS)

Yang, Jin-Yun; Ma, Wen-Xiu; Qin, Zhenyun

2017-06-01

Based on the Hirota bilinear form of the (2+1) -dimensional Ito equation, one class of lump solutions and two classes of interaction solutions between lumps and line solitons are generated through analysis and symbolic computations with Maple. Analyticity is naturally guaranteed for the presented lump and interaction solutions, and the interaction solutions reduce to lumps (or line solitons) while the hyperbolic-cosine (or the quadratic function) disappears. Three-dimensional plots and contour plots are made for two specific examples of the resulting interaction solutions.

SIMPLE MODEL OF ICE SEGREGATION USING AN ANALYTIC FUNCTION TO MODEL HEAT AND SOIL-WATER FLOW.

USGS Publications Warehouse

Hromadka, T.V.; Guymon, G.L.

1984-01-01

This paper reports on the development of a simple two-dimensional model of coupled heat and soil-water flow in freezing or thawing soil. The model also estimates ice-segregation (frost-heave) evolution. Ice segregation in soil results from water drawn into a freezing zone by hydraulic gradients created by the freezing of soil-water. Thus, with a favorable balance between the rate of heat extraction and the rate of water transport to a freezing zone, segregated ice lenses may form.

Thermodynamic Model of Afterburning in Explosions

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

Kuhl, A L; Howard, M; Fried, L

2003-04-23

Thermodynamic states encountered during afterburning of explosion products gases in air were analyzed with the Cheetah code. Results are displayed in the form of Le Chatelier diagrams: the locus of states of specific internal energy versus temperature, for six different condensed explosives charges. Accuracy of the results was confirmed by comparing the fuel and products curves with the heats of detonation and combustion, and species composition as measured in bomb calorimeter experiments. Results were fit with analytic functions u = f ( T ) suitable for specifying the thermodynamic properties required for gas-dynamic models of afterburning in explosions.

Building the analytical response in frequency domain of AC biased bolometers. Application to Planck/HFI

NASA Astrophysics Data System (ADS)

Sauvé, Alexandre; Montier, Ludovic

2016-12-01

Context: Bolometers are high sensitivity detector commonly used in Infrared astronomy. The HFI instrument of the Planck satellite makes extensive use of them, but after the satellite launch two electronic related problems revealed critical. First an unexpected excess response of detectors at low optical excitation frequency for ν < 1 Hz, and secondly the Analog To digital Converter (ADC) component had been insufficiently characterized on-ground. These two problems require an exquisite knowledge of detector response. However bolometers have highly nonlinear characteristics, coming from their electrical and thermal coupling making them very difficult to model. Goal: We present a method to build the analytical transfer function in frequency domain which describe the voltage response of an Alternative Current (AC) biased bolometer to optical excitation, based on the standard bolometer model. This model is built using the setup of the Planck/HFI instrument and offers the major improvement of being based on a physical model rather than the currently in use had-hoc model based on Direct Current (DC) bolometer theory. Method: The analytical transfer function expression will be presented in matrix form. For this purpose, we build linearized versions of the bolometer electro thermal equilibrium. A custom description of signals in frequency is used to solve the problem with linear algebra. The model performances is validated using time domain simulations. Results: The provided expression is suitable for calibration and data processing. It can also be used to provide constraints for fitting optical transfer function using real data from steady state electronic response and optical response. The accurate description of electronic response can also be used to improve the ADC nonlinearity correction for quickly varying optical signals.

Cognitive-analytical therapy for a patient with functional neurological symptom disorder-conversion disorder (psychogenic myopia): A case study.

PubMed

Nasiri, Hamid; Ebrahimi, Amrollah; Zahed, Arash; Arab, Mostafa; Samouei, Rahele

2015-05-01

Functional neurological symptom disorder commonly presents with symptoms and defects of sensory and motor functions. Therefore, it is often mistaken for a medical condition. It is well known that functional neurological symptom disorder more often caused by psychological factors. There are three main approaches namely analytical, cognitive and biological to manage conversion disorder. Any of such approaches can be applied through short-term treatment programs. In this case, study a 12-year-old boy with the diagnosed functional neurological symptom disorder (psychogenic myopia) was put under a cognitive-analytical treatment. The outcome of this treatment modality was proved successful.

Paper microfluidic-based enzyme catalyzed double microreactor.

PubMed

Ferrer, Ivonne M; Valadez, Hector; Estala, Lissette; Gomez, Frank A

2014-08-01

We describe a paper microfluidic-based enzyme catalyzed double microreactor assay using fluorescent detection. Here, solutions of lactate dehydrogenase (LDH) and diaphorase (DI) were directly spotted onto the microfluidic paper-based analytical device (μPAD). Samples containing lactic acid, resazurin, and nicotinamide adenine dinucleotide oxidized form (NAD(+) ), potassium chloride (KCl), and BSA, in MES buffer were separately spotted onto the μPAD and MES buffer flowed through the device. A cascade reaction occurs upon the sample spot overlapping with LDH to form pyruvate and nicotinamide adenine dinucleotide reduced form (NADH). Subsequently, NADH is used in the conversion of resazurin to fluorescent resorufin by DI. The μPAD avoids the need of surface functionalization or enzyme immobilization steps. These microreactor devices are low cost and easy to fabricate and effect reaction based solely on buffer capillary action. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Recent Studies in Functional Analytic Psychotherapy

ERIC Educational Resources Information Center

Garcia, Rafael Ferro

2008-01-01

Functional Analytic Psychotherapy (FAP), based on the principles of radical behaviorism, emphasizes the impact of eventualities that occur during therapeutic sessions, the therapist-client interaction context, functional equivalence between environments, natural reinforcement and shaping by the therapist. This paper reviews recent studies of FAP…

Parametric study of minimum reactor mass in energy-storage dc-to-dc converters

NASA Technical Reports Server (NTRS)

Wong, R. C.; Owen, H. A., Jr.; Wilson, T. G.

1981-01-01

Closed-form analytical solutions for the design equations of a minimum-mass reactor for a two-winding voltage-or-current step-up converter are derived. A quantitative relationship between the three parameters - minimum total reactor mass, maximum output power, and switching frequency - is extracted from these analytical solutions. The validity of the closed-form solution is verified by a numerical minimization procedure. A computer-aided design procedure using commercially available toroidal cores and magnet wires is also used to examine how the results from practical designs follow the predictions of the analytical solutions.

WHAEM: PROGRAM DOCUMENTATION FOR THE WELLHEAD ANALYTIC ELEMENT MODEL (EPA/600/SR-94/210)

EPA Science Inventory

A new computer program has been developed to determine time-of-travel capture zones in relatively simple geohydrological settings. The WhAEM package contains an analytic element model that uses superposition of (many) closed form analytical solutions to generate a groundwater flo...

Functional Interfaces Constructed by Controlled/Living Radical Polymerization for Analytical Chemistry.

PubMed

Wang, Huai-Song; Song, Min; Hang, Tai-Jun

2016-02-10

The high-value applications of functional polymers in analytical science generally require well-defined interfaces, including precisely synthesized molecular architectures and compositions. Controlled/living radical polymerization (CRP) has been developed as a versatile and powerful tool for the preparation of polymers with narrow molecular weight distributions and predetermined molecular weights. Among the CRP system, atom transfer radical polymerization (ATRP) and reversible addition-fragmentation chain transfer (RAFT) are well-used to develop new materials for analytical science, such as surface-modified core-shell particles, monoliths, MIP micro- or nanospheres, fluorescent nanoparticles, and multifunctional materials. In this review, we summarize the emerging functional interfaces constructed by RAFT and ATRP for applications in analytical science. Various polymers with precisely controlled architectures including homopolymers, block copolymers, molecular imprinted copolymers, and grafted copolymers were synthesized by CRP methods for molecular separation, retention, or sensing. We expect that the CRP methods will become the most popular technique for preparing functional polymers that can be broadly applied in analytical chemistry.

Optimal guidance law development for an advanced launch system

NASA Technical Reports Server (NTRS)

Calise, Anthony J.; Leung, Martin S. K.

1995-01-01

The objective of this research effort was to develop a real-time guidance approach for launch vehicles ascent to orbit injection. Various analytical approaches combined with a variety of model order and model complexity reduction have been investigated. Singular perturbation methods were first attempted and found to be unsatisfactory. The second approach based on regular perturbation analysis was subsequently investigated. It also fails because the aerodynamic effects (ignored in the zero order solution) are too large to be treated as perturbations. Therefore, the study demonstrates that perturbation methods alone (both regular and singular perturbations) are inadequate for use in developing a guidance algorithm for the atmospheric flight phase of a launch vehicle. During a second phase of the research effort, a hybrid analytic/numerical approach was developed and evaluated. The approach combines the numerical methods of collocation and the analytical method of regular perturbations. The concept of choosing intelligent interpolating functions is also introduced. Regular perturbation analysis allows the use of a crude representation for the collocation solution, and intelligent interpolating functions further reduce the number of elements without sacrificing the approximation accuracy. As a result, the combined method forms a powerful tool for solving real-time optimal control problems. Details of the approach are illustrated in a fourth order nonlinear example. The hybrid approach is then applied to the launch vehicle problem. The collocation solution is derived from a bilinear tangent steering law, and results in a guidance solution for the entire flight regime that includes both atmospheric and exoatmospheric flight phases.

Analytical and experimental comparisons of electromechanical vibration response of a piezoelectric bimorph beam for power harvesting

NASA Astrophysics Data System (ADS)

Lumentut, M. F.; Howard, I. M.

2013-03-01

Power harvesters that extract energy from vibrating systems via piezoelectric transduction show strong potential for powering smart wireless sensor devices in applications of health condition monitoring of rotating machinery and structures. This paper presents an analytical method for modelling an electromechanical piezoelectric bimorph beam with tip mass under two input base transverse and longitudinal excitations. The Euler-Bernoulli beam equations were used to model the piezoelectric bimorph beam. The polarity-electric field of the piezoelectric element is excited by the strain field caused by base input excitation, resulting in electrical charge. The governing electromechanical dynamic equations were derived analytically using the weak form of the Hamiltonian principle to obtain the constitutive equations. Three constitutive electromechanical dynamic equations based on independent coefficients of virtual displacement vectors were formulated and then further modelled using the normalised Ritz eigenfunction series. The electromechanical formulations include both the series and parallel connections of the piezoelectric bimorph. The multi-mode frequency response functions (FRFs) under varying electrical load resistance were formulated using Laplace transformation for the multi-input mechanical vibrations to provide the multi-output dynamic displacement, velocity, voltage, current and power. The experimental and theoretical validations reduced for the single mode system were shown to provide reasonable predictions. The model results from polar base excitation for off-axis input motions were validated with experimental results showing the change to the electrical power frequency response amplitude as a function of excitation angle, with relevance for practical implementation.

Measuring myokines with cardiovascular functions: pre-analytical variables affecting the analytical output.

PubMed

Lombardi, Giovanni; Sansoni, Veronica; Banfi, Giuseppe

2017-08-01

In the last few years, a growing number of molecules have been associated to an endocrine function of the skeletal muscle. Circulating myokine levels, in turn, have been associated with several pathophysiological conditions including the cardiovascular ones. However, data from different studies are often not completely comparable or even discordant. This would be due, at least in part, to the whole set of situations related to the preparation of the patient prior to blood sampling, blood sampling procedure, processing and/or store. This entire process constitutes the pre-analytical phase. The importance of the pre-analytical phase is often not considered. However, in routine diagnostics, the 70% of the errors are in this phase. Moreover, errors during the pre-analytical phase are carried over in the analytical phase and affects the final output. In research, for example, when samples are collected over a long time and by different laboratories, a standardized procedure for sample collecting and the correct procedure for sample storage are acknowledged. In this review, we discuss the pre-analytical variables potentially affecting the measurement of myokines with cardiovascular functions.

Q{sub 2} evolution of parton distributions at small values of x: Effective scale for combined H1 and ZEUS data on the structure function F{sub 2}

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

Kotikov, A. V., E-mail: kotikov@theor.jinr.ru; Shaikhatdenov, B. G.

2015-06-15

An expression for the structure function F{sub 2} in the form of Bessel functions at small values of the Bjorken variable x is used. This expression was derived for a flat initial condition in the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations. The argument of the strong coupling constant was chosen in such a way as to annihilate the singular part of the anomalous dimensions in the next-to-leading-order of perturbation theory. This choice, together with the frozen and analytic versions of the strong coupling constant, is used to analyze combined data of the H1 and ZEUS Collaborations obtained recently for the structure functionmore » F{sub 2}.« less

Quantum calculus of classical vortex images, integrable models and quantum states

NASA Astrophysics Data System (ADS)

Pashaev, Oktay K.

2016-10-01

From two circle theorem described in terms of q-periodic functions, in the limit q→1 we have derived the strip theorem and the stream function for N vortex problem. For regular N-vortex polygon we find compact expression for the velocity of uniform rotation and show that it represents a nonlinear oscillator. We describe q-dispersive extensions of the linear and nonlinear Schrodinger equations, as well as the q-semiclassical expansions in terms of Bernoulli and Euler polynomials. Different kind of q-analytic functions are introduced, including the pq-analytic and the golden analytic functions.

Dynamic response of gold nanoparticle chemiresistors to organic analytes in aqueous solution.

PubMed

Müller, Karl-Heinz; Chow, Edith; Wieczorek, Lech; Raguse, Burkhard; Cooper, James S; Hubble, Lee J

2011-10-28

We investigate the response dynamics of 1-hexanethiol-functionalized gold nanoparticle chemiresistors exposed to the analyte octane in aqueous solution. The dynamic response is studied as a function of the analyte-water flow velocity, the thickness of the gold nanoparticle film and the analyte concentration. A theoretical model for analyte limited mass-transport is used to model the analyte diffusion into the film, the partitioning of the analyte into the 1-hexanethiol capping layers and the subsequent swelling of the film. The degree of swelling is then used to calculate the increase of the electron tunnel resistance between adjacent nanoparticles which determines the resistance change of the film. In particular, the effect of the nonlinear relationship between resistance and swelling on the dynamic response is investigated at high analyte concentration. Good agreement between experiment and the theoretical model is achieved. This journal is © the Owner Societies 2011

Analytic solution of field distribution and demagnetization function of ideal hollow cylindrical field source

NASA Astrophysics Data System (ADS)

Xu, Xiaonong; Lu, Dingwei; Xu, Xibin; Yu, Yang; Gu, Min

2017-09-01

The Halbach type hollow cylindrical permanent magnet array (HCPMA) is a volume compact and energy conserved field source, which have attracted intense interests in many practical applications. Here, using the complex variable integration method based on the Biot-Savart Law (including current distributions inside the body and on the surfaces of magnet), we derive analytical field solutions to an ideal multipole HCPMA in entire space including the interior of magnet. The analytic field expression inside the array material is used to construct an analytic demagnetization function, with which we can explain the origin of demagnetization phenomena in HCPMA by taking into account an ideal magnetic hysteresis loop with finite coercivity. These analytical field expressions and demagnetization functions provide deeper insight into the nature of such permanent magnet array systems and offer guidance in designing optimized array system.

A density functional theory study of the correlation between analyte basicity, ZnPc adsorption strength, and sensor response.

PubMed

Tran, N L; Bohrer, F I; Trogler, W C; Kummel, A C

2009-05-28

Density functional theory (DFT) simulations were used to determine the binding strength of 12 electron-donating analytes to the zinc metal center of a zinc phthalocyanine molecule (ZnPc monomer). The analyte binding strengths were compared to the analytes' enthalpies of complex formation with boron trifluoride (BF(3)), which is a direct measure of their electron donating ability or Lewis basicity. With the exception of the most basic analyte investigated, the ZnPc binding energies were found to correlate linearly with analyte basicities. Based on natural population analysis calculations, analyte complexation to the Zn metal of the ZnPc monomer resulted in limited charge transfer from the analyte to the ZnPc molecule, which increased with analyte-ZnPc binding energy. The experimental analyte sensitivities from chemiresistor ZnPc sensor data were proportional to an exponential of the binding energies from DFT calculations consistent with sensitivity being proportional to analyte coverage and binding strength. The good correlation observed suggests DFT is a reliable method for the prediction of chemiresistor metallophthalocyanine binding strengths and response sensitivities.

Nonequilibrium approach regarding metals from a linearised kappa distribution

NASA Astrophysics Data System (ADS)

Domenech-Garret, J. L.

2017-10-01

The widely used kappa distribution functions develop high-energy tails through an adjustable kappa parameter. The aim of this work is to show that such a parameter can itself be regarded as a function, which entangles information about the sources of disequilibrium. We first derive and analyse an expanded Fermi-Dirac kappa distribution. Later, we use this expanded form to obtain an explicit analytical expression for the kappa parameter of a heated metal on which an external electric field is applied. We show that such a kappa index causes departures from equilibrium depending on the physical magnitudes. Finally, we study the role of temperature and electric field on such a parameter, which characterises the electron population of a metal out of equilibrium.

Rapid calculation of acoustic fields from arbitrary continuous-wave sources.

PubMed

Treeby, Bradley E; Budisky, Jakub; Wise, Elliott S; Jaros, Jiri; Cox, B T

2018-01-01

A Green's function solution is derived for calculating the acoustic field generated by phased array transducers of arbitrary shape when driven by a single frequency continuous wave excitation with spatially varying amplitude and phase. The solution is based on the Green's function for the homogeneous wave equation expressed in the spatial frequency domain or k-space. The temporal convolution integral is solved analytically, and the remaining integrals are expressed in the form of the spatial Fourier transform. This allows the acoustic pressure for all spatial positions to be calculated in a single step using two fast Fourier transforms. The model is demonstrated through several numerical examples, including single element rectangular and spherically focused bowl transducers, and multi-element linear and hemispherical arrays.

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

NASA Astrophysics Data System (ADS)

Bubin, Sergiy; Adamowicz, Ludwik

2006-06-01

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

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

PubMed

Bubin, Sergiy; Adamowicz, Ludwik

2006-06-14

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

Electron Distribution Functions in the Diffusion Region of Asymmetric Magnetic Reconnection

NASA Technical Reports Server (NTRS)

Bessho, N.; Chen, L.-J.; Hesse, M.

2016-01-01

We study electron distribution functions in a diffusion region of antiparallel asymmetric reconnection by means of particle-in-cell simulations and analytical theory. At the electron stagnation point, the electron distribution comprises a crescent-shaped population and a core component. The crescent-shaped distribution is due to electrons coming from the magnetosheath toward the stagnation point and accelerated mainly by electric field normal to the current sheet. Only a part of magnetosheath electrons can reach the stagnation point and form the crescent-shaped distribution that has a boundary of a parabolic curve. The penetration length of magnetosheath electrons into the magnetosphere is derived. We expect that satellite observations can detect crescent-shaped electron distributions during magnetopause reconnection.

Theoretical studies of system performance and adaptive optics design parameters

NASA Astrophysics Data System (ADS)

Tyson, Robert K.

1990-08-01

The ultimate performance of an adaptive optics (AO) system can be sensitive to specific design parameters of individual components. The type and configuration of a wavefront sensor or the shape of individual deformable mirror actuator influence functions can have a profound effect on the correctability of the AO system. This paper will discuss the results of a theoretical study which employed both closed form analytic solutions and computer models. A parametric analysis of wavefront sensor characteristics, noise, and subaperture geometry are independently evaluated against system response to an aberrated wave characteristic of atmospheric turbulence. Similarly, the shape and extent of the deformable mirror influence function and the placement and number of actuators is evaluated to characterize the effects of fitting error and coupling.

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

NASA Astrophysics Data System (ADS)

Banerjee, J. R.; Ananthapuvirajah, A.

2018-05-01

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

Using Functional Analytic Therapy to Train Therapists in Acceptance and Commitment Therapy, a Conceptual and Practical Framework

ERIC Educational Resources Information Center

Schoendorff, Benjamin; Steinwachs, Joanne

2012-01-01

How can therapists be effectively trained in clinical functional contextualism? In this conceptual article we propose a new way of training therapists in Acceptance and Commitment Therapy skills using tools from Functional Analytic Psychotherapy in a training context functionally similar to the therapeutic relationship. FAP has been successfully…

Adaptive learning in complex reproducing kernel Hilbert spaces employing Wirtinger's subgradients.

PubMed

Bouboulis, Pantelis; Slavakis, Konstantinos; Theodoridis, Sergios

2012-03-01

This paper presents a wide framework for non-linear online supervised learning tasks in the context of complex valued signal processing. The (complex) input data are mapped into a complex reproducing kernel Hilbert space (RKHS), where the learning phase is taking place. Both pure complex kernels and real kernels (via the complexification trick) can be employed. Moreover, any convex, continuous and not necessarily differentiable function can be used to measure the loss between the output of the specific system and the desired response. The only requirement is the subgradient of the adopted loss function to be available in an analytic form. In order to derive analytically the subgradients, the principles of the (recently developed) Wirtinger's calculus in complex RKHS are exploited. Furthermore, both linear and widely linear (in RKHS) estimation filters are considered. To cope with the problem of increasing memory requirements, which is present in almost all online schemes in RKHS, the sparsification scheme, based on projection onto closed balls, has been adopted. We demonstrate the effectiveness of the proposed framework in a non-linear channel identification task, a non-linear channel equalization problem and a quadrature phase shift keying equalization scheme, using both circular and non circular synthetic signal sources.

Determining optimal parameters in magnetic spacecraft stabilization via attitude feedback

NASA Astrophysics Data System (ADS)

Bruni, Renato; Celani, Fabio

2016-10-01

The attitude control of a spacecraft using magnetorquers can be achieved by a feedback control law which has four design parameters. However, the practical determination of appropriate values for these parameters is a critical open issue. We propose here an innovative systematic approach for finding these values: they should be those that minimize the convergence time to the desired attitude. This a particularly diffcult optimization problem, for several reasons: 1) such time cannot be expressed in analytical form as a function of parameters and initial conditions; 2) design parameters may range over very wide intervals; 3) convergence time depends also on the initial conditions of the spacecraft, which are not known in advance. To overcome these diffculties, we present a solution approach based on derivative-free optimization. These algorithms do not need to write analytically the objective function: they only need to compute it in a number of points. We also propose a fast probing technique to identify which regions of the search space have to be explored densely. Finally, we formulate a min-max model to find robust parameters, namely design parameters that minimize convergence time under the worst initial conditions. Results are very promising.

Higher order alchemical derivatives from coupled perturbed self-consistent field theory.

PubMed

Lesiuk, Michał; Balawender, Robert; Zachara, Janusz

2012-01-21

We present an analytical approach to treat higher order derivatives of Hartree-Fock (HF) and Kohn-Sham (KS) density functional theory energy in the Born-Oppenheimer approximation with respect to the nuclear charge distribution (so-called alchemical derivatives). Modified coupled perturbed self-consistent field theory is used to calculate molecular systems response to the applied perturbation. Working equations for the second and the third derivatives of HF/KS energy are derived. Similarly, analytical forms of the first and second derivatives of orbital energies are reported. The second derivative of Kohn-Sham energy and up to the third derivative of Hartree-Fock energy with respect to the nuclear charge distribution were calculated. Some issues of practical calculations, in particular the dependence of the basis set and Becke weighting functions on the perturbation, are considered. For selected series of isoelectronic molecules values of available alchemical derivatives were computed and Taylor series expansion was used to predict energies of the "surrounding" molecules. Predicted values of energies are in unexpectedly good agreement with the ones computed using HF/KS methods. Presented method allows one to predict orbital energies with the error less than 1% or even smaller for valence orbitals. © 2012 American Institute of Physics

Analytic Guidance for the First Entry in a Skip Atmospheric Entry

NASA Technical Reports Server (NTRS)

Garcia-Llama, Eduardo

2007-01-01

This paper presents an analytic method to generate a reference drag trajectory for the first entry portion of a skip atmospheric entry. The drag reference, expressed as a polynomial function of the velocity, will meet the conditions necessary to fit the requirements of the complete entry phase. The generic method proposed to generate the drag reference profile is further simplified by thinking of the drag and the velocity as density and cumulative distribution functions respectively. With this notion it will be shown that the reference drag profile can be obtained by solving a linear algebraic system of equations. The resulting drag profile is flown using the feedback linearization method of differential geometric control as guidance law with the error dynamics of a second order homogeneous equation in the form of a damped oscillator. This approach was first proposed as a revisited version of the Space Shuttle Orbiter entry guidance. However, this paper will show that it can be used to fly the first entry in a skip entry trajectory. In doing so, the gains in the error dynamics will be changed at a certain point along the trajectory to improve the tracking performance.

State-dependent anisotrophy: Comparison of quasi-analytical solutions with stochastic results for steady gravity drainage

USGS Publications Warehouse

Green, Timothy R.; Freyberg, David L.

1995-01-01

Anisotropy in large-scale unsaturated hydraulic conductivity of layered soils changes with the moisture state. Here, state-dependent anisotropy is computed under conditions of large-scale gravity drainage. Soils represented by Gardner's exponential function are perfectly stratified, periodic, and inclined. Analytical integration of Darcy’s law across each layer results in a system of nonlinear equations that is solved iteratively for capillary suction at layer interfaces and for the Darcy flux normal to layering. Computed fluxes and suction profiles are used to determine both upscaled hydraulic conductivity in the principal directions and the corresponding “state-dependent” anisotropy ratio as functions of the mean suction. Three groups of layered soils are analyzed and compared with independent predictions from the stochastic results of Yeh et al. (1985b). The small-perturbation approach predicts appropriate behaviors for anisotropy under nonarid conditions. However, the stochastic results are limited to moderate values of mean suction; this limitation is linked to a Taylor series approximation in terms of a group of statistical and geometric parameters. Two alternative forms of the Taylor series provide upper and lower bounds for the state-dependent anisotropy of relatively dry soils.

Gaussian Process Regression (GPR) Representation in Predictive Model Markup Language (PMML)

PubMed Central

Lechevalier, D.; Ak, R.; Ferguson, M.; Law, K. H.; Lee, Y.-T. T.; Rachuri, S.

2017-01-01

This paper describes Gaussian process regression (GPR) models presented in predictive model markup language (PMML). PMML is an extensible-markup-language (XML) -based standard language used to represent data-mining and predictive analytic models, as well as pre- and post-processed data. The previous PMML version, PMML 4.2, did not provide capabilities for representing probabilistic (stochastic) machine-learning algorithms that are widely used for constructing predictive models taking the associated uncertainties into consideration. The newly released PMML version 4.3, which includes the GPR model, provides new features: confidence bounds and distribution for the predictive estimations. Both features are needed to establish the foundation for uncertainty quantification analysis. Among various probabilistic machine-learning algorithms, GPR has been widely used for approximating a target function because of its capability of representing complex input and output relationships without predefining a set of basis functions, and predicting a target output with uncertainty quantification. GPR is being employed to various manufacturing data-analytics applications, which necessitates representing this model in a standardized form for easy and rapid employment. In this paper, we present a GPR model and its representation in PMML. Furthermore, we demonstrate a prototype using a real data set in the manufacturing domain. PMID:29202125

Gaussian Process Regression (GPR) Representation in Predictive Model Markup Language (PMML).

PubMed

Park, J; Lechevalier, D; Ak, R; Ferguson, M; Law, K H; Lee, Y-T T; Rachuri, S

2017-01-01

This paper describes Gaussian process regression (GPR) models presented in predictive model markup language (PMML). PMML is an extensible-markup-language (XML) -based standard language used to represent data-mining and predictive analytic models, as well as pre- and post-processed data. The previous PMML version, PMML 4.2, did not provide capabilities for representing probabilistic (stochastic) machine-learning algorithms that are widely used for constructing predictive models taking the associated uncertainties into consideration. The newly released PMML version 4.3, which includes the GPR model, provides new features: confidence bounds and distribution for the predictive estimations. Both features are needed to establish the foundation for uncertainty quantification analysis. Among various probabilistic machine-learning algorithms, GPR has been widely used for approximating a target function because of its capability of representing complex input and output relationships without predefining a set of basis functions, and predicting a target output with uncertainty quantification. GPR is being employed to various manufacturing data-analytics applications, which necessitates representing this model in a standardized form for easy and rapid employment. In this paper, we present a GPR model and its representation in PMML. Furthermore, we demonstrate a prototype using a real data set in the manufacturing domain.

Analytical Solution for Optimum Design of Furrow Irrigation Systems

NASA Astrophysics Data System (ADS)

Kiwan, M. E.

1996-05-01

An analytical solution for the optimum design of furrow irrigation systems is derived. The non-linear calculus optimization method is used to formulate a general form for designing the optimum system elements under circumstances of maximizing the water application efficiency of the system during irrigation. Different system bases and constraints are considered in the solution. A full irrigation water depth is considered to be achieved at the tail of the furrow line. The solution is based on neglecting the recession and depletion times after off-irrigation. This assumption is valid in the case of open-end (free gradient) furrow systems rather than closed-end (closed dike) systems. Illustrative examples for different systems are presented and the results are compared with the output obtained using an iterative numerical solution method. The final derived solution is expressed as a function of the furrow length ratio (the furrow length to the water travelling distance). The function of water travelling developed by Reddy et al. is considered for reaching the optimum solution. As practical results from the study, the optimum furrow elements for free gradient systems can be estimated to achieve the maximum application efficiency, i.e. furrow length, water inflow rate and cutoff irrigation time.

A classifier neural network for rotordynamic systems

NASA Astrophysics Data System (ADS)

Ganesan, R.; Jionghua, Jin; Sankar, T. S.

1995-07-01

A feedforward backpropagation neural network is formed to identify the stability characteristic of a high speed rotordynamic system. The principal focus resides in accounting for the instability due to the bearing clearance effects. The abnormal operating condition of 'normal-loose' Coulomb rub, that arises in units supported by hydrodynamic bearings or rolling element bearings, is analysed in detail. The multiple-parameter stability problem is formulated and converted to a set of three-parameter algebraic inequality equations. These three parameters map the wider range of physical parameters of commonly-used rotordynamic systems into a narrow closed region, that is used in the supervised learning of the neural network. A binary-type state of the system is expressed through these inequalities that are deduced from the analytical simulation of the rotor system. Both the hidden layer as well as functional-link networks are formed and the superiority of the functional-link network is established. Considering the real time interpretation and control of the rotordynamic system, the network reliability and the learning time are used as the evaluation criteria to assess the superiority of the functional-link network. This functional-link network is further trained using the parameter values of selected rotor systems, and the classifier network is formed. The success rate of stability status identification is obtained to assess the potentials of this classifier network. The classifier network is shown that it can also be used, for control purposes, as an 'advisory' system that suggests the optimum way of parameter adjustment.

Focused analyte spray emission apparatus and process for mass spectrometric analysis

DOEpatents

Roach, Patrick J [Kennewick, WA; Laskin, Julia [Richland, WA; Laskin, Alexander [Richland, WA

2012-01-17

An apparatus and process are disclosed that deliver an analyte deposited on a substrate to a mass spectrometer that provides for trace analysis of complex organic analytes. Analytes are probed using a small droplet of solvent that is formed at the junction between two capillaries. A supply capillary maintains the droplet of solvent on the substrate; a collection capillary collects analyte desorbed from the surface and emits analyte ions as a focused spray to the inlet of a mass spectrometer for analysis. The invention enables efficient separation of desorption and ionization events, providing enhanced control over transport and ionization of the analyte.

Superfund CLP National Functional Guidelines for Data Review

EPA Pesticide Factsheets

A collection of all the national functional guidelines for data review written and maintained by EPA OSWER OSRTI's Analytical Services Branch (ASB). Used for review of analytical data generated using CLP SOWs.

Analytical mass formula and nuclear surface properties in the ETF approximation. Part I: symmetric nuclei

NASA Astrophysics Data System (ADS)

Aymard, François; Gulminelli, Francesca; Margueron, Jérôme

2016-08-01

The problem of determination of nuclear surface energy is addressed within the framework of the extended Thomas Fermi (ETF) approximation using Skyrme functionals. We propose an analytical model for the density profiles with variationally determined diffuseness parameters. In this first paper, we consider the case of symmetric nuclei. In this situation, the ETF functional can be exactly integrated, leading to an analytical formula expressing the surface energy as a function of the couplings of the energy functional. The importance of non-local terms is stressed and it is shown that they cannot be deduced simply from the local part of the functional, as it was suggested in previous works.

Cylindrical optical resonators: fundamental properties and bio-sensing characteristics

NASA Astrophysics Data System (ADS)

Khozeymeh, Foroogh; Razaghi, Mohammad

2018-04-01

In this paper, detailed theoretical analysis of cylindrical resonators is demonstrated. As illustrated, these kinds of resonators can be used as optical bio-sensing devices. The proposed structure is analyzed using an analytical method based on Lam's approximation. This method is systematic and has simplified the tedious process of whispering-gallery mode (WGM) wavelength analysis in optical cylindrical biosensors. By this method, analysis of higher radial orders of high angular momentum WGMs has been possible. Using closed-form analytical equations, resonance wavelengths of higher radial and angular order WGMs of TE and TM polarization waves are calculated. It is shown that high angular momentum WGMs are more appropriate for bio-sensing applications. Some of the calculations are done using a numerical non-linear Newton method. A perfect match of 99.84% between the analytical and the numerical methods has been achieved. In order to verify the validity of the calculations, Meep simulations based on the finite difference time domain (FDTD) method are performed. In this case, a match of 96.70% between the analytical and FDTD results has been obtained. The analytical predictions are in good agreement with other experimental work (99.99% match). These results validate the proposed analytical modelling for the fast design of optical cylindrical biosensors. It is shown that by extending the proposed two-layer resonator structure analyzing scheme, it is possible to study a three-layer cylindrical resonator structure as well. Moreover, by this method, fast sensitivity optimization in cylindrical resonator-based biosensors has been possible. Sensitivity of the WGM resonances is analyzed as a function of the structural parameters of the cylindrical resonators. Based on the results, fourth radial order WGMs, with a resonator radius of 50 μm, display the most bulk refractive index sensitivity of 41.50 (nm/RIU).

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

PubMed

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

2007-06-14

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

Mechanical and Metallurgical Evolution of Stainless Steel 321 in a Multi-step Forming Process

NASA Astrophysics Data System (ADS)

Anderson, M.; Bridier, F.; Gholipour, J.; Jahazi, M.; Wanjara, P.; Bocher, P.; Savoie, J.

2016-04-01

This paper examines the metallurgical evolution of AISI Stainless Steel 321 (SS 321) during multi-step forming, a process that involves cycles of deformation with intermediate heat treatment steps. The multi-step forming process was simulated by implementing interrupted uniaxial tensile testing experiments. Evolution of the mechanical properties as well as the microstructural features, such as twins and textures of the austenite and martensite phases, was studied as a function of the multi-step forming process. The characteristics of the Strain-Induced Martensite (SIM) were also documented for each deformation step and intermediate stress relief heat treatment. The results indicated that the intermediate heat treatments considerably increased the formability of SS 321. Texture analysis showed that the effect of the intermediate heat treatment on the austenite was minor and led to partial recrystallization, while deformation was observed to reinforce the crystallographic texture of austenite. For the SIM, an Olson-Cohen equation type was identified to analytically predict its formation during the multi-step forming process. The generated SIM was textured and weakened with increasing deformation.

Using Multicriteria Analysis in Issues Concerning Adaptation of Historic Facilities for the Needs of Public Utility Buildings with a Function of a Theatre

NASA Astrophysics Data System (ADS)

Obracaj, Piotr; Fabianowski, Dariusz

2017-10-01

Implementations concerning adaptation of historic facilities for public utility objects are associated with the necessity of solving many complex, often conflicting expectations of future users. This mainly concerns the function that includes construction, technology and aesthetic issues. The list of issues is completed with proper protection of historic values, different in each case. The procedure leading to obtaining the expected solution is a multicriteria procedure, usually difficult to accurately define and requiring designer’s large experience. An innovative approach has been used for the analysis, namely - the modified EA FAHP (Extent Analysis Fuzzy Analytic Hierarchy Process) Chang’s method of a multicriteria analysis for the assessment of complex functional and spatial issues. Selection of optimal spatial form of an adapted historic building intended for the multi-functional public utility facility was analysed. The assumed functional flexibility was determined in the scope of: education, conference, and chamber spectacles, such as drama, concerts, in different stage-audience layouts.

Tiopronin Gold Nanoparticle Precursor Forms Aurophilic Ring Tetramer

PubMed Central

Simpson, Carrie A.; Farrow, Christopher L.; Tian, Peng; Billinge, Simon J.L.; Huffman, Brian J.; Harkness, Kellen M.; Cliffel, David E.

2010-01-01

In the two step synthesis of thiolate-monolayer protected clusters (MPCs), the first step of the reaction is a mild reduction of gold(III) by thiols that generates gold(I) thiolate complexes as intermediates. Using tiopronin (Tio) as the thiol reductant, the characterization of the intermediate Au4Tio4 complex was accomplished with various analytical and structural techniques. Nuclear magnetic resonance (NMR), elemental analysis, thermogravimetric analysis (TGA), and matrix-assisted laser desorption/ionization-mass spectrometry (MALDI-MS) were all consistent with a cyclic gold(I)-thiol tetramer structure, and final structural analysis was gathered through the use of powder diffraction and pair distribution functions (PDF). Crystallographic data has proved challenging for almost all previous gold(I)-thiolate complexes. Herein, a novel characterization technique when combined with standard analytical assessment to elucidate structure without crystallographic data proved invaluable to the study of these complexes. This in conjunction with other analytical techniques, in particular mass spectrometry, can elucidate a structure when crystallographic data is unavailable. In addition, luminescent properties provided evidence of aurophilicity within the molecule. The concept of aurophilicity has been introduced to describe a select group of gold-thiolate structures, which possess unique characteristics, mainly red photoluminescence and a distinct Au-Au intramolecular distance indicating a weak metal-metal bond as also evidenced by the structural model of the tetramer. Significant features of both the tetrameric and aurophilic properties of the intermediate gold(I) tiopronin complex are retained after borohydride reduction to form the MPC, including gold(I) tiopronin partial rings as capping motifs, or “staples”, and weak red photoluminescence that extends into the Near Infrared region. PMID:21067183

Application of the Life Cycle Analysis and the Building Information Modelling Software in the Architectural Climate Change-Oriented Design Process

NASA Astrophysics Data System (ADS)

Gradziński, Piotr

2017-10-01

Whereas World’s climate is changing (inter alia, under the influence of architecture activity), the author attempts to reorientations design practice primarily in a direction the use and adapt to the climatic conditions. Architectural Design using in early stages of the architectural Design Process of the building, among other Life Cycle Analysis (LCA) and digital analytical tools BIM (Building Information Modelling) defines the overriding requirements which the designer/architect should meet. The first part, the text characterized the architecture activity influences (by consumption, pollution, waste, etc.) and the use of building materials (embodied energy, embodied carbon, Global Warming Potential, etc.) within the meaning of the direct negative environmental impact. The second part, the paper presents the revision of the methods and analytical techniques prevent negative influences. Firstly, showing the study of the building by using the Life Cycle Analysis of the structure (e.g. materials) and functioning (e.g. energy consumptions) of the architectural object (stages: before use, use, after use). Secondly, the use of digital analytical tools for determining the benefits of running multi-faceted simulations in terms of environmental factors (exposure to light, shade, wind) directly affecting shaping the form of the building. The conclusion, author’s research results highlight the fact that indicates the possibility of building design using the above-mentioned elements (LCA, BIM) causes correction, early designs decisions in the design process of architectural form, minimizing the impact on nature, environment. The work refers directly to the architectural-environmental dimensions, orienting the design process of buildings in respect of widely comprehended climatic changes.

Semi-Analytic Galaxies - I. Synthesis of environmental and star-forming regulation mechanisms

NASA Astrophysics Data System (ADS)

Cora, Sofía A.; Vega-Martínez, Cristian A.; Hough, Tomás; Ruiz, Andrés N.; Orsi, Álvaro; Muñoz Arancibia, Alejandra M.; Gargiulo, Ignacio D.; Collacchioni, Florencia; Padilla, Nelson D.; Gottlöber, Stefan; Yepes, Gustavo

2018-05-01

We present results from the semi-analytic model of galaxy formation SAG applied on the MULTIDARK simulation MDPL2. SAG features an updated supernova (SN) feedback scheme and a robust modelling of the environmental effects on satellite galaxies. This incorporates a gradual starvation of the hot gas halo driven by the action of ram pressure stripping (RPS), that can affect the cold gas disc, and tidal stripping (TS), which can act on all baryonic components. Galaxy orbits of orphan satellites are integrated providing adequate positions and velocities for the estimation of RPS and TS. The star formation history and stellar mass assembly of galaxies are sensitive to the redshift dependence implemented in the SN feedback model. We discuss a variant of our model that allows to reconcile the predicted star formation rate density at z ≳ 3 with the observed one, at the expense of an excess in the faint end of the stellar mass function at z = 2. The fractions of passive galaxies as a function of stellar mass, halo mass and the halo-centric distances are consistent with observational measurements. The model also reproduces the evolution of the main sequence of star forming central and satellite galaxies. The similarity between them is a result of the gradual starvation of the hot gas halo suffered by satellites, in which RPS plays a dominant role. RPS of the cold gas does not affect the fraction of quenched satellites but it contributes to reach the right atomic hydrogen gas content for more massive satellites (M⋆ ≳ 1010 M⊙).

Boron-doped diamond electrode: synthesis, characterization, functionalization and analytical applications.

PubMed

Luong, John H T; Male, Keith B; Glennon, Jeremy D

2009-10-01

In recent years, conductive diamond electrodes for electrochemical applications have been a major focus of research and development. The impetus behind such endeavors could be attributed to their wide potential window, low background current, chemical inertness, and mechanical durability. Several analytes can be oxidized by conducting diamond compared to other carbon-based materials before the breakdown of water in aqueous electrolytes. This is important for detecting and/or identifying species in solution since oxygen and hydrogen evolution do not interfere with the analysis. Thus, conductive diamond electrodes take electrochemical detection into new areas and extend their usefulness to analytes which are not feasible with conventional electrode materials. Different types of diamond electrodes, polycrystalline, microcrystalline, nanocrystalline and ultrananocrystalline, have been synthesized and characterized. Of particular interest is the synthesis of boron-doped diamond (BDD) films by chemical vapor deposition on various substrates. In the tetrahedral diamond lattice, each carbon atom is covalently bonded to its neighbors forming an extremely robust crystalline structure. Some carbon atoms in the lattice are substituted with boron to provide electrical conductivity. Modification strategies of doped diamond electrodes with metallic nanoparticles and/or electropolymerized films are of importance to impart novel characteristics or to improve the performance of diamond electrodes. Biofunctionalization of diamond films is also feasible to foster several useful bioanalytical applications. A plethora of opportunities for nanoscale analytical devices based on conducting diamond is anticipated in the very near future.