Analytical approximations for spatial stochastic gene expression in single cells and tissues

PubMed Central

Smith, Stephen; Cianci, Claudia; Grima, Ramon

2016-01-01

Gene expression occurs in an environment in which both stochastic and diffusive effects are significant. Spatial stochastic simulations are computationally expensive compared with their deterministic counterparts, and hence little is currently known of the significance of intrinsic noise in a spatial setting. Starting from the reaction–diffusion master equation (RDME) describing stochastic reaction–diffusion processes, we here derive expressions for the approximate steady-state mean concentrations which are explicit functions of the dimensionality of space, rate constants and diffusion coefficients. The expressions have a simple closed form when the system consists of one effective species. These formulae show that, even for spatially homogeneous systems, mean concentrations can depend on diffusion coefficients: this contradicts the predictions of deterministic reaction–diffusion processes, thus highlighting the importance of intrinsic noise. We confirm our theory by comparison with stochastic simulations, using the RDME and Brownian dynamics, of two models of stochastic and spatial gene expression in single cells and tissues. PMID:27146686

Estimation and Simulation of Slow Crack Growth Parameters from Constant Stress Rate Data

NASA Technical Reports Server (NTRS)

Salem, Jonathan A.; Weaver, Aaron S.

2003-01-01

Closed form, approximate functions for estimating the variances and degrees-of-freedom associated with the slow crack growth parameters n, D, B, and A(sup *) as measured using constant stress rate ('dynamic fatigue') testing were derived by using propagation of errors. Estimates made with the resulting functions and slow crack growth data for a sapphire window were compared to the results of Monte Carlo simulations. The functions for estimation of the variances of the parameters were derived both with and without logarithmic transformation of the initial slow crack growth equations. The transformation was performed to make the functions both more linear and more normal. Comparison of the Monte Carlo results and the closed form expressions derived with propagation of errors indicated that linearization is not required for good estimates of the variances of parameters n and D by the propagation of errors method. However, good estimates variances of the parameters B and A(sup *) could only be made when the starting slow crack growth equation was transformed and the coefficients of variation of the input parameters were not too large. This was partially a result of the skewered distributions of B and A(sup *). Parametric variation of the input parameters was used to determine an acceptable range for using closed form approximate equations derived from propagation of errors.

Elastic model for crimped collagen fibrils

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Doehring, Todd C.

2005-01-01

A physiologic constitutive expression is presented in algorithmic format for the nonlinear elastic response of wavy collagen fibrils found in soft connective tissues. The model is based on the observation that crimped fibrils in a fascicle have a three-dimensional structure at the micron scale that we approximate as a helical spring. The symmetry of this wave form allows the force/displacement relationship derived from Castigliano's theorem to be solved in closed form: all integrals become analytic. Model predictions are in good agreement with experimental observations for mitral-valve chordae tendinece.

The passage of an infinite swept airfoil through an oblique gust. [approximate solution for aerodynamic response

NASA Technical Reports Server (NTRS)

Adamczyk, J. L.

1974-01-01

An approximate solution is reported for the unsteady aerodynamic response of an infinite swept wing encountering a vertical oblique gust in a compressible stream. The approximate expressions are of closed form and do not require excessive computer storage or computation time, and further, they are in good agreement with the results of exact theory. This analysis is used to predict the unsteady aerodynamic response of a helicopter rotor blade encountering the trailing vortex from a previous blade. Significant effects of three dimensionality and compressibility are evident in the results obtained. In addition, an approximate solution for the unsteady aerodynamic forces associated with the pitching or plunging motion of a two dimensional airfoil in a subsonic stream is presented. The mathematical form of this solution approaches the incompressible solution as the Mach number vanishes, the linear transonic solution as the Mach number approaches one, and the solution predicted by piston theory as the reduced frequency becomes large.

Flapping response characteristics of hingeless rotor blades by a gereralized harmonic balance method

NASA Technical Reports Server (NTRS)

Peters, D. A.; Ormiston, R. A.

1975-01-01

Linearized equations of motion for the flapping response of flexible rotor blades in forward flight are derived in terms of generalized coordinates. The equations are solved using a matrix form of the method of linear harmonic balance, yielding response derivatives for each harmonic of the blade deformations and of the hub forces and moments. Numerical results and approximate closed-form expressions for rotor derivatives are used to illustrate the relationships between rotor parameters, modeling assumptions, and rotor response characteristics. Finally, basic hingeless rotor response derivatives are presented in tabular and graphical form for a wide range of configuration parameters and operating conditions.

The natural frequencies of symmetric angle-ply laminates derived from eigensensitivity analysis

NASA Technical Reports Server (NTRS)

Reiss, Robert; Ramachandran, S.; Qian, BO

1988-01-01

In this paper, a new closed-form approximate solution for the natural frequencies of symmetric rectangular angle-ply laminates simply supported on all four edges is derived. The solution, obtained from eigensensitivity analysis, is expressed as a truncated Fourier series in the ply angle. Results show that the prediction for the fundamental frequency is quite accurate for engineering applications, often within 1-2 percent of the true frequency.

Thin airfoil theory based on approximate solution of the transonic flow equation

NASA Technical Reports Server (NTRS)

Spreiter, John R; Alksne, Alberta Y

1957-01-01

A method is presented for the approximate solution of the nonlinear equations transonic flow theory. Solutions are found for two-dimensional flows at a Mach number of 1 and for purely subsonic and purely supersonic flows. Results are obtained in closed analytic form for a large and significant class of nonlifting airfoils. At a Mach number of 1 general expressions are given for the pressure distribution on an airfoil of specified geometry and for the shape of an airfoil having a prescribed pressure distribution. Extensive comparisons are made with available data, particularly for a Mach number of 1, and with existing solutions.

An accurate analytic description of neutrino oscillations in matter

NASA Astrophysics Data System (ADS)

Akhmedov, E. Kh.; Niro, Viviana

2008-12-01

A simple closed-form analytic expression for the probability of two-flavour neutrino oscillations in a matter with an arbitrary density profile is derived. Our formula is based on a perturbative expansion and allows an easy calculation of higher order corrections. The expansion parameter is small when the density changes relatively slowly along the neutrino path and/or neutrino energy is not very close to the Mikheyev-Smirnov-Wolfenstein (MSW) resonance energy. Our approximation is not equivalent to the adiabatic approximation and actually goes beyond it. We demonstrate the validity of our results using a few model density profiles, including the PREM density profile of the Earth. It is shown that by combining the results obtained from the expansions valid below and above the MSW resonance one can obtain a very good description of neutrino oscillations in matter in the entire energy range, including the resonance region.

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

Closed form expressions for ABER and capacity over EGK fading channel in presence of CCI

NASA Astrophysics Data System (ADS)

Singh, S. Pratap; Kumar, Sanjay

2017-03-01

Goal of next generation wireless communication system is to achieve very high data rate. Femto-cell is one of the possibilities to achieve the above target. However, co-channel interference (CCI) is the important concern in femto-cell. This paper presents closed form expressions for average bit error rate (ABER) and capacity for different adaptive schemes under extended generalised-K (EGK) fading channel in the presence of CCI. A novel conditional unified expression (CUE) is derived, which results different conditional error probability and normalised average capacity. Using CUE, a generic expression for ABER is obtained. In addition, closed form expressions for ABER for different modulation schemes under EGK fading channel in presence of CCI are also derived. Further, it is shown that generic ABER expression results into ABER of different modulation schemes. Besides, the closed form expressions of capacity for different adaptive schemes under EGK in presence of CCI are derived. Finally, analytical and simulated results are obtained with excellent agreement.

Natural occupation numbers in two-electron quantum rings.

PubMed

Tognetti, Vincent; Loos, Pierre-François

2016-02-07

Natural orbitals (NOs) are central constituents for evaluating correlation energies through efficient approximations. Here, we report the closed-form expression of the NOs of two-electron quantum rings, which are prototypical finite-extension systems and new starting points for the development of exchange-correlation functionals in density functional theory. We also show that the natural occupation numbers for these two-electron paradigms are in general non-vanishing and follow the same power law decay as atomic and molecular two-electron systems.

Elastic Response of Crimped Collagen Fibrils

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Doehring, Todd C.

2005-01-01

A physiologic constitutive expression is presented in algorithmic format for the elastic response of wavy collagen fibrils found in soft connective tissues. The model is based on the observation that crimped fibrils have a three-dimensional structure at the micrometer scale that we approximate as a helical spring. The symmetry of this waveform allows the force/displacement relationship derived from Castigliano's theorem to be solved in closed form. Model predictions are in good agreement with experimental observations for mitral-valve chordae tendineae

Franck-Condon factor formulae for astrophysical and other molecules

NASA Technical Reports Server (NTRS)

Nicholls, R. W.

1981-01-01

Simple closed-form, approximate, analytic expressions for Franck-Condon factors are given. They provide reliable estimates for Franck-Condon factor arrays for molecular band systems for which only vibrational-frequency, equilibrium internuclear separation and reduced mass values are known, as is often the case for astrophysically interesting molecules such as CeO, CoH, CrH, CrO, CuH, GeH, LaO, NiH, SnH, and ZnH for band systems of which Franck-Condon arrays have been calculated.

Natural occupation numbers in two-electron quantum rings

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

Tognetti, Vincent, E-mail: vincent.tognetti@univ-rouen.fr; Loos, Pierre-François

2016-02-07

Natural orbitals (NOs) are central constituents for evaluating correlation energies through efficient approximations. Here, we report the closed-form expression of the NOs of two-electron quantum rings, which are prototypical finite-extension systems and new starting points for the development of exchange-correlation functionals in density functional theory. We also show that the natural occupation numbers for these two-electron paradigms are in general non-vanishing and follow the same power law decay as atomic and molecular two-electron systems.

Transfer matrix method for four-flux radiative transfer.

PubMed

Slovick, Brian; Flom, Zachary; Zipp, Lucas; Krishnamurthy, Srini

2017-07-20

We develop a transfer matrix method for four-flux radiative transfer, which is ideally suited for studying transport through multiple scattering layers. The model predicts the specular and diffuse reflection and transmission of multilayer composite films, including interface reflections, for diffuse or collimated incidence. For spherical particles in the diffusion approximation, we derive closed-form expressions for the matrix coefficients and show remarkable agreement with numerical Monte Carlo simulations for a range of absorption values and film thicknesses, and for an example multilayer slab.

First and second order approximations to stage numbers in multicomponent enrichment cascades

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

Scopatz, A.

2013-07-01

This paper describes closed form, Taylor series approximations to the number product stages in a multicomponent enrichment cascade. Such closed form approximations are required when a symbolic, rather than a numeric, algorithm is used to compute the optimal cascade state. Both first and second order approximations were implemented. The first order solution was found to be grossly incorrect, having the wrong functional form over the entire domain. On the other hand, the second order solution shows excellent agreement with the 'true' solution over the domain of interest. An implementation of the symbolic, second order solver is available in the freemore » and open source PyNE library. (authors)« less

Channel correlation and BER performance analysis of coherent optical communication systems with receive diversity over moderate-to-strong non-Kolmogorov turbulence.

PubMed

Fu, Yulong; Ma, Jing; Tan, Liying; Yu, Siyuan; Lu, Gaoyuan

2018-04-10

In this paper, new expressions of the channel-correlation coefficient and its components (the large- and small-scale channel-correlation coefficients) for a plane wave are derived for a horizontal link in moderate-to-strong non-Kolmogorov turbulence using a generalized effective atmospheric spectrum which includes finite-turbulence inner and outer scales and high-wave-number "bump". The closed-form expression of the average bit error rate (BER) of the coherent free-space optical communication system is derived using the derived channel-correlation coefficients and an α-μ distribution to approximate the sum of the square root of arbitrarily correlated Gamma-Gamma random variables. Analytical results are provided to investigate the channel correlation and evaluate the average BER performance. The validity of the proposed approximation is illustrated by Monte Carlo simulations. This work will help with further investigation of the fading correlation in spatial diversity systems.

Solution of the mean spherical approximation for polydisperse multi-Yukawa hard-sphere fluid mixture using orthogonal polynomial expansions

NASA Astrophysics Data System (ADS)

Kalyuzhnyi, Yurij V.; Cummings, Peter T.

2006-03-01

The Blum-Høye [J. Stat. Phys. 19 317 (1978)] solution of the mean spherical approximation for a multicomponent multi-Yukawa hard-sphere fluid is extended to a polydisperse multi-Yukawa hard-sphere fluid. Our extension is based on the application of the orthogonal polynomial expansion method of Lado [Phys. Rev. E 54, 4411 (1996)]. Closed form analytical expressions for the structural and thermodynamic properties of the model are presented. They are given in terms of the parameters that follow directly from the solution. By way of illustration the method of solution is applied to describe the thermodynamic properties of the one- and two-Yukawa versions of the model.

Approximate analytical solution for induction heating of solid cylinders

DOE PAGES

Jankowski, Todd Andrew; Pawley, Norma Helen; Gonzales, Lindsey Michal; ...

2015-10-20

An approximate solution to the mathematical model for induction heating of a solid cylinder in a cylindrical induction coil is presented here. The coupled multiphysics model includes equations describing the electromagnetic field in the heated object, a heat transfer simulation to determine temperature of the heated object, and an AC circuit simulation of the induction heating power supply. A multiple-scale perturbation method is used to solve the multiphysics model. The approximate analytical solution yields simple closed-form expressions for the electromagnetic field and heat generation rate in the solid cylinder, for the equivalent impedance of the associated tank circuit, and formore » the frequency response of a variable frequency power supply driving the tank circuit. The solution developed here is validated by comparing predicted power supply frequency to both experimental measurements and calculated values from finite element analysis for heating of graphite cylinders in an induction furnace. The simple expressions from the analytical solution clearly show the functional dependence of the power supply frequency on the material properties of the load and the geometrical characteristics of the furnace installation. In conclusion, the expressions developed here provide physical insight into observations made during load signature analysis of induction heating.« less

Application of the probabilistic approximate analysis method to a turbopump blade analysis. [for Space Shuttle Main Engine

NASA Technical Reports Server (NTRS)

Thacker, B. H.; Mcclung, R. C.; Millwater, H. R.

1990-01-01

An eigenvalue analysis of a typical space propulsion system turbopump blade is presented using an approximate probabilistic analysis methodology. The methodology was developed originally to investigate the feasibility of computing probabilistic structural response using closed-form approximate models. This paper extends the methodology to structures for which simple closed-form solutions do not exist. The finite element method will be used for this demonstration, but the concepts apply to any numerical method. The results agree with detailed analysis results and indicate the usefulness of using a probabilistic approximate analysis in determining efficient solution strategies.

Maximum-entropy probability distributions under Lp-norm constraints

NASA Technical Reports Server (NTRS)

Dolinar, S.

1991-01-01

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

Neural-network-based state feedback control of a nonlinear discrete-time system in nonstrict feedback form.

PubMed

Jagannathan, Sarangapani; He, Pingan

2008-12-01

In this paper, a suite of adaptive neural network (NN) controllers is designed to deliver a desired tracking performance for the control of an unknown, second-order, nonlinear discrete-time system expressed in nonstrict feedback form. In the first approach, two feedforward NNs are employed in the controller with tracking error as the feedback variable whereas in the adaptive critic NN architecture, three feedforward NNs are used. In the adaptive critic architecture, two action NNs produce virtual and actual control inputs, respectively, whereas the third critic NN approximates certain strategic utility function and its output is employed for tuning action NN weights in order to attain the near-optimal control action. Both the NN control methods present a well-defined controller design and the noncausal problem in discrete-time backstepping design is avoided via NN approximation. A comparison between the controller methodologies is highlighted. The stability analysis of the closed-loop control schemes is demonstrated. The NN controller schemes do not require an offline learning phase and the NN weights can be initialized at zero or random. Results show that the performance of the proposed controller schemes is highly satisfactory while meeting the closed-loop stability.

An approximate theoretical treatment of ion transfer processes at asymmetric microscopic and nanoscopic liquid-liquid interfaces: Single and double potential pulse techniques

NASA Astrophysics Data System (ADS)

Molina, A.; Laborda, E.; Compton, R. G.

2014-03-01

Simple theory for the electrochemical study of reversible ion transfer processes at micro- and nano-liquid|liquid interfaces supported on a capillary is presented. Closed-form expressions are obtained for the response in normal pulse and differential double pulse voltammetries, which describe adequately the particular behaviour of these systems due to the ‘asymmetric’ ion diffusion inside and outside the capillary. The use of different potential pulse techniques for the determination of the formal potential and diffusion coefficients of the ion is examined. For this, very simple analytical expressions are presented for the half-wave potential in NPV and the peak potential in DDPV.

Exact and Approximate Statistical Inference for Nonlinear Regression and the Estimating Equation Approach.

PubMed

Demidenko, Eugene

2017-09-01

The exact density distribution of the nonlinear least squares estimator in the one-parameter regression model is derived in closed form and expressed through the cumulative distribution function of the standard normal variable. Several proposals to generalize this result are discussed. The exact density is extended to the estimating equation (EE) approach and the nonlinear regression with an arbitrary number of linear parameters and one intrinsically nonlinear parameter. For a very special nonlinear regression model, the derived density coincides with the distribution of the ratio of two normally distributed random variables previously obtained by Fieller (1932), unlike other approximations previously suggested by other authors. Approximations to the density of the EE estimators are discussed in the multivariate case. Numerical complications associated with the nonlinear least squares are illustrated, such as nonexistence and/or multiple solutions, as major factors contributing to poor density approximation. The nonlinear Markov-Gauss theorem is formulated based on the near exact EE density approximation.

Simplified multiple scattering model for radiative transfer in turbid water

NASA Technical Reports Server (NTRS)

Ghovanlou, A. H.; Gupta, G. N.

1978-01-01

Quantitative analytical procedures for relating selected water quality parameters to the characteristics of the backscattered signals, measured by remote sensors, require the solution of the radiative transport equation in turbid media. Presented is an approximate closed form solution of this equation and based on this solution, the remote sensing of sediments is discussed. The results are compared with other standard closed form solutions such as quasi-single scattering approximations.

Precision of Sensitivity in the Design Optimization of Indeterminate Structures

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Pai, Shantaram S.; Hopkins, Dale A.

2006-01-01

Design sensitivity is central to most optimization methods. The analytical sensitivity expression for an indeterminate structural design optimization problem can be factored into a simple determinate term and a complicated indeterminate component. Sensitivity can be approximated by retaining only the determinate term and setting the indeterminate factor to zero. The optimum solution is reached with the approximate sensitivity. The central processing unit (CPU) time to solution is substantially reduced. The benefit that accrues from using the approximate sensitivity is quantified by solving a set of problems in a controlled environment. Each problem is solved twice: first using the closed-form sensitivity expression, then using the approximation. The problem solutions use the CometBoards testbed as the optimization tool with the integrated force method as the analyzer. The modification that may be required, to use the stiffener method as the analysis tool in optimization, is discussed. The design optimization problem of an indeterminate structure contains many dependent constraints because of the implicit relationship between stresses, as well as the relationship between the stresses and displacements. The design optimization process can become problematic because the implicit relationship reduces the rank of the sensitivity matrix. The proposed approximation restores the full rank and enhances the robustness of the design optimization method.

Signatures of nonlinearity in single cell noise-induced oscillations.

PubMed

Thomas, Philipp; Straube, Arthur V; Timmer, Jens; Fleck, Christian; Grima, Ramon

2013-10-21

A class of theoretical models seeks to explain rhythmic single cell data by postulating that they are generated by intrinsic noise in biochemical systems whose deterministic models exhibit only damped oscillations. The main features of such noise-induced oscillations are quantified by the power spectrum which measures the dependence of the oscillatory signal's power with frequency. In this paper we derive an approximate closed-form expression for the power spectrum of any monostable biochemical system close to a Hopf bifurcation, where noise-induced oscillations are most pronounced. Unlike the commonly used linear noise approximation which is valid in the macroscopic limit of large volumes, our theory is valid over a wide range of volumes and hence affords a more suitable description of single cell noise-induced oscillations. Our theory predicts that the spectra have three universal features: (i) a dominant peak at some frequency, (ii) a smaller peak at twice the frequency of the dominant peak and (iii) a peak at zero frequency. Of these, the linear noise approximation predicts only the first feature while the remaining two stem from the combination of intrinsic noise and nonlinearity in the law of mass action. The theoretical expressions are shown to accurately match the power spectra determined from stochastic simulations of mitotic and circadian oscillators. Furthermore it is shown how recently acquired single cell rhythmic fibroblast data displays all the features predicted by our theory and that the experimental spectrum is well described by our theory but not by the conventional linear noise approximation. © 2013 Elsevier Ltd. All rights reserved.

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

State-dependent differential Riccati equation to track control of time-varying systems with state and control nonlinearities.

PubMed

Korayem, M H; Nekoo, S R

2015-07-01

This work studies an optimal control problem using the state-dependent Riccati equation (SDRE) in differential form to track for time-varying systems with state and control nonlinearities. The trajectory tracking structure provides two nonlinear differential equations: the state-dependent differential Riccati equation (SDDRE) and the feed-forward differential equation. The independence of the governing equations and stability of the controller are proven along the trajectory using the Lyapunov approach. Backward integration (BI) is capable of solving the equations as a numerical solution; however, the forward solution methods require the closed-form solution to fulfill the task. A closed-form solution is introduced for SDDRE, but the feed-forward differential equation has not yet been obtained. Different ways of solving the problem are expressed and analyzed. These include BI, closed-form solution with corrective assumption, approximate solution, and forward integration. Application of the tracking problem is investigated to control robotic manipulators possessing rigid or flexible joints. The intention is to release a general program for automatic implementation of an SDDRE controller for any manipulator that obeys the Denavit-Hartenberg (D-H) principle when only D-H parameters are received as input data. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Surface-slip equations for multicomponent nonequilibrium air flow

NASA Technical Reports Server (NTRS)

Gupta, R. N.; Scott, C. D.; Moss, J. N.

1985-01-01

Equations are presented for the surface-slip (or jump) values of species concentration, pressure, velocity, and temperature in the low-Reynolds number, high-altitude flight regime of a space vehicle. The equations are obtained from closed form solutions of the mass, momentum, and energy flux equations using the Chapman-Enskog velocity distribution function. This function represents a solution of the Boltzmann equation in the Navier-Stokes approximation. The analysis, obtained for nonequilibrium multicomponent air flow, includes the finite-rate surface catalytic recombination and changes in the internal energy during reflection from the surface. Expressions for the various slip quantities were obtained in a form which can be employed in flowfield computations. A consistent set of equations is provided for multicomponent, binary, and single species mixtures. Expression is also provided for the finite-rate, species-concentration boundary condition for a multicomponent mixture in absence of slip.

Surface-slip equations for multicomponent, nonequilibrium air flow

NASA Technical Reports Server (NTRS)

Gupta, Roop N.; Scott, Carl D.; Moss, James N.; Goglia, Gene

1985-01-01

Equations are presented for the surface slip (or jump) values of species concentration, pressure, velocity, and temperature in the low-Reynolds-number, high-altitude flight regime of a space vehicle. These are obtained from closed-form solutions of the mass, momentum, and energy flux equations using the Chapman-Enskog velocity distribution function. This function represents a solution of the Boltzmann equation in the Navier-Stokes approximation. The analysis, obtained for nonequilibrium multicomponent air flow, includes the finite-rate surface catalytic recombination and changes in the internal energy during reflection from the surface. Expressions for the various slip quantities have been obtained in a form which can readily be employed in flow-field computations. A consistent set of equations is provided for multicomponent, binary, and single species mixtures. Expression is also provided for the finite-rate species-concentration boundary condition for a multicomponent mixture in absence of slip.

Closed-form expressions for state-to-state charge-transfer differential cross sections in a modified Faddeev three-body approach

NASA Astrophysics Data System (ADS)

Adivi, E. Ghanbari; Brunger, M. J.; Bolorizadeh, M. A.; Campbell, L.

2007-02-01

The second-order Faddeev-Watson-Lovelace approximation in a modified form is applied to charge transfer from hydrogenlike target atoms by a fully stripped energetic projectile ion. The state-to-state, nlm→n'l'm' , partial transition amplitudes are calculated analytically. The method is specifically applied to the collision of protons with hydrogen atoms, where differential cross sections of different transitions are calculated for incident energies of 2.8 and 5.0MeV . It is shown that the Thomas peak is present in all transition cross sections. The partial cross sections are then summed and compared with the available forward-angle experimental data, showing good agreement.

Perturbation solutions of combustion instability problems

NASA Technical Reports Server (NTRS)

Googerdy, A.; Peddieson, J., Jr.; Ventrice, M.

1979-01-01

A method involving approximate modal analysis using the Galerkin method followed by an approximate solution of the resulting modal-amplitude equations by the two-variable perturbation method (method of multiple scales) is applied to two problems of pressure-sensitive nonlinear combustion instability in liquid-fuel rocket motors. One problem exhibits self-coupled instability while the other exhibits mode-coupled instability. In both cases it is possible to carry out the entire linear stability analysis and significant portions of the nonlinear stability analysis in closed form. In the problem of self-coupled instability the nonlinear stability boundary and approximate forms of the limit-cycle amplitudes and growth and decay rates are determined in closed form while the exact limit-cycle amplitudes and growth and decay rates are found numerically. In the problem of mode-coupled instability the limit-cycle amplitudes are found in closed form while the growth and decay rates are found numerically. The behavior of the solutions found by the perturbation method are in agreement with solutions obtained using complex numerical methods.

Realistic Analytical Polyhedral MRI Phantoms

PubMed Central

Ngo, Tri M.; Fung, George S. K.; Han, Shuo; Chen, Min; Prince, Jerry L.; Tsui, Benjamin M. W.; McVeigh, Elliot R.; Herzka, Daniel A.

2015-01-01

Purpose Analytical phantoms have closed form Fourier transform expressions and are used to simulate MRI acquisitions. Existing 3D analytical phantoms are unable to accurately model shapes of biomedical interest. It is demonstrated that polyhedral analytical phantoms have closed form Fourier transform expressions and can accurately represent 3D biomedical shapes. Theory The derivations of the Fourier transform of a polygon and polyhedron are presented. Methods The Fourier transform of a polyhedron was implemented and its accuracy in representing faceted and smooth surfaces was characterized. Realistic anthropomorphic polyhedral brain and torso phantoms were constructed and their use in simulated 3D/2D MRI acquisitions was described. Results Using polyhedra, the Fourier transform of faceted shapes can be computed to within machine precision. Smooth surfaces can be approximated with increasing accuracy by increasing the number of facets in the polyhedron; the additional accumulated numerical imprecision of the Fourier transform of polyhedra with many faces remained small. Simulations of 3D/2D brain and 2D torso cine acquisitions produced realistic reconstructions free of high frequency edge aliasing as compared to equivalent voxelized/rasterized phantoms. Conclusion Analytical polyhedral phantoms are easy to construct and can accurately simulate shapes of biomedical interest. PMID:26479724

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.

On the Probabilistic Deployment of Smart Grid Networks in TV White Space.

PubMed

Cacciapuoti, Angela Sara; Caleffi, Marcello; Paura, Luigi

2016-05-10

To accommodate the rapidly increasing demand for wireless broadband communications in Smart Grid (SG) networks, research efforts are currently ongoing to enable the SG networks to utilize the TV spectrum according to the Cognitive Radio paradigm. To this aim, in this letter, we develop an analytical framework for the optimal deployment of multiple closely-located SG Neighborhood Area Networks (NANs) concurrently using the same TV spectrum. The objective is to derive the optimal values for both the number of NANs and their coverage. More specifically, regarding the number of NANs, we derive the optimal closed-form expression, i.e., the closed-form expression that assures the deployment of the maximum number of NANs in the considered region satisfying a given collision constraint on the transmissions of the NANs. Regarding the NAN coverage, we derive the optimal closed-form expression, i.e., the closed-form expression of the NAN transmission range that assures the maximum coverage of each NAN in the considered region satisfying the given collision constraint. All the theoretical results are derived by adopting a stochastic approach. Finally, numerical results validate the theoretical analysis.

Dispersion in Rectangular Networks: Effective Diffusivity and Large-Deviation Rate Function

NASA Astrophysics Data System (ADS)

Tzella, Alexandra; Vanneste, Jacques

2016-09-01

The dispersion of a diffusive scalar in a fluid flowing through a network has many applications including to biological flows, porous media, water supply, and urban pollution. Motivated by this, we develop a large-deviation theory that predicts the evolution of the concentration of a scalar released in a rectangular network in the limit of large time t ≫1 . This theory provides an approximation for the concentration that remains valid for large distances from the center of mass, specifically for distances up to O (t ) and thus much beyond the O (t1 /2) range where a standard Gaussian approximation holds. A byproduct of the approach is a closed-form expression for the effective diffusivity tensor that governs this Gaussian approximation. Monte Carlo simulations of Brownian particles confirm the large-deviation results and demonstrate their effectiveness in describing the scalar distribution when t is only moderately large.

Closed-Form Evaluation of Mutual Coupling in a Planar Array of Circular Apertures

NASA Technical Reports Server (NTRS)

Bailey, M. C.

1996-01-01

The integral expression for the mutual admittance between circular apertures in a planar array is evaluated in closed form. Very good accuracy is realized when compared with values that were obtained by numerical integration. Utilization of this closed-form expression, for all element pairs that are separated by more than one element spacing, yields extremely accurate results and significantly reduces the computation time that is required to analyze the performance of a large electronically scanning antenna array.

Line-source excited impulsive EM field response of thin plasmonic metal films

NASA Astrophysics Data System (ADS)

Štumpf, Martin; Vandenbosch, Guy A. E.

2013-08-01

In this paper, reflection against and transmission through thin plasmonic metal films, basic building blocks of many plasmonic devices, are analytically investigated directly in the time domain for an impulsive electric and magnetic line-source excitation. The electromagnetic properties of thin metallic films are modeled via the Drude model. The problem is formulated with the help of approximate thin-sheet boundary conditions and the analysis is carried out using the Cagniard-DeHoop technique. Closed-form space-time expressions are found and discussed. The obtained time-domain analytical expressions reveal the existence of the phenomenon of transient oscillatory surface effects along a plasmonic metal thin sheet. Illustrative numerical examples of transmitted/reflected pulsed fields are provided.

Analytical approximations for the collapse of an empty spherical bubble.

PubMed

Obreschkow, D; Bruderer, M; Farhat, M

2012-06-01

The Rayleigh equation 3/2R+RR+pρ(-1)=0 with initial conditions R(0)=R(0), R(0)=0 models the collapse of an empty spherical bubble of radius R(T) in an ideal, infinite liquid with far-field pressure p and density ρ. The solution for r≡R/R(0) as a function of time t≡T/T(c), where R(T(c))≡0, is independent of R(0), p, and ρ. While no closed-form expression for r(t) is known, we find that r(0)(t)=(1-t(2))(2/5) approximates r(t) with an error below 1%. A systematic development in orders of t(2) further yields the 0.001% approximation r(*)(t)=r(0)(t)[1-a(1)Li(2.21)(t(2))], where a(1)≈-0.01832099 is a constant and Li is the polylogarithm. The usefulness of these approximations is demonstrated by comparison to high-precision cavitation data obtained in microgravity.

On the quantum Landau collision operator and electron collisions in dense plasmas

NASA Astrophysics Data System (ADS)

Daligault, Jérôme

2016-03-01

The quantum Landau collision operator, which extends the widely used Landau/Fokker-Planck collision operator to include quantum statistical effects, is discussed. The quantum extension can serve as a reference model for including electron collisions in non-equilibrium dense plasmas, in which the quantum nature of electrons cannot be neglected. In this paper, the properties of the Landau collision operator that have been useful in traditional plasma kinetic theory and plasma transport theory are extended to the quantum case. We outline basic properties in connection with the conservation laws, the H-theorem, and the global and local equilibrium distributions. We discuss the Fokker-Planck form of the operator in terms of three potentials that extend the usual two Rosenbluth potentials. We establish practical closed-form expressions for these potentials under local thermal equilibrium conditions in terms of Fermi-Dirac and Bose-Einstein integrals. We study the properties of linearized quantum Landau operator, and extend two popular approximations used in plasma physics to include collisions in kinetic simulations. We apply the quantum Landau operator to the classic test-particle problem to illustrate the physical effects embodied in the quantum extension. We present useful closed-form expressions for the electron-ion momentum and energy transfer rates. Throughout the paper, similarities and differences between the quantum and classical Landau collision operators are emphasized.

Two-way DF relaying assisted D2D communication: ergodic rate and power allocation

NASA Astrophysics Data System (ADS)

Ni, Yiyang; Wang, Yuxi; Jin, Shi; Wong, Kai-Kit; Zhu, Hongbo

2017-12-01

In this paper, we investigate the ergodic rate for a device-to-device (D2D) communication system aided by a two-way decode-and-forward (DF) relay node. We first derive closed-form expressions for the ergodic rate of the D2D link under asymmetric and symmetric cases, respectively. We subsequently discuss two special scenarios including weak interference case and high signal-to-noise ratio case. Then we derive the tight approximations for each of the considered scenarios. Assuming that each transmitter only has access to its own statistical channel state information (CSI), we further derive closed-form power allocation strategy to improve the system performance according to the analytical results of the ergodic rate. Furthermore, some insights are provided for the power allocation strategy based on the analytical results. The strategies are easy to compute and require to know only the channel statistics. Numerical results show the accuracy of the analysis results under various conditions and test the availability of the power allocation strategy.

Electronic transport across a junction between armchair graphene nanotube and zigzag nanoribbon. Transmission in an armchair nanotube without a zigzag half-line of dimers

NASA Astrophysics Data System (ADS)

Sharma, Basant Lal

2018-05-01

Based on the well known nearest-neighbor tight-binding approximation for graphene, an exact expression for the electronic conductance across a zigzag nanoribbon/armchair nanotube junction is presented for non-interacting electrons. The junction results from the removal of a half-row of zigzag dimers in armchair nanotube, or equivalently by partial rolling of zigzag nanoribbon and insertion of a half-row of zigzag dimers in between. From the former point of view, a discrete form of Dirichlet condition is imposed on a zigzag half-line of dimers assuming the vanishing of wave function outside the physical structure. A closed form expression is provided for the reflection and transmission moduli for the outgoing wave modes for each given electronic wave mode incident from either side of the junction. It is demonstrated that such a contact junction between the nanotube and nanoribbon exhibits negligible backscattering, and the transmission has been found to be nearly ballistic. In contrast to the previously reported studies for partially unzipped carbon nanotubes (CNTs), using the same tight binding model, it is found that due to the "defect" there is certain amount of mixing between the electronic wave modes with even and odd reflection symmetries. But the junction remains a perfect valley filter for CNTs at certain energy ranges. Applications aside from the electronic case, include wave propagation in quasi-one-dimensional honeycomb structures of graphene-like constitution. The paper includes several numerical calculations, analytical derivations, and graphical results, which complement the provision of succinct closed form expressions.

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.

From Lobatto Quadrature to the Euler Constant "e"

ERIC Educational Resources Information Center

Khattri, Sanjay Kumar

2010-01-01

Based on the Lobatto quadrature, we develop several new closed form approximations to the mathematical constant "e." For validating effectiveness of our approximations, a comparison of our results to the existing approximations is also presented. Another objective of our work is to inspire students to formulate other better approximations by using…

CBR anisotropy from primordial gravitational waves in inflationary cosmologies

NASA Astrophysics Data System (ADS)

Allen, Bruce; Koranda, Scott

1994-09-01

We examine stochastic temperature fluctuations of the cosmic background radiation (CBR) arising via the Sachs-Wolfe effect from gravitational wave perturbations produced in the early Universe. These temperature fluctuations are described by an angular correlation function C(γ). A new (more concise and general) derivation of C(γ) is given, and evaluated for inflationary-universe cosmologies. This yields standard results for angles γ greater than a few degrees, but new results for smaller angles, because we do not make standard long-wavelength approximations to the gravitational wave mode functions. The function C(γ) may be expanded in a series of Legendre polynomials; we use numerical methods to compare the coefficients of the resulting expansion in our exact calculation with standard (approximate) results. We also report some progress towards finding a closed form expression for C(γ).

The Galaxy Count Correlation Function in Redshift Space Revisited

NASA Astrophysics Data System (ADS)

Campagne, J.-E.; Plaszczynski, S.; Neveu, J.

2017-08-01

In the near future, cosmology will enter the wide and deep galaxy survey era, enabling high-precision studies of the large-scale structure of the universe in three dimensions. To test cosmological models and determine their parameters accurately, it is necessary to use data with exact theoretical expectations expressed in observational parameter space (angles and redshift). The data-driven, galaxy number count fluctuations on redshift shells can be used to build correlation functions ξ (θ ,{z}1,{z}2) on and between shells to probe the baryonic acoustic oscillations and distance-redshift distortions, as well as gravitational lensing and other relativistic effects. To obtain a numerical estimation of ξ (θ ,{z}1,{z}2) from a cosmological model, it is typical to use either a closed form derived from a tripolar spherical expansion or to compute the power spectrum {C}{\\ell }({z}1,{z}2) and perform a Legendre polynomial {P}{\\ell }(\\cos θ ) expansion. Here, we present a new derivation of a ξ (θ ,{z}1,{z}2) closed form using the spherical harmonic expansion and proceeding to an infinite sum over multipoles thanks to an addition theorem. We demonstrate that this new expression is perfectly compatible with the existing closed forms but is simpler to establish and manipulate. We provide formulas for the leading density and redshift-space contributions, but also show how Doppler-like and lensing terms can be easily included in this formalism. We have implemented and made publicly available software for computing those correlations efficiently, without any Limber approximation, and validated this software with the CLASSgal code. It is available at https://gitlab.in2p3.fr/campagne/AngPow.

A homogenization approach for the effective drained viscoelastic properties of 2D porous media and an application for cortical bone.

PubMed

Nguyen, Sy-Tuan; Vu, Mai-Ba; Vu, Minh-Ngoc; To, Quy-Dong

2018-02-01

Closed-form solutions for the effective rheological properties of a 2D viscoelastic drained porous medium made of a Generalized Maxwell viscoelastic matrix and pore inclusions are developed and applied for cortical bone. The in-plane (transverse) effective viscoelastic bulk and shear moduli of the Generalized Maxwell rheology of the homogenized medium are expressed as functions of the porosity and the viscoelastic properties of the solid phase. When deriving these functions, the classical inverse Laplace-Carson transformation technique is avoided, due to its complexity, by considering the short and long term approximations. The approximated results are validated against exact solutions obtained from the inverse Laplace-Carson transform for a simple configuration when the later is available. An application for cortical bone with assumption of circular pore in the transverse plane shows that the proposed approximation fit very well with experimental data. Copyright © 2017 Elsevier Ltd. All rights reserved.

A simple model for indentation creep

NASA Astrophysics Data System (ADS)

Ginder, Ryan S.; Nix, William D.; Pharr, George M.

2018-03-01

A simple model for indentation creep is developed that allows one to directly convert creep parameters measured in indentation tests to those observed in uniaxial tests through simple closed-form relationships. The model is based on the expansion of a spherical cavity in a power law creeping material modified to account for indentation loading in a manner similar to that developed by Johnson for elastic-plastic indentation (Johnson, 1970). Although only approximate in nature, the simple mathematical form of the new model makes it useful for general estimation purposes or in the development of other deformation models in which a simple closed-form expression for the indentation creep rate is desirable. Comparison to a more rigorous analysis which uses finite element simulation for numerical evaluation shows that the new model predicts uniaxial creep rates within a factor of 2.5, and usually much better than this, for materials creeping with stress exponents in the range 1 ≤ n ≤ 7. The predictive capabilities of the model are evaluated by comparing it to the more rigorous analysis and several sets of experimental data in which both the indentation and uniaxial creep behavior have been measured independently.

Two-dimensional subsonic compressible flow past elliptic cylinders

NASA Technical Reports Server (NTRS)

Kaplan, Carl

1938-01-01

The method of Poggi is used to calculate, for perfect fluids, the effect of compressibility upon the flow on the surface of an elliptic cylinder at zero angle of attack and with no circulation. The result is expressed in a closed form and represents a rigorous determination of the velocity of the fluid at the surface of the obstacle insofar as the second approximation is concerned. Comparison is made with Hooker's treatment of the same problem according to the method of Janzen and Rayleight and it is found that, for thick elliptic cylinders, the two methods agree very well. The labor of computation is considerably reduced by the present solution.

Attosecond polarization control in atomic RABBITT-like experiments assisted by a circularly polarized laser

NASA Astrophysics Data System (ADS)

Boll, D. I. R.; Fojón, O. A.

2017-12-01

We study theoretically the single ionization of noble gas atoms by the combined action of an attosecond pulse train with linear polarization and an assistant laser field with circular polarization. We employ a non-perturbative model that under certain approximations gives closed-form expressions for the angular distributions of photoelectrons. Interestingly, our model allow us to interpret these angular distributions as two-centre interferences where the orientation and the modulus of the separation vector between the virtual emitters is governed by the assistant laser field. Additionally, we show that such a configuration of light fields is similar to the polarization control technique, where both the attosecond pulse train and the assistant laser field have linear polarizations whose relative orientation may be controlled. Moreover, in order to compare our results with the available experimental data, we obtain analytical expressions for the cross sections integrated over the photoelectron emission angles. By means of these expressions, we define the ‘magic time’ as the delay for which the total cross sections for atomic targets exhibit the same functional form as the one of the monochromatic photoionization of diatomic molecular targets.

Random matrix models, double-time Painlevé equations, and wireless relaying

NASA Astrophysics Data System (ADS)

Chen, Yang; Haq, Nazmus S.; McKay, Matthew R.

2013-06-01

This paper gives an in-depth study of a multiple-antenna wireless communication scenario in which a weak signal received at an intermediate relay station is amplified and then forwarded to the final destination. The key quantity determining system performance is the statistical properties of the signal-to-noise ratio (SNR) γ at the destination. Under certain assumptions on the encoding structure, recent work has characterized the SNR distribution through its moment generating function, in terms of a certain Hankel determinant generated via a deformed Laguerre weight. Here, we employ two different methods to describe the Hankel determinant. First, we make use of ladder operators satisfied by orthogonal polynomials to give an exact characterization in terms of a "double-time" Painlevé differential equation, which reduces to Painlevé V under certain limits. Second, we employ Dyson's Coulomb fluid method to derive a closed form approximation for the Hankel determinant. The two characterizations are used to derive closed-form expressions for the cumulants of γ, and to compute performance quantities of engineering interest.

Dysregulation of Ezrin phosphorylation prevents metastasis and alters cellular metabolism in osteosarcoma

PubMed Central

Ren, Ling; Hong, Sung-Hyeok; Chen, Qing-Rong; Briggs, Joseph; Cassavaugh, Jessica; Srinivasan, Satish; Lizardo, Michael M.; Mendoza, Arnulfo; Xia, Ashley Y.; Avadhani, Narayan; Khan, Javed; Khanna, Chand

2013-01-01

Ezrin links the plasma membrane to the actin cytoskeleton where it plays a pivotal role in the metastatic progression of several human cancers (1, 2), however, the precise mechanistic basis for its role remains unknown. Here we define transitions between active (phosphorylated open) and inactive (dephosphorylated closed) forms of Ezrin that occur during metastatic progression in osteosarcoma. In our evaluation of these conformations we expressed C-terminal mutant forms of Ezrin that are open (phosphomimetic T567D) or closed (phosphodeficient T567A) and compared their biological characteristics to full length wild-type Ezrin in osteosarcoma cells. Unexpectedly, cells expressing open, active Ezrin could form neither primary orthotopic tumors nor lung metastases. In contrast, cells expressing closed, inactive Ezrin were also deficient in metastasis but were unaffected in their capacity for primary tumor growth. By imaging single metastatic cells in the lung, we found that cells expressing either open or closed Ezrin displayed increased levels of apoptosis early after their arrival in the lung. Gene expression analysis suggested dysregulation of genes that are functionally linked to carbohydrate and amino acid metabolism. In particular, cells expressing closed, inactive Ezrin exhibited reduced lactate production and basal or ATP-dependent oxygen consumption. Collectively, our results suggest that dynamic regulation of Ezrin phosphorylation at amino acid T567 that controls structural transitions of this protein plays a pivotal role in tumor progression and metastasis, possibly in part by altering cellular metabolism. PMID:22147261

A Spherical Harmonic Analysis of the Ooty Wide Field Array (OWFA) Visibility Signal

NASA Astrophysics Data System (ADS)

Chatterjee, Suman; Bharadwaj, Somnath

2018-04-01

Considering redshifted 21-cm intensity mapping with the upcoming OWFA whose field of view subtends ˜57° in the N-S direction, we present a formalism which relates the measured visibilities to the spherical harmonic coefficients of the sky signal. We use this to calculate window functions which relate the two-visibility correlations i.e. the correlation between the visibilities measured at two baselines and two frequencies, to different multipoles of the multi-frequency angular power spectrum Cℓ(ν1, ν2). The formalism here is validated using simulations. We also present approximate closed form analytical expressions which can be used to calculate the window functions. Comparing the widely adopted flat sky approximation, we find that its predictions match those of our spherical harmonic formalism to within 16% across the entire OWFA baseline range. The match improves at large baselines where we have <5% deviations.

Simplified Antenna Group Determination of RS Overhead Reduced Massive MIMO for Wireless Sensor Networks.

PubMed

Lee, Byung Moo

2017-12-29

Massive multiple-input multiple-output (MIMO) systems can be applied to support numerous internet of things (IoT) devices using its excessive amount of transmitter (TX) antennas. However, one of the big obstacles for the realization of the massive MIMO system is the overhead of reference signal (RS), because the number of RS is proportional to the number of TX antennas and/or related user equipments (UEs). It has been already reported that antenna group-based RS overhead reduction can be very effective to the efficient operation of massive MIMO, but the method of deciding the number of antennas needed in each group is at question. In this paper, we propose a simplified determination scheme of the number of antennas needed in each group for RS overhead reduced massive MIMO to support many IoT devices. Supporting many distributed IoT devices is a framework to configure wireless sensor networks. Our contribution can be divided into two parts. First, we derive simple closed-form approximations of the achievable spectral efficiency (SE) by using zero-forcing (ZF) and matched filtering (MF) precoding for the RS overhead reduced massive MIMO systems with channel estimation error. The closed-form approximations include a channel error factor that can be adjusted according to the method of the channel estimation. Second, based on the closed-form approximation, we present an efficient algorithm determining the number of antennas needed in each group for the group-based RS overhead reduction scheme. The algorithm depends on the exact inverse functions of the derived closed-form approximations of SE. It is verified with theoretical analysis and simulation that the proposed algorithm works well, and thus can be used as an important tool for massive MIMO systems to support many distributed IoT devices.

Simplified Antenna Group Determination of RS Overhead Reduced Massive MIMO for Wireless Sensor Networks

PubMed Central

2017-01-01

Massive multiple-input multiple-output (MIMO) systems can be applied to support numerous internet of things (IoT) devices using its excessive amount of transmitter (TX) antennas. However, one of the big obstacles for the realization of the massive MIMO system is the overhead of reference signal (RS), because the number of RS is proportional to the number of TX antennas and/or related user equipments (UEs). It has been already reported that antenna group-based RS overhead reduction can be very effective to the efficient operation of massive MIMO, but the method of deciding the number of antennas needed in each group is at question. In this paper, we propose a simplified determination scheme of the number of antennas needed in each group for RS overhead reduced massive MIMO to support many IoT devices. Supporting many distributed IoT devices is a framework to configure wireless sensor networks. Our contribution can be divided into two parts. First, we derive simple closed-form approximations of the achievable spectral efficiency (SE) by using zero-forcing (ZF) and matched filtering (MF) precoding for the RS overhead reduced massive MIMO systems with channel estimation error. The closed-form approximations include a channel error factor that can be adjusted according to the method of the channel estimation. Second, based on the closed-form approximation, we present an efficient algorithm determining the number of antennas needed in each group for the group-based RS overhead reduction scheme. The algorithm depends on the exact inverse functions of the derived closed-form approximations of SE. It is verified with theoretical analysis and simulation that the proposed algorithm works well, and thus can be used as an important tool for massive MIMO systems to support many distributed IoT devices. PMID:29286339

On the quantum Landau collision operator and electron collisions in dense plasmas

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

Daligault, Jérôme, E-mail: daligaul@lanl.gov

2016-03-15

The quantum Landau collision operator, which extends the widely used Landau/Fokker-Planck collision operator to include quantum statistical effects, is discussed. The quantum extension can serve as a reference model for including electron collisions in non-equilibrium dense plasmas, in which the quantum nature of electrons cannot be neglected. In this paper, the properties of the Landau collision operator that have been useful in traditional plasma kinetic theory and plasma transport theory are extended to the quantum case. We outline basic properties in connection with the conservation laws, the H-theorem, and the global and local equilibrium distributions. We discuss the Fokker-Planck formmore » of the operator in terms of three potentials that extend the usual two Rosenbluth potentials. We establish practical closed-form expressions for these potentials under local thermal equilibrium conditions in terms of Fermi-Dirac and Bose-Einstein integrals. We study the properties of linearized quantum Landau operator, and extend two popular approximations used in plasma physics to include collisions in kinetic simulations. We apply the quantum Landau operator to the classic test-particle problem to illustrate the physical effects embodied in the quantum extension. We present useful closed-form expressions for the electron-ion momentum and energy transfer rates. Throughout the paper, similarities and differences between the quantum and classical Landau collision operators are emphasized.« less

Analytic saddlepoint approximation for ionization energy loss distributions

DOE PAGES

Sjue, Sky K. L.; George, Jr., Richard Neal; Mathews, David Gregory

2017-07-27

Here, we present a saddlepoint approximation for ionization energy loss distributions, valid for arbitrary relativistic velocities of the incident particle 0 < v/c < 1, provided that ionizing collisions are still the dominant energy loss mechanism. We derive a closed form solution closely related to Moyal’s distribution. This distribution is intended for use in simulations with relatively low computational overhead. The approximation generally reproduces the Vavilov most probable energy loss and full width at half maximum to better than 1% and 10%, respectively, with significantly better agreement as Vavilov’s κ approaches 1.

Analytic saddlepoint approximation for ionization energy loss distributions

NASA Astrophysics Data System (ADS)

Sjue, S. K. L.; George, R. N.; Mathews, D. G.

2017-09-01

We present a saddlepoint approximation for ionization energy loss distributions, valid for arbitrary relativistic velocities of the incident particle 0 < v / c < 1 , provided that ionizing collisions are still the dominant energy loss mechanism. We derive a closed form solution closely related to Moyal's distribution. This distribution is intended for use in simulations with relatively low computational overhead. The approximation generally reproduces the Vavilov most probable energy loss and full width at half maximum to better than 1% and 10%, respectively, with significantly better agreement as Vavilov's κ approaches 1.

Analytic saddlepoint approximation for ionization energy loss distributions

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

Sjue, Sky K. L.; George, Jr., Richard Neal; Mathews, David Gregory

Here, we present a saddlepoint approximation for ionization energy loss distributions, valid for arbitrary relativistic velocities of the incident particle 0 < v/c < 1, provided that ionizing collisions are still the dominant energy loss mechanism. We derive a closed form solution closely related to Moyal’s distribution. This distribution is intended for use in simulations with relatively low computational overhead. The approximation generally reproduces the Vavilov most probable energy loss and full width at half maximum to better than 1% and 10%, respectively, with significantly better agreement as Vavilov’s κ approaches 1.

On computing closed forms for summations. [polynomials and rational functions

NASA Technical Reports Server (NTRS)

Moenck, R.

1977-01-01

The problem of finding closed forms for a summation involving polynomials and rational functions is considered. A method closely related to Hermite's method for integration of rational functions derived. The method expresses the sum of a rational function as a rational function part and a transcendental part involving derivatives of the gamma function.

Analytical expressions for the nonlinear interference in dispersion managed transmission coherent optical systems

NASA Astrophysics Data System (ADS)

Qiao, Yaojun; Li, Ming; Yang, Qiuhong; Xu, Yanfei; Ji, Yuefeng

2015-01-01

Closed-form expressions of nonlinear interference of dense wavelength-division-multiplexed (WDM) systems with dispersion managed transmission (DMT) are derived. We carry out a simulative validation by addressing an ample and significant set of the Nyquist-WDM systems based on polarization multiplexed quadrature phase-shift keying (PM-QPSK) subcarriers at a baud rate of 32 Gbaud per channel. Simulation results show the simple closed-form analytical expressions can provide an effective tool for the quick and accurate prediction of system performance in DMT coherent optical systems.

Is Approximate Number Precision a Stable Predictor of Math Ability?

ERIC Educational Resources Information Center

Libertus, Melissa E.; Feigenson, Lisa; Halberda, Justin

2013-01-01

Previous research shows that children's ability to estimate numbers of items using their Approximate Number System (ANS) predicts later math ability. To more closely examine the predictive role of early ANS acuity on later abilities, we assessed the ANS acuity, math ability, and expressive vocabulary of preschoolers twice, six months apart. We…

The high-frequency dispersion coefficient for the Rayleigh velocity in a vertically inhomogeneous anisotropic half-space.

PubMed

Shuvalov, A L

2008-05-01

For an arbitrary anisotropic half-space with continuous vertical variation of material properties, an explicit closed-form expression for the coefficient B of high-frequency dispersion of the Rayleigh velocity v(R)(omega) approximately v(R)(0)(1+B/omega) is derived. The result involves two matrices, one consisting of the surface-traction derivatives in velocity and the other of its Wentzel-Kramers-Brillouin coefficients, which are contracted with an amplitude vector of the Rayleigh wave in the reference homogeneous half-space. The "ingredients" are routinely defined through the fundamental elasticity matrix and its first derivative, both taken at v=v(R)(0) and referred to the surface.

Many-body formulation of carriers capture time in quantum dots applicable in device simulation codes

NASA Astrophysics Data System (ADS)

Vallone, Marco

2010-03-01

We present an application of Green's functions formalism to calculate in a simplified but rigorous way electrons and holes capture time in quantum dots in closed form as function of carrier density, levels confinement potential, and temperature. Carrier-carrier (Auger) scattering and single LO-phonon emission are both addressed accounting for dynamic effects of the potential screening in the single plasmon pole approximation of the dielectric function. Regarding the LO-phonons interaction, the formulation evidences the role of the dynamic screening from wetting-layer carriers in comparison with its static limit, describes the interplay between screening and Fermi band filling, and offers simple expressions for capture time, suitable for modeling implementation.

Barnacles resist removal by crack trapping

PubMed Central

Hui, Chung-Yuen; Long, Rong; Wahl, Kathryn J.; Everett, Richard K.

2011-01-01

We study the mechanics of pull-off of a barnacle adhering to a thin elastic layer which is bonded to a rigid substrate. We address the case of barnacles having acorn shell geometry and hard, calcarious base plates. Pull-off is initiated by the propagation of an interface edge crack between the base plate and the layer. We compute the energy release rate of this crack as it grows along the interface using a finite element method. We also develop an approximate analytical model to interpret our numerical results and to give a closed-form expression for the energy release rate. Our result shows that the resistance of barnacles to interfacial failure arises from a crack-trapping mechanism. PMID:21208968

SER Analysis of MPPM-Coded MIMO-FSO System over Uncorrelated and Correlated Gamma-Gamma Atmospheric Turbulence Channels

NASA Astrophysics Data System (ADS)

Khallaf, Haitham S.; Garrido-Balsells, José M.; Shalaby, Hossam M. H.; Sampei, Seiichi

2015-12-01

The performance of multiple-input multiple-output free space optical (MIMO-FSO) communication systems, that adopt multipulse pulse position modulation (MPPM) techniques, is analyzed. Both exact and approximate symbol-error rates (SERs) are derived for both cases of uncorrelated and correlated channels. The effects of background noise, receiver shot-noise, and atmospheric turbulence are taken into consideration in our analysis. The random fluctuations of the received optical irradiance, produced by the atmospheric turbulence, is modeled by the widely used gamma-gamma statistical distribution. Uncorrelated MIMO channels are modeled by the α-μ distribution. A closed-form expression for the probability density function of the optical received irradiance is derived for the case of correlated MIMO channels. Using our analytical expressions, the degradation of the system performance with the increment of the correlation coefficients between MIMO channels is corroborated.

An analytical solution for the elastic response to surface loads imposed on a layered, transversely isotropic and self-gravitating Earth

NASA Astrophysics Data System (ADS)

Pan, E.; Chen, J. Y.; Bevis, M.; Bordoni, A.; Barletta, V. R.; Molavi Tabrizi, A.

2015-12-01

We present an analytical solution for the elastic deformation of an elastic, transversely isotropic, layered and self-gravitating Earth by surface loads. We first introduce the vector spherical harmonics to express the physical quantities in the layered Earth. This reduces the governing equations to a linear system of equations for the expansion coefficients. We then solve for the expansion coefficients analytically under the assumption (i.e. approximation) that in the mantle, the density in each layer varies as 1/r (where r is the radial coordinate) while the gravity is constant and that in the core the gravity in each layer varies linearly in r with constant density. These approximations dramatically simplify the subsequent mathematical analysis and render closed-form expressions for the expansion coefficients. We implement our solution in a MATLAB code and perform a benchmark which shows both the correctness of our solution and the implementation. We also calculate the load Love numbers (LLNs) of the PREM Earth for different degrees of the Legendre function for both isotropic and transversely isotropic, layered mantles with different core models, demonstrating for the first time the effect of Earth anisotropy on the LLNs.

Chiral discrimination of the Japanese beetle sex pheromone and a behavioral antagonist by a pheromone-degrading enzyme.

PubMed

Ishida, Yuko; Leal, Walter S

2008-07-01

The sophistication of the insect olfactory system is elegantly demonstrated by the reception of sex pheromone by the Japanese beetle. In this insect, two olfactory receptor neurons housed in antennal sensilla placodea are highly sensitive. One neuron specifically detects the sex pheromone produced by conspecific females (R,Z)-5-(-)-(1-decenyl)oxacyclopentan-2-one [(R)-japonilure]. The other neuron is tuned to (S)-japonilure, a sex pheromone from a closely related species and a behavioral antagonist for the Japanese beetle. These chemical signals are enzymatically terminated by antennal esterases that open the lactone rings to form physiologically inactive hydroxyacids. We have isolated a pheromone-degrading enzyme, PjapPDE, from >100,000 antennae of the Japanese beetle. PjapPDE was demonstrated to be expressed only in the antennal tissues housing the pheromone-detecting sensilla placodea. Baculovirus expression generated recombinant PjapPDE with likely the same posttranslational modifications as the native enzyme. Kinetic studies with pure native and recombinant PjapPDE showed a clear substrate preference, with an estimated half-life in vivo for the sex pheromone and a behavioral antagonist of approximately 30 and approximately 90 ms, respectively.

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.

Comments on "A Closed-Form Solution to Tensor Voting: Theory and Applications".

PubMed

Maggiori, Emmanuel; Lotito, Pablo; Manterola, Hugo Luis; del Fresno, Mariana

2014-12-01

We comment on a paper that describes a closed-form formulation to Tensor Voting, a technique to perceptually group clouds of points, usually applied to infer features in images. The authors proved an analytic solution to the technique, a highly relevant contribution considering that the original formulation required numerical integration, a time-consuming task. Their work constitutes the first closed-form expression for the Tensor Voting framework. In this work we first observe that the proposed formulation leads to unexpected results which do not satisfy the constraints for a Tensor Voting output, hence they cannot be interpreted. Given that the closed-form expression is said to be an analytic equivalent solution, unexpected outputs should not be encountered unless there are flaws in the proof. We analyzed the underlying math to find which were the causes of these unexpected results. In this commentary we show that their proposal does not in fact provide a proper analytic solution to Tensor Voting and we indicate the flaws in the proof.

Trajectory And Heating Of A Hypervelocity Projectile

NASA Technical Reports Server (NTRS)

Tauber, Michael E.

1992-01-01

Technical paper presents derivation of approximate, closed-form equation for relationship between velocity of projectile and density of atmosphere. Results of calculations based on approximate equation agree well with results from numerical integrations of exact equations of motion. Comparisons of results presented in series of graphs.

Closed-form solutions of performability. [in computer systems

NASA Technical Reports Server (NTRS)

Meyer, J. F.

1982-01-01

It is noted that if computing system performance is degradable then system evaluation must deal simultaneously with aspects of both performance and reliability. One approach is the evaluation of a system's performability which, relative to a specified performance variable Y, generally requires solution of the probability distribution function of Y. The feasibility of closed-form solutions of performability when Y is continuous are examined. In particular, the modeling of a degradable buffer/multiprocessor system is considered whose performance Y is the (normalized) average throughput rate realized during a bounded interval of time. Employing an approximate decomposition of the model, it is shown that a closed-form solution can indeed be obtained.

Magnetohydrodynamic motion of a two-fluid plasma

DOE PAGES

Burby, Joshua W.

2017-07-21

Here, the two-fluid Maxwell system couples frictionless electron and ion fluids via Maxwell’s equations. When the frequencies of light waves, Langmuir waves, and single-particle cyclotron motion are scaled to be asymptotically large, the two-fluid Maxwell system becomes a fast-slow dynamical system. This fast-slow system admits a formally-exact single-fluid closure that may be computed systematically with any desired order of accuracy through the use of a functional partial differential equation. In the leading order approximation, the closure reproduces magnetohydrodynamics (MHD). Higher order truncations of the closure give an infinite hierarchy of extended MHD models that allow for arbitrary mass ratio, asmore » well as perturbative deviations from charge neutrality. The closure is interpreted geometrically as an invariant slow manifold in the infinite-dimensional two-fluid phase space, on which two-fluid motions are free of high-frequency oscillations. This perspective shows that the full closure inherits a Hamiltonian structure from two-fluid theory. By employing infinite-dimensional Lie transforms, the Poisson bracket for the all-orders closure may be obtained in closed form. Thus, conservative truncations of the single-fluid closure may be obtained by simply truncating the single-fluid Hamiltonian. Moreover, the closed-form expression for the all-orders bracket gives explicit expressions for a number of the full closure’s conservation laws. Notably, the full closure, as well as any of its Hamiltonian truncations, admits a pair of independent circulation invariants.« less

Magnetohydrodynamic motion of a two-fluid plasma

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

Burby, Joshua W.

Here, the two-fluid Maxwell system couples frictionless electron and ion fluids via Maxwell’s equations. When the frequencies of light waves, Langmuir waves, and single-particle cyclotron motion are scaled to be asymptotically large, the two-fluid Maxwell system becomes a fast-slow dynamical system. This fast-slow system admits a formally-exact single-fluid closure that may be computed systematically with any desired order of accuracy through the use of a functional partial differential equation. In the leading order approximation, the closure reproduces magnetohydrodynamics (MHD). Higher order truncations of the closure give an infinite hierarchy of extended MHD models that allow for arbitrary mass ratio, asmore » well as perturbative deviations from charge neutrality. The closure is interpreted geometrically as an invariant slow manifold in the infinite-dimensional two-fluid phase space, on which two-fluid motions are free of high-frequency oscillations. This perspective shows that the full closure inherits a Hamiltonian structure from two-fluid theory. By employing infinite-dimensional Lie transforms, the Poisson bracket for the all-orders closure may be obtained in closed form. Thus, conservative truncations of the single-fluid closure may be obtained by simply truncating the single-fluid Hamiltonian. Moreover, the closed-form expression for the all-orders bracket gives explicit expressions for a number of the full closure’s conservation laws. Notably, the full closure, as well as any of its Hamiltonian truncations, admits a pair of independent circulation invariants.« less

Optimal Power Allocation Strategy in a Joint Bistatic Radar and Communication System Based on Low Probability of Intercept

PubMed Central

Wang, Fei; Salous, Sana; Zhou, Jianjiang

2017-01-01

In this paper, we investigate a low probability of intercept (LPI)-based optimal power allocation strategy for a joint bistatic radar and communication system, which is composed of a dedicated transmitter, a radar receiver, and a communication receiver. The joint system is capable of fulfilling the requirements of both radar and communications simultaneously. First, assuming that the signal-to-noise ratio (SNR) corresponding to the target surveillance path is much weaker than that corresponding to the line of sight path at radar receiver, the analytically closed-form expression for the probability of false alarm is calculated, whereas the closed-form expression for the probability of detection is not analytically tractable and is approximated due to the fact that the received signals are not zero-mean Gaussian under target presence hypothesis. Then, an LPI-based optimal power allocation strategy is presented to minimize the total transmission power for information signal and radar waveform, which is constrained by a specified information rate for the communication receiver and the desired probabilities of detection and false alarm for the radar receiver. The well-known bisection search method is employed to solve the resulting constrained optimization problem. Finally, numerical simulations are provided to reveal the effects of several system parameters on the power allocation results. It is also demonstrated that the LPI performance of the joint bistatic radar and communication system can be markedly improved by utilizing the proposed scheme. PMID:29186850

Optimal Power Allocation Strategy in a Joint Bistatic Radar and Communication System Based on Low Probability of Intercept.

PubMed

Shi, Chenguang; Wang, Fei; Salous, Sana; Zhou, Jianjiang

2017-11-25

In this paper, we investigate a low probability of intercept (LPI)-based optimal power allocation strategy for a joint bistatic radar and communication system, which is composed of a dedicated transmitter, a radar receiver, and a communication receiver. The joint system is capable of fulfilling the requirements of both radar and communications simultaneously. First, assuming that the signal-to-noise ratio (SNR) corresponding to the target surveillance path is much weaker than that corresponding to the line of sight path at radar receiver, the analytically closed-form expression for the probability of false alarm is calculated, whereas the closed-form expression for the probability of detection is not analytically tractable and is approximated due to the fact that the received signals are not zero-mean Gaussian under target presence hypothesis. Then, an LPI-based optimal power allocation strategy is presented to minimize the total transmission power for information signal and radar waveform, which is constrained by a specified information rate for the communication receiver and the desired probabilities of detection and false alarm for the radar receiver. The well-known bisection search method is employed to solve the resulting constrained optimization problem. Finally, numerical simulations are provided to reveal the effects of several system parameters on the power allocation results. It is also demonstrated that the LPI performance of the joint bistatic radar and communication system can be markedly improved by utilizing the proposed scheme.

Looping probabilities of elastic chains: a path integral approach.

PubMed

Cotta-Ramusino, Ludovica; Maddocks, John H

2010-11-01

We consider an elastic chain at thermodynamic equilibrium with a heat bath, and derive an approximation to the probability density function, or pdf, governing the relative location and orientation of the two ends of the chain. Our motivation is to exploit continuum mechanics models for the computation of DNA looping probabilities, but here we focus on explaining the novel analytical aspects in the derivation of our approximation formula. Accordingly, and for simplicity, the current presentation is limited to the illustrative case of planar configurations. A path integral formalism is adopted, and, in the standard way, the first approximation to the looping pdf is obtained from a minimal energy configuration satisfying prescribed end conditions. Then we compute an additional factor in the pdf which encompasses the contributions of quadratic fluctuations about the minimum energy configuration along with a simultaneous evaluation of the partition function. The original aspects of our analysis are twofold. First, the quadratic Lagrangian describing the fluctuations has cross-terms that are linear in first derivatives. This, seemingly small, deviation from the structure of standard path integral examples complicates the necessary analysis significantly. Nevertheless, after a nonlinear change of variable of Riccati type, we show that the correction factor to the pdf can still be evaluated in terms of the solution to an initial value problem for the linear system of Jacobi ordinary differential equations associated with the second variation. The second novel aspect of our analysis is that we show that the Hamiltonian form of these linear Jacobi equations still provides the appropriate correction term in the inextensible, unshearable limit that is commonly adopted in polymer physics models of, e.g. DNA. Prior analyses of the inextensible case have had to introduce nonlinear and nonlocal integral constraints to express conditions on the relative displacement of the end points. Our approximation formula for the looping pdf is of quite general applicability as, in contrast to most prior approaches, no assumption is made of either uniformity of the elastic chain, nor of a straight intrinsic shape. If the chain is uniform the Jacobi system evaluated at certain minimum energy configurations has constant coefficients. In such cases our approximate pdf can be evaluated in an entirely explicit, closed form. We illustrate our analysis with a planar example of this type and compute an approximate probability of cyclization, i.e., of forming a closed loop, from a uniform elastic chain whose intrinsic shape is an open circular arc.

Finding Dantzig Selectors with a Proximity Operator based Fixed-point Algorithm

DTIC Science & Technology

2014-11-01

experiments showed that this method usually outperforms the method in [2] in terms of CPU time while producing solutions of comparable quality. The... method proposed in [19]. To alleviate the difficulty caused by the subprob- lem without a closed form solution , a linearized ADM was proposed for the...a closed form solution , but the β-related subproblem does not and is solved approximately by using the nonmonotone gradient method in [18]. The

A parallel offline CFD and closed-form approximation strategy for computationally efficient analysis of complex fluid flows

NASA Astrophysics Data System (ADS)

Allphin, Devin

Computational fluid dynamics (CFD) solution approximations for complex fluid flow problems have become a common and powerful engineering analysis technique. These tools, though qualitatively useful, remain limited in practice by their underlying inverse relationship between simulation accuracy and overall computational expense. While a great volume of research has focused on remedying these issues inherent to CFD, one traditionally overlooked area of resource reduction for engineering analysis concerns the basic definition and determination of functional relationships for the studied fluid flow variables. This artificial relationship-building technique, called meta-modeling or surrogate/offline approximation, uses design of experiments (DOE) theory to efficiently approximate non-physical coupling between the variables of interest in a fluid flow analysis problem. By mathematically approximating these variables, DOE methods can effectively reduce the required quantity of CFD simulations, freeing computational resources for other analytical focuses. An idealized interpretation of a fluid flow problem can also be employed to create suitably accurate approximations of fluid flow variables for the purposes of engineering analysis. When used in parallel with a meta-modeling approximation, a closed-form approximation can provide useful feedback concerning proper construction, suitability, or even necessity of an offline approximation tool. It also provides a short-circuit pathway for further reducing the overall computational demands of a fluid flow analysis, again freeing resources for otherwise unsuitable resource expenditures. To validate these inferences, a design optimization problem was presented requiring the inexpensive estimation of aerodynamic forces applied to a valve operating on a simulated piston-cylinder heat engine. The determination of these forces was to be found using parallel surrogate and exact approximation methods, thus evidencing the comparative benefits of this technique. For the offline approximation, latin hypercube sampling (LHS) was used for design space filling across four (4) independent design variable degrees of freedom (DOF). Flow solutions at the mapped test sites were converged using STAR-CCM+ with aerodynamic forces from the CFD models then functionally approximated using Kriging interpolation. For the closed-form approximation, the problem was interpreted as an ideal 2-D converging-diverging (C-D) nozzle, where aerodynamic forces were directly mapped by application of the Euler equation solutions for isentropic compression/expansion. A cost-weighting procedure was finally established for creating model-selective discretionary logic, with a synthesized parallel simulation resource summary provided.

Correlation energy functional within the GW -RPA: Exact forms, approximate forms, and challenges

NASA Astrophysics Data System (ADS)

Ismail-Beigi, Sohrab

2010-05-01

In principle, the Luttinger-Ward Green’s-function formalism allows one to compute simultaneously the total energy and the quasiparticle band structure of a many-body electronic system from first principles. We present approximate and exact expressions for the correlation energy within the GW -random-phase approximation that are more amenable to computation and allow for developing efficient approximations to the self-energy operator and correlation energy. The exact form is a sum over differences between plasmon and interband energies. The approximate forms are based on summing over screened interband transitions. We also demonstrate that blind extremization of such functionals leads to unphysical results: imposing physical constraints on the allowed solutions (Green’s functions) is necessary. Finally, we present some relevant numerical results for atomic systems.

Heat Conduction in Ceramic Coatings: Relationship Between Microstructure and Effective Thermal Conductivity

NASA Technical Reports Server (NTRS)

Kachanov, Mark

1998-01-01

Analysis of the effective thermal conductivity of ceramic coatings and its relation to the microstructure continued. Results (obtained in Task 1) for the three-dimensional problem of heat conduction in a solid containing an inclusion (or, in particular, cavity - thermal insulator) of the ellipsoidal shape, were further advanced in the following two directions: (1) closed form expressions of H tensor have been derived for special cases of ellipsoidal cavity geometry: spheroid, crack-like spheroidal cavity and needle shaped spheroidal cavity; (2) these results for one cavity have been incorporated to construct heat energy potential for a solid with many spheroidal cavities (in the approximation of non-interacting defects). This problem constitutes a basic building block for further analyses.

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.

Compressible flow about symmetrical Joukowski profiles

NASA Technical Reports Server (NTRS)

Kaplan, Carl

1938-01-01

The method of Poggi is employed for the determination of the effects of compressibility upon the flow past an obstacle. A general expression for the velocity increment due to compressibility is obtained. The general result holds whatever the shape of the obstacle; but, in order to obtain the complete solution, it is necessary to know a certain Fourier expansion of the square of the velocity of flow past the obstacle. An application is made to the case flow of a symmetrical Joukowski profile with a sharp trailing edge, fixed in a stream of an arbitrary angle of attack and with the circulation determined by the Kutta condition. The results are obtained in a closed form and are exact insofar as the second approximation to the compressible flow is concerned, the first approximation being the result for the corresponding incompressible flow. Formulas for lift and moment analogous to the Blasius formulas in incompressible flow are developed and are applied to thin symmetrical Joukowski profiles for small angles of attack.

Log-amplitude statistics for Beck-Cohen superstatistics

NASA Astrophysics Data System (ADS)

Kiyono, Ken; Konno, Hidetoshi

2013-05-01

As a possible generalization of Beck-Cohen superstatistical processes, we study non-Gaussian processes with temporal heterogeneity of local variance. To characterize the variance heterogeneity, we define log-amplitude cumulants and log-amplitude autocovariance and derive closed-form expressions of the log-amplitude cumulants for χ2, inverse χ2, and log-normal superstatistical distributions. Furthermore, we show that χ2 and inverse χ2 superstatistics with degree 2 are closely related to an extreme value distribution, called the Gumbel distribution. In these cases, the corresponding superstatistical distributions result in the q-Gaussian distribution with q=5/3 and the bilateral exponential distribution, respectively. Thus, our finding provides a hypothesis that the asymptotic appearance of these two special distributions may be explained by a link with the asymptotic limit distributions involving extreme values. In addition, as an application of our approach, we demonstrated that non-Gaussian fluctuations observed in a stock index futures market can be well approximated by the χ2 superstatistical distribution with degree 2.

Transcriptomes define distinct subgroups of salivary gland adenoid cystic carcinoma with different driver mutations and outcomes

PubMed Central

Frerich, Candace A.; Brayer, Kathryn J.; Painter, Brandon M.; Kang, Huining; Mitani, Yoshitsugu; El-Naggar, Adel K.; Ness, Scott A.

2018-01-01

The relative rarity of salivary gland adenoid cystic carcinoma (ACC) and its slow growing yet aggressive nature has complicated the development of molecular markers for patient stratification. To analyze molecular differences linked to the protracted disease course of ACC and metastases that form 5 or more years after diagnosis, detailed RNA-sequencing (RNA-seq) analysis was performed on 68 ACC tumor samples, starting with archived, formalin-fixed paraffin-embedded (FFPE) samples up to 25 years old, so that clinical outcomes were available. A statistical peak-finding approach was used to classify the tumors that expressed MYB or MYBL1, which had overlapping gene expression signatures, from a group that expressed neither oncogene and displayed a unique phenotype. Expression of MYB or MYBL1 was closely correlated to the expression of the SOX4 and EN1 genes, suggesting that they are direct targets of Myb proteins in ACC tumors. Unsupervised hierarchical clustering identified a subgroup of approximately 20% of patients with exceptionally poor overall survival (median less than 30 months) and a unique gene expression signature resembling embryonic stem cells. The results provide a strategy for stratifying ACC patients and identifying the high-risk, poor-outcome group that are candidates for personalized therapies. PMID:29484115

Neutron Multiplicity: LANL W Covariance Matrix for Curve Fitting

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

Wendelberger, James G.

2016-12-08

In neutron multiplicity counting one may fit a curve by minimizing an objective function, χmore » $$2\\atop{n}$$. The objective function includes the inverse of an n by n matrix of covariances, W. The inverse of the W matrix has a closed form solution. In addition W -1 is a tri-diagonal matrix. The closed form and tridiagonal nature allows for a simpler expression of the objective function χ$$2\\atop{n}$$. Minimization of this simpler expression will provide the optimal parameters for the fitted curve.« less

Polarimetric image reconstruction algorithms

NASA Astrophysics Data System (ADS)

Valenzuela, John R.

In the field of imaging polarimetry Stokes parameters are sought and must be inferred from noisy and blurred intensity measurements. Using a penalized-likelihood estimation framework we investigate reconstruction quality when estimating intensity images and then transforming to Stokes parameters (traditional estimator), and when estimating Stokes parameters directly (Stokes estimator). We define our cost function for reconstruction by a weighted least squares data fit term and a regularization penalty. It is shown that under quadratic regularization, the traditional and Stokes estimators can be made equal by appropriate choice of regularization parameters. It is empirically shown that, when using edge preserving regularization, estimating the Stokes parameters directly leads to lower RMS error in reconstruction. Also, the addition of a cross channel regularization term further lowers the RMS error for both methods especially in the case of low SNR. The technique of phase diversity has been used in traditional incoherent imaging systems to jointly estimate an object and optical system aberrations. We extend the technique of phase diversity to polarimetric imaging systems. Specifically, we describe penalized-likelihood methods for jointly estimating Stokes images and optical system aberrations from measurements that contain phase diversity. Jointly estimating Stokes images and optical system aberrations involves a large parameter space. A closed-form expression for the estimate of the Stokes images in terms of the aberration parameters is derived and used in a formulation that reduces the dimensionality of the search space to the number of aberration parameters only. We compare the performance of the joint estimator under both quadratic and edge-preserving regularization. The joint estimator with edge-preserving regularization yields higher fidelity polarization estimates than with quadratic regularization. Under quadratic regularization, using the reduced-parameter search strategy, accurate aberration estimates can be obtained without recourse to regularization "tuning". Phase-diverse wavefront sensing is emerging as a viable candidate wavefront sensor for adaptive-optics systems. In a quadratically penalized weighted least squares estimation framework a closed form expression for the object being imaged in terms of the aberrations in the system is available. This expression offers a dramatic reduction of the dimensionality of the estimation problem and thus is of great interest for practical applications. We have derived an expression for an approximate joint covariance matrix for object and aberrations in the phase diversity context. Our expression for the approximate joint covariance is compared with the "known-object" Cramer-Rao lower bound that is typically used for system parameter optimization. Estimates of the optimal amount of defocus in a phase-diverse wavefront sensor derived from the joint-covariance matrix, the known-object Cramer-Rao bound, and Monte Carlo simulations are compared for an extended scene and a point object. It is found that our variance approximation, that incorporates the uncertainty of the object, leads to an improvement in predicting the optimal amount of defocus to use in a phase-diverse wavefront sensor.

An exact closed form solution for constant area compressible flow with friction and heat transfer

NASA Technical Reports Server (NTRS)

Sturas, J. I.

1971-01-01

The well-known differential equation for the one-dimensional flow of a compressible fluid with heat transfer and wall friction has no known solution in closed form for the general case. This report presents a closed form solution for the special case of constant heat flux per unit length and constant specific heat. The solution was obtained by choosing the square of a dimensionless flow parameter as one of the independent variables to describe the flow. From this exact solution, an approximate simplified form is derived that is applicable for predicting subsonic flow performance characteristics for many types of constant area passages in internal flow. The data included in this report are considered sufficiently accurate for use as a guide in analyzing and designing internal gas flow systems.

Hamilton's Principle and Approximate Solutions to Problems in Classical Mechanics

ERIC Educational Resources Information Center

Schlitt, D. W.

1977-01-01

Shows how to use the Ritz method for obtaining approximate solutions to problems expressed in variational form directly from the variational equation. Application of this method to classical mechanics is given. (MLH)

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

Hashimoto, Muneaki, E-mail: muneaki@juntendo.ac.jp; Nara, Takeshi, E-mail: tnara@juntendo.ac.jp; Enomoto, Masahiro, E-mail: menomoto@uhnres.utoronto.ca

Inositol 1,4,5-trisphosphate receptor (IP{sub 3}R) is a key regulator of intracellular Ca{sup 2+} concentration that release Ca{sup 2+} from Ca{sup 2+} stores in response to various external stimuli. IP{sub 3}R also works as a signal hub which form a platform for interacting with various proteins involved in diverse cell signaling. Previously, we have identified an IP{sub 3}R homolog in the parasitic protist, Trypanosoma cruzi (TcIP{sub 3}R). Parasites expressing reduced or increased levels of TcIP{sub 3}R displayed defects in growth, transformation, and infectivity. In the present study, we established parasitic strains expressing a dominant negative form of TcIP{sub 3}R, named DN-TcIP{submore » 3}R, to further investigate the physiological role(s) of TcIP{sub 3}R. We found that the growth of epimastigotes expressing DN-TcIP{sub 3}R was significantly slower than that of parasites with TcIP{sub 3}R expression levels that were approximately 65% of wild-type levels. The expression of DN-TcIP{sub 3}R in epimastigotes induced metacyclogenesis even in the normal growth medium. Furthermore, these epimastigotes showed the presence of dense mitochondria under a transmission electron microscope. Our findings confirm that TcIP{sub 3}R is crucial for epimastigote growth, as previously reported. They also suggest that a strong inhibition of the IP{sub 3}R-mediated signaling induces metacyclogenesis and that mitochondrial integrity is closely associated with this signaling. - Highlights: • We established T. cruzi strains expressing a dominant negative form of the TcIP{sub 3}R. • DN-TcIP{sub 3}R expression inhibits epimastigote growth and induces metacyclogenesis. • Microscopic analysis indicated TcIP{sub 3}R role in maintaining mitochondrial integrity. • Growth, but not microbial density, was altered by mammalian IP{sub 3}R inhibitor (2-APB).« less

Transverse signal decay under the weak field approximation: Theory and validation.

PubMed

Berman, Avery J L; Pike, G Bruce

2018-07-01

To derive an expression for the transverse signal time course from systems in the motional narrowing regime, such as water diffusing in blood. This was validated in silico and experimentally with ex vivo blood samples. A closed-form solution (CFS) for transverse signal decay under any train of refocusing pulses was derived using the weak field approximation. The CFS was validated via simulations of water molecules diffusing in the presence of spherical perturbers, with a range of sizes and under various pulse sequences. The CFS was compared with more conventional fits assuming monoexponential decay, including chemical exchange, using ex vivo blood Carr-Purcell-Meiboom-Gill data. From simulations, the CFS was shown to be valid in the motional narrowing regime and partially into the intermediate dephasing regime, with increased accuracy with increasing Carr-Purcell-Meiboom-Gill refocusing rate. In theoretical calculations of the CFS, fitting for the transverse relaxation rate (R 2 ) gave excellent agreement with the weak field approximation expression for R 2 for Carr-Purcell-Meiboom-Gill sequences, but diverged for free induction decay. These same results were confirmed in the ex vivo analysis. Transverse signal decay in the motional narrowing regime can be accurately described analytically. This theory has applications in areas such as tissue iron imaging, relaxometry of blood, and contrast agent imaging. Magn Reson Med 80:341-350, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

Approximate spatial reasoning

NASA Technical Reports Server (NTRS)

Dutta, Soumitra

1988-01-01

A model for approximate spatial reasoning using fuzzy logic to represent the uncertainty in the environment is presented. Algorithms are developed which can be used to reason about spatial information expressed in the form of approximate linguistic descriptions similar to the kind of spatial information processed by humans. Particular attention is given to static spatial reasoning.

Ligand binding turns moth pheromone-binding protein into a pH sensor: effect on the Antheraea polyphemus PBP1 conformation.

PubMed

Katre, Uma V; Mazumder, Suman; Prusti, Rabi K; Mohanty, Smita

2009-11-13

In moths, pheromone-binding proteins (PBPs) are responsible for the transport of the hydrophobic pheromones to the membrane-bound receptors across the aqueous sensillar lymph. We report here that recombinant Antheraea polyphemus PBP1 (ApolPBP1) picks up hydrophobic molecule(s) endogenous to the Escherichia coli expression host that keeps the protein in the "open" (bound) conformation at high pH but switches to the "closed" (free) conformation at low pH. This finding has bearing on the solution structures of undelipidated lepidopteran moth PBPs determined thus far. Picking up a hydrophobic molecule from the host expression system could be a common feature for lipid-binding proteins. Thus, delipidation is critical for bacterially expressed lipid-binding proteins. We have shown for the first time that the delipidated ApolPBP1 exists primarily in the closed form at all pH levels. Thus, current views on the pH-induced conformational switch of PBPs hold true only for the ligand-bound open conformation of the protein. Binding of various ligands to delipidated ApolPBP1 studied by solution NMR revealed that the protein in the closed conformation switches to the open conformation only at or above pH 6.0 with a protein to ligand stoichiometry of approximately 1:1. Mutation of His(70) and His(95) to alanine drives the equilibrium toward the open conformation even at low pH for the ligand-bound protein by eliminating the histidine-dependent pH-induced conformational switch. Thus, the delipidated double mutant can bind ligand even at low pH in contrast to the wild type protein as revealed by fluorescence competitive displacement assay using 1-aminoanthracene and solution NMR.

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.

Light scattering from laser induced pit ensembles on high power laser optics

DOE PAGES

Feigenbaum, Eyal; Elhadj, Selim; Matthews, Manyalibo J.

2015-01-01

Far-field light scattering characteristics from randomly arranged shallow Gaussian-like shaped laser induced pits, found on optics exposed to high energy laser pulses, is studied. Closed-form expressions for the far-field intensity distribution and scattered power are derived for individual pits and validated using numerical calculations of both Fourier optics and FDTD solutions to Maxwell’s equations. It is found that the scattered power is proportional to the square of the pit width and approximately also to the square of the pit depth, with the proportionality factor scaling with pit depth. As a result, the power scattered from shallow pitted optics is expectedmore » to be substantially lower than assuming complete scattering from the total visible footprint of the pits.« less

Unsteady seepage flow over sloping beds in response to multiple localized recharge

NASA Astrophysics Data System (ADS)

Bansal, Rajeev K.

2017-05-01

New generalized solutions of linearized Boussinesq equation are derived to approximate the dynamic behavior of subsurface seepage flow induced by multiple localized time-varying recharges over sloping ditch-drain aquifer system. The mathematical model is based on extended Dupuit-Forchheimer assumption and treats the spatial location of recharge basins as additional parameter. Closed form analytic expressions for spatio-temporal variations in water head distribution and discharge rate into the drains are obtained by solving the governing flow equation using eigenvalue-eigenfunction method. Downward and zero-sloping aquifers are treated as special cases of main results. A numerical example is used for illustration of combined effects of various parameters such as spatial coordinates of the recharge basin, aquifer's bed slope, and recharge rate on the dynamic profiles of phreatic surface.

Quantum search algorithms on a regular lattice

NASA Astrophysics Data System (ADS)

Hein, Birgit; Tanner, Gregor

2010-07-01

Quantum algorithms for searching for one or more marked items on a d-dimensional lattice provide an extension of Grover’s search algorithm including a spatial component. We demonstrate that these lattice search algorithms can be viewed in terms of the level dynamics near an avoided crossing of a one-parameter family of quantum random walks. We give approximations for both the level splitting at the avoided crossing and the effectively two-dimensional subspace of the full Hilbert space spanning the level crossing. This makes it possible to give the leading order behavior for the search time and the localization probability in the limit of large lattice size including the leading order coefficients. For d=2 and d=3, these coefficients are calculated explicitly. Closed form expressions are given for higher dimensions.

Closed-form recursive formula for an optimal tracker with terminal constraints

NASA Technical Reports Server (NTRS)

Juang, J.-N.; Turner, J. D.; Chun, H. M.

1984-01-01

Feedback control laws are derived for a class of optimal finite time tracking problems with terminal constraints. Analytical solutions are obtained for the feedback gain and the closed-loop response trajectory. Such formulations are expressed in recursive forms so that a real-time computer implementation becomes feasible. Two examples are given to illustrate the validity and usefulness of the formulations.

Quasi-linear diffusion coefficients for highly oblique whistler mode waves

NASA Astrophysics Data System (ADS)

Albert, J. M.

2017-05-01

Quasi-linear diffusion coefficients are considered for highly oblique whistler mode waves, which exhibit a singular "resonance cone" in cold plasma theory. The refractive index becomes both very large and rapidly varying as a function of wave parameters, making the diffusion coefficients difficult to calculate and to characterize. Since such waves have been repeatedly observed both outside and inside the plasmasphere, this problem has received renewed attention. Here the diffusion equations are analytically treated in the limit of large refractive index μ. It is shown that a common approximation to the refractive index allows the associated "normalization integral" to be evaluated in closed form and that this can be exploited in the numerical evaluation of the exact expression. The overall diffusion coefficient formulas for large μ are then reduced to a very simple form, and the remaining integral and sum over resonances are approximated analytically. These formulas are typically written for a modeled distribution of wave magnetic field intensity, but this may not be appropriate for highly oblique whistlers, which become quasi-electrostatic. Thus, the analysis is also presented in terms of wave electric field intensity. The final results depend strongly on the maximum μ (or μ∥) used to model the wave distribution, so realistic determination of these limiting values becomes paramount.

A Bidirectional Brain-Machine Interface Algorithm That Approximates Arbitrary Force-Fields

PubMed Central

Semprini, Marianna; Mussa-Ivaldi, Ferdinando A.; Panzeri, Stefano

2014-01-01

We examine bidirectional brain-machine interfaces that control external devices in a closed loop by decoding motor cortical activity to command the device and by encoding the state of the device by delivering electrical stimuli to sensory areas. Although it is possible to design this artificial sensory-motor interaction while maintaining two independent channels of communication, here we propose a rule that closes the loop between flows of sensory and motor information in a way that approximates a desired dynamical policy expressed as a field of forces acting upon the controlled external device. We previously developed a first implementation of this approach based on linear decoding of neural activity recorded from the motor cortex into a set of forces (a force field) applied to a point mass, and on encoding of position of the point mass into patterns of electrical stimuli delivered to somatosensory areas. However, this previous algorithm had the limitation that it only worked in situations when the position-to-force map to be implemented is invertible. Here we overcome this limitation by developing a new non-linear form of the bidirectional interface that can approximate a virtually unlimited family of continuous fields. The new algorithm bases both the encoding of position information and the decoding of motor cortical activity on an explicit map between spike trains and the state space of the device computed with Multi-Dimensional-Scaling. We present a detailed computational analysis of the performance of the interface and a validation of its robustness by using synthetic neural responses in a simulated sensory-motor loop. PMID:24626393

A forecast for extinction debt in the presence of speciation.

PubMed

Sgardeli, Vasiliki; Iwasa, Yoh; Varvoglis, Harry; Halley, John M

2017-02-21

Predicting biodiversity relaxation following a disturbance is of great importance to conservation biology. Recently-developed models of stochastic community assembly allow us to predict the evolution of communities on the basis of mechanistic processes at the level of individuals. The neutral model of biodiversity, in particular, has provided closed-form solutions for the relaxation of biodiversity in isolated communities (no immigration or speciation). Here, we extend these results by deriving a relaxation curve for a neutral community in which new species are introduced through the mechanism of random fission speciation (RFS). The solution provides simple closed-form expressions for the equilibrium species richness, the relaxation time and the species-individual curve, which are good approximation to the more complicated formulas existing for the same model. The derivation of the relaxation curve is based on the assumption of a broken-stick species-abundance distribution (SAD) as an initial community configuration; yet for commonly observed SADs, the maximum deviation from the curve does not exceed 10%. Importantly, the solution confirms theoretical results and observations showing that the relaxation time increases with community size and thus habitat area. Such simple and analytically tractable models can help crystallize our ideas on the leading factors affecting biodiversity loss. Copyright © 2016 Elsevier Ltd. All rights reserved.

Power-efficient distributed resource allocation under goodput QoS constraints for heterogeneous networks

NASA Astrophysics Data System (ADS)

Andreotti, Riccardo; Del Fiorentino, Paolo; Giannetti, Filippo; Lottici, Vincenzo

2016-12-01

This work proposes a distributed resource allocation (RA) algorithm for packet bit-interleaved coded OFDM transmissions in the uplink of heterogeneous networks (HetNets), characterized by small cells deployed over a macrocell area and sharing the same band. Every user allocates its transmission resources, i.e., bits per active subcarrier, coding rate, and power per subcarrier, to minimize the power consumption while both guaranteeing a target quality of service (QoS) and accounting for the interference inflicted by other users transmitting over the same band. The QoS consists of the number of information bits delivered in error-free packets per unit of time, or goodput (GP), estimated at the transmitter by resorting to an efficient effective SNR mapping technique. First, the RA problem is solved in the point-to-point case, thus deriving an approximate yet accurate closed-form expression for the power allocation (PA). Then, the interference-limited HetNet case is examined, where the RA problem is described as a non-cooperative game, providing a solution in terms of generalized Nash equilibrium. Thanks to the closed-form of the PA, the solution analysis is based on the best response concept. Hence, sufficient conditions for existence and uniqueness of the solution are analytically derived, along with a distributed algorithm capable of reaching the game equilibrium.

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.

Linearized Lifting-Surface and Lifting-line Evaluations of Sidewash Behind Rolling Triangular Wings at Supersonic Speeds

NASA Technical Reports Server (NTRS)

Bobbitt, Percy J

1957-01-01

The lifting-surface sidewash behind rolling triangular wings has been derived for a range of supersonic Mach numbers for which the wing leading edges remain swept behind the mark cone emanating from the wing apex. Variations of the sidewash with longitudinal distance in the vertical plane of symmetry are presented in graphical form. An approximate expression for the sidewash has been developed by means of an approach using a horseshoe-vortex approximate-lifting-line theory. By use of this approximate expression, sidewash may be computed for wings of arbitrary plan form and span loading. A comparison of the sidewash computed by lifting-surface and lifting-line expressions for the triangular wing showed good agreement except in the vicinity of the trailing edge when the leading edge approached the sonic condition. An illustrative calculation has been made of the force induced by the wing sidewash on a vertical tail located in various longitudinal positions.

Analytical Expressions for Deformation from an Arbitrarily Oriented Spheroid in a Half-Space

NASA Astrophysics Data System (ADS)

Cervelli, P. F.

2013-12-01

Deformation from magma chambers can be modeled by an elastic half-space with an embedded cavity subject to uniform pressure change along its interior surface. For a small number of cavity shapes, such as a sphere or a prolate spheroid, closed-form, analytical expressions for deformation have been derived, although these only approximate the uniform-pressure-change boundary condition, with the approximation becoming more accurate as the ratio of source depth to source dimension increases. Using the method of Elshelby [1957] and Yang [1988], which consists of a distribution of double forces and centers of dilatation along the vertical axis, I have derived expressions for displacement from a finite spheroid of arbitrary orientation and aspect ratio that are exact in an infinite elastic medium and approximate in a half-space. The approximation, like those for other cavity shapes, becomes increasingly accurate as the depth to source ratio grows larger, and is accurate to within a few percent in most real-world cases. I have also derived expressions for the deformation-gradient tensor, i.e., the derivatives of each component of displacement with respect to each coordinate direction. These can be transformed easily into the strain and stress tensors. The expressions give deformation both at the surface and at any point within the half-space, and include conditional statements that account for limiting cases that would otherwise prove singular. I have developed MATLAB code for these expressions (and their derivatives), which I use to demonstrate the accuracy of the approximation by showing how well the uniform-pressure-change boundary condition is satisfied in a variety of cases. I also show that a vertical, oblate spheroid with a zero-length vertical axis is equivalent to the penny-shaped crack of Fialko [2001] in an infinite medium and an excellent approximation in a half-space. Finally, because, in many cases, volume change is more tangible than pressure change, I have derived an equation that relates these two quantities for the spheroid: volume change equals pressure change × 2/3 × π/μ × a constant that depends on Poisson's ratio and the spheroid geometry. Eshelby, J. D., The determination of the elastic field of an ellipsoidal inclusion and related problems, Proc. R. Soc. London, Ser. A, 241, 376-396, 1957. Fialko, Y., Khazan, Y, and Simons, M. Deformation due to a pressurized horizontal circular crack in an elastic half-space, with applications to volcano geodesy, Geophys. J. Int., no. 146, 181-190, 2001. Yang, X., Davis, P. M., and Dieterich, J.H, Deformation from inflation of a dipping finite prolate spheroid in an Elastic Half-Space as a model for volcanic stressing, J. Geophys. Res., vol. 93, no. B5, 4249-4257, 1988.

Heterosubunit composition and crystal structures of a novel bacterial M16B metallopeptidase.

PubMed

Maruyama, Yukie; Chuma, Asako; Mikami, Bunzo; Hashimoto, Wataru; Murata, Kousaku

2011-03-18

Three subfamilies of metallopeptidase family M16 enzymes--M16A, M16B, and M16C--are widely distributed among eukaryotes and prokaryotes. SPH2681, a periplasmic M16B protein found in Sphingomonas sp. strain A1, contains an HXXEH motif essential for Zn(2+) binding and catalytic activity. SPH2682 is another member of M16B, which lacks the metal-binding motif but conserves an active-site R/Y pair commonly found in the C-terminal half of M16 enzymes. Two genes coding for SPH2681 and SPH2682 assemble into a single operon in the bacterial genome. This study determined SPH2681 to be constitutively expressed in strain A1 cells grown on different carbon sources, suggesting a more general cellular function. SPH2681 and SPH2681/SPH2682 were overexpressed in Escherichia coli, purified, and characterized. SPH2681 was found to associate with SPH2682, forming a heterosubunit enzyme with peptidase activity, while SPH2681 alone exhibited no enzymatic activity. X-ray crystallography of the SPH2681/SPH2682 complex revealed two conformations (open and closed heterodimeric forms) within the same crystal. Compared with the closed form, the open form contains two subunits rotated away from each other by approximately 8°, increasing the distance between the zinc ion and active-site residues by up to 8 Å. In addition, many hydrogen bonds are formed or broken on change between the conformations of the heterodimers, suggesting that subunit dynamics is a prerequisite for catalysis. To our knowledge, this is the first report on both conformational forms of the same M16 peptidase, providing a unique insight into the general proteolytic mechanism of M16 proteases. Copyright © 2011 Elsevier Ltd. All rights reserved.

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.

The sagitta and lens thickness: the exact solution and a matrix approximation for lenses with toric, spherical, and cylindrical surfaces.

PubMed

Harris, W F

1989-03-01

The exact equation for sagitta of spherical surfaces is generalized to toric surfaces which include spherical and cylindrical surfaces as special cases. Lens thickness, therefore, can be calculated accurately anywhere on a lens even in cases of extreme spherical and cylindrical powers and large diameters. The sagittae of tire- and barrel-form toric surfaces differ off the principal meridians, as is shown by a numerical example. The same holds for pulley- and capstan-form toric surfaces. A general expression is given for thickness at an arbitrary point on a toric lens. Approximate expressions are derived and re-expressed in terms of matrices. The matrix provides an elegant means of generalizing equations for spherical surfaces and lenses to toric surfaces and lenses.

Collapse of composite tubes under end moments

NASA Technical Reports Server (NTRS)

Stockwell, Alan E.; Cooper, Paul A.

1992-01-01

Cylindrical tubes of moderate wall thickness such as those proposed for the original space station truss, may fail due to the gradual collapse of the tube cross section as it distorts under load. Sometimes referred to as the Brazier instability, it is a nonlinear phenomenon. This paper presents an extension of an approximate closed form solution of the collapse of isotropic tubes subject to end moments developed by Reissner in 1959 to include specially orthotropic material. The closed form solution was verified by an extensive nonlinear finite element analysis of the collapse of long tubes under applied end moments for radius to thickness ratios and composite layups in the range proposed for recent space station truss framework designs. The finite element analysis validated the assumption of inextensional deformation of the cylindrical cross section and the approximation of the material as specially orthotropic.

Erratum: A Comparison of Closures for Stochastic Advection-Diffusion Equations

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

Jarman, Kenneth D.; Tartakovsky, Alexandre M.

2015-01-01

This note corrects an error in the authors' article [SIAM/ASA J. Uncertain. Quantif., 1 (2013), pp. 319 347] in which the cited work [Neuman, Water Resour. Res., 29(3) (1993), pp. 633 645] was incorrectly represented and attributed. Concentration covariance equations presented in our article as new were in fact previously derived in the latter work. In the original abstract, the phrase " . . .we propose a closed-form approximation to two-point covariance as a measure of uncertainty. . ." should be replaced by the phrase " . . .we study a closed-form approximation to two-point covariance, previously derived in [Neumanmore » 1993], as a measure of uncertainty." The primary results in our article--the analytical and numerical comparison of existing closure methods for specific example problems are not changed by this correction.« less

Approximate analytical relationships for linear optimal aeroelastic flight control laws

NASA Astrophysics Data System (ADS)

Kassem, Ayman Hamdy

1998-09-01

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

Closed-form Capacity Expressions for the α-μ Fading Channel with SC Diversity under Different Adaptive Transmission Strategies

NASA Astrophysics Data System (ADS)

Mohamed, Refaat; Ismail, Mahmoud H.; Newagy, Fatma; Mourad, Heba M.

2013-03-01

Stemming from the fact that the α-μ fading distribution is one of the very general fading models used in the literature to describe the small scale fading phenomenon, in this paper, closed-form expressions for the Shannon capacity of the α-μ fading channel operating under four main adaptive transmission strategies are derived assuming integer values for μ. These expressions are derived for the case of no diversity as well as for selection combining diversity with independent and identically distributed branches. The obtained expressions reduce to those previously derived in the literature for the Weibull as well as the Rayleigh fading cases, which are both special cases of the α-μ channel. Numerical results are presented for the capacity under the four adaptive transmission strategies and the effect of the fading parameter as well as the number of diversity branches is studied.

The Effective Resistance of the -Cycle Graph with Four Nearest Neighbors

NASA Astrophysics Data System (ADS)

Chair, Noureddine

2014-02-01

The exact expression for the effective resistance between any two vertices of the -cycle graph with four nearest neighbors , is given. It turns out that this expression is written in terms of the effective resistance of the -cycle graph , the square of the Fibonacci numbers, and the bisected Fibonacci numbers. As a consequence closed form formulas for the total effective resistance, the first passage time, and the mean first passage time for the simple random walk on the the -cycle graph with four nearest neighbors are obtained. Finally, a closed form formula for the effective resistance of with all first neighbors removed is obtained.

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

Anomalous momentum and energy transfer rates for electrostatic ion-cyclotron turbulence in downward auroral-current regions of the Earth's magnetosphere. III

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

Jasperse, John R.; Basu, Bamandas; Lund, Eric J.

2010-06-15

Recently, a new multimoment fluid theory was developed for inhomogeneous, nonuniformly magnetized plasma in the guiding-center and gyrotropic approximation that includes the effect of electrostatic, turbulent, wave-particle interactions (see Jasperse et al. [Phys. Plasmas 13, 072903 (2006); ibid.13, 112902 (2006)]). In the present paper, which is intended as a sequel, it is concluded from FAST satellite data that the electrostatic ion-cyclotron turbulence that appears is due to the operation of an electron, bump-on-tail-driven ion-cyclotron instability for downward currents in the long-range potential region of the Earth's magnetosphere. Approximate closed-form expressions for the anomalous momentum and energy transfer rates for themore » ion-cyclotron turbulence are obtained. The turbulent, inhomogeneous, nonuniformly magnetized, multimoment fluid theory given above, in the limit of a turbulent, homogeneous, uniformly magnetized, quasisteady plasma, yields the well-known formula for the anomalous resistivity given by Gary and Paul [Phys. Rev. Lett. 26, 1097 (1971)] and Tange and Ichimaru [J. Phys. Soc. Jpn. 36, 1437 (1974)].« less

On a numerical method for solving integro-differential equations with variable coefficients with applications in finance

NASA Astrophysics Data System (ADS)

Kudryavtsev, O.; Rodochenko, V.

2018-03-01

We propose a new general numerical method aimed to solve integro-differential equations with variable coefficients. The problem under consideration arises in finance where in the context of pricing barrier options in a wide class of stochastic volatility models with jumps. To handle the effect of the correlation between the price and the variance, we use a suitable substitution for processes. Then we construct a Markov-chain approximation for the variation process on small time intervals and apply a maturity randomization technique. The result is a system of boundary problems for integro-differential equations with constant coefficients on the line in each vertex of the chain. We solve the arising problems using a numerical Wiener-Hopf factorization method. The approximate formulae for the factors are efficiently implemented by means of the Fast Fourier Transform. Finally, we use a recurrent procedure that moves backwards in time on the variance tree. We demonstrate the convergence of the method using Monte-Carlo simulations and compare our results with the results obtained by the Wiener-Hopf method with closed-form expressions of the factors.

Buildup Index as an Expression of Moisture Content in Duff

Treesearch

Von J. Johnson

1968-01-01

The relation between Buildup index and moisture content of grouped litter and duff samples from beneath four medium-site forest stands closely approximated the relation between Buildup index and moisture equivalent of 5-day timelag fuels having an equilibrium moisture content of 15 percent

Analytic studies of the hard dumbell fluid

NASA Astrophysics Data System (ADS)

Morriss, G. P.; Cummings, P. T.

A closed form analytic theory for the structure of the hard dumbell fluid is introduced and evaluated. It is found to be comparable in accuracy to the reference interaction site approximation (RISA) of Chandler and Andersen.

Fundamental gaps with approximate density functionals: The derivative discontinuity revealed from ensemble considerations

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

Kraisler, Eli; Kronik, Leeor

2014-05-14

The fundamental gap is a central quantity in the electronic structure of matter. Unfortunately, the fundamental gap is not generally equal to the Kohn-Sham gap of density functional theory (DFT), even in principle. The two gaps differ precisely by the derivative discontinuity, namely, an abrupt change in slope of the exchange-correlation energy as a function of electron number, expected across an integer-electron point. Popular approximate functionals are thought to be devoid of a derivative discontinuity, strongly compromising their performance for prediction of spectroscopic properties. Here we show that, in fact, all exchange-correlation functionals possess a derivative discontinuity, which arises naturallymore » from the application of ensemble considerations within DFT, without any empiricism. This derivative discontinuity can be expressed in closed form using only quantities obtained in the course of a standard DFT calculation of the neutral system. For small, finite systems, addition of this derivative discontinuity indeed results in a greatly improved prediction for the fundamental gap, even when based on the most simple approximate exchange-correlation density functional – the local density approximation (LDA). For solids, the same scheme is exact in principle, but when applied to LDA it results in a vanishing derivative discontinuity correction. This failure is shown to be directly related to the failure of LDA in predicting fundamental gaps from total energy differences in extended systems.« less

A newly-detected reductase from Rauvolfia closes a gap in the biosynthesis of the antiarrhythmic alkaloid ajmaline.

PubMed

Gao, Shujuan; von Schumann, Gerald; Stöckigt, Joachim

2002-10-01

A new enzyme, 1,2-dihydrovomilenine reductase (E.C. 1.3.1), has been detected in Rauvolfia cell suspension cultures. The enzyme specifically converts 2beta( R)-1,2-dihydrovomilenine through an NADPH-dependent reaction into 17-O-acetylnorajmaline, a close biosynthetic precursor of the antiarrhythmic alkaloid ajmaline from Rauvolfia. A five-step purification procedure using SOURCE 30Q chromatography, hydroxyapatite chromatography, 2',5'-ADP Sepharose 4B affinity chromatography and ion exchange chromatography on DEAE Sepharose and Mono Q delivered an approximately 200-fold enriched enzyme in a yield of approximately 6%. SDS-PAGE showed an M r for the enzyme of approximately 48 kDa. Optimum pH and optimum temperature of the reductase were at pH 6.0 and 37 degrees C. The enzyme shows a limited distribution in cell cultures expressing ajmaline biosynthesis, and is obviously highly specific for the ajmaline pathway.

A three-dimensional semi-analytical solution for predicting drug release through the orifice of a spherical device.

PubMed

Simon, Laurent; Ospina, Juan

2016-07-25

Three-dimensional solute transport was investigated for a spherical device with a release hole. The governing equation was derived using the Fick's second law. A mixed Neumann-Dirichlet condition was imposed at the boundary to represent diffusion through a small region on the surface of the device. The cumulative percentage of drug released was calculated in the Laplace domain and represented by the first term of an infinite series of Legendre and modified Bessel functions of the first kind. Application of the Zakian algorithm yielded the time-domain closed-form expression. The first-order solution closely matched a numerical solution generated by Mathematica(®). The proposed method allowed computation of the characteristic time. A larger surface pore resulted in a smaller effective time constant. The agreement between the numerical solution and the semi-analytical method improved noticeably as the size of the orifice increased. It took four time constants for the device to release approximately ninety-eight of its drug content. Copyright © 2016 Elsevier B.V. All rights reserved.

Electromagnetic pulses, localized and causal

NASA Astrophysics Data System (ADS)

Lekner, John

2018-01-01

We show that pulse solutions of the wave equation can be expressed as time Fourier superpositions of scalar monochromatic beam wave functions (solutions of the Helmholtz equation). This formulation is shown to be equivalent to Bateman's integral expression for solutions of the wave equation, for axially symmetric solutions. A closed-form one-parameter solution of the wave equation, containing no backward-propagating parts, is constructed from a beam which is the tight-focus limit of two families of beams. Application is made to transverse electric and transverse magnetic pulses, with evaluation of the energy, momentum and angular momentum for a pulse based on the general localized and causal form. Such pulses can be represented as superpositions of photons. Explicit total energy and total momentum values are given for the one-parameter closed-form pulse.

A Dictionary of Hindi Verbal Expressions (Hindi-English). Final Report.

ERIC Educational Resources Information Center

Bahl, Kali Charan, Comp.

This dictionary covers approximately 28,277 verbal expressions in modern standard Hindi and their rendered English equivalents. The study lists longer verbal expressions which are generally matched by single verbs in English. The lexicographer notes that the majority of entries in this dictionary do not appear in their present form in most other…

Closed-form recursive formula for an optimal tracker with terminal constraints

NASA Technical Reports Server (NTRS)

Juang, J. N.; Turner, J. D.; Chun, H. M.

1986-01-01

Feedback control laws are derived for a class of optimal finite time tracking problems with terminal constraints. Analytical solutions are obtained for the feedback gain and the closed-loop response trajectory. Such formulations are expressed in recursive forms so that a real-time computer implementation becomes feasible. An example involving the feedback slewing of a flexible spacecraft is given to illustrate the validity and usefulness of the formulations.

A simple method to calculate first-passage time densities with arbitrary initial conditions

NASA Astrophysics Data System (ADS)

Nyberg, Markus; Ambjörnsson, Tobias; Lizana, Ludvig

2016-06-01

Numerous applications all the way from biology and physics to economics depend on the density of first crossings over a boundary. Motivated by the lack of general purpose analytical tools for computing first-passage time densities (FPTDs) for complex problems, we propose a new simple method based on the independent interval approximation (IIA). We generalise previous formulations of the IIA to include arbitrary initial conditions as well as to deal with discrete time and non-smooth continuous time processes. We derive a closed form expression for the FPTD in z and Laplace-transform space to a boundary in one dimension. Two classes of problems are analysed in detail: discrete time symmetric random walks (Markovian) and continuous time Gaussian stationary processes (Markovian and non-Markovian). Our results are in good agreement with Langevin dynamics simulations.

Limiting Forces on Transit Trucks in Steady-State Curving

DOT National Transportation Integrated Search

1981-05-01

This study develops conservative bounds on wheel/rail forces and flange forces for several types of rigid and flexible trucks in steady-state curving conditions. The approximate analysis presented provides closed-form relations for estimating forces,...

Kalman Filters for Time Delay of Arrival-Based Source Localization

NASA Astrophysics Data System (ADS)

Klee, Ulrich; Gehrig, Tobias; McDonough, John

2006-12-01

In this work, we propose an algorithm for acoustic source localization based on time delay of arrival (TDOA) estimation. In earlier work by other authors, an initial closed-form approximation was first used to estimate the true position of the speaker followed by a Kalman filtering stage to smooth the time series of estimates. In the proposed algorithm, this closed-form approximation is eliminated by employing a Kalman filter to directly update the speaker's position estimate based on the observed TDOAs. In particular, the TDOAs comprise the observation associated with an extended Kalman filter whose state corresponds to the speaker's position. We tested our algorithm on a data set consisting of seminars held by actual speakers. Our experiments revealed that the proposed algorithm provides source localization accuracy superior to the standard spherical and linear intersection techniques. Moreover, the proposed algorithm, although relying on an iterative optimization scheme, proved efficient enough for real-time operation.

Diagnostics of seeded RF plasmas: An experimental study related to the gaseous core reactor

NASA Technical Reports Server (NTRS)

Thompson, S. D.; Clement, J. D.; Williams, J. R.

1974-01-01

Measurements of the temperature profiles in an RF argon plasma were made over magnetic field intensities ranging from 20 amp turns/cm to 80 amp turns/cm. The results were compared with a one-dimensional numerical treatment of the governing equations and with an approximate closed form analytical solution that neglected radiation losses. The average measured temperatures in the plasma compared well with the numerical treatment, though the experimental profile showed less of an off center temperature peak than predicted by theory. This may be a result of the complex turbulent flow pattern present in the experimental torch and not modeled in the numerical treatment. The radiation term cannot be neglected for argon at the power levels investigated. The closed form analytical approximation that neglected radiation led to temperature predictions on the order of 1000 K to 2000 K higher than measured or predicted by the numerical treatment which considered radiation losses.

Closed-form solutions of performability. [modeling of a degradable buffer/multiprocessor system

NASA Technical Reports Server (NTRS)

Meyer, J. F.

1981-01-01

Methods which yield closed form performability solutions for continuous valued variables are developed. The models are similar to those employed in performance modeling (i.e., Markovian queueing models) but are extended so as to account for variations in structure due to faults. In particular, the modeling of a degradable buffer/multiprocessor system is considered whose performance Y is the (normalized) average throughput rate realized during a bounded interval of time. To avoid known difficulties associated with exact transient solutions, an approximate decomposition of the model is employed permitting certain submodels to be solved in equilibrium. These solutions are then incorporated in a model with fewer transient states and by solving the latter, a closed form solution of the system's performability is obtained. In conclusion, some applications of this solution are discussed and illustrated, including an example of design optimization.

Point Charges Optimally Placed to Represent the Multipole Expansion of Charge Distributions

PubMed Central

Onufriev, Alexey V.

2013-01-01

We propose an approach for approximating electrostatic charge distributions with a small number of point charges to optimally represent the original charge distribution. By construction, the proposed optimal point charge approximation (OPCA) retains many of the useful properties of point multipole expansion, including the same far-field asymptotic behavior of the approximate potential. A general framework for numerically computing OPCA, for any given number of approximating charges, is described. We then derive a 2-charge practical point charge approximation, PPCA, which approximates the 2-charge OPCA via closed form analytical expressions, and test the PPCA on a set of charge distributions relevant to biomolecular modeling. We measure the accuracy of the new approximations as the RMS error in the electrostatic potential relative to that produced by the original charge distribution, at a distance the extent of the charge distribution–the mid-field. The error for the 2-charge PPCA is found to be on average 23% smaller than that of optimally placed point dipole approximation, and comparable to that of the point quadrupole approximation. The standard deviation in RMS error for the 2-charge PPCA is 53% lower than that of the optimal point dipole approximation, and comparable to that of the point quadrupole approximation. We also calculate the 3-charge OPCA for representing the gas phase quantum mechanical charge distribution of a water molecule. The electrostatic potential calculated by the 3-charge OPCA for water, in the mid-field (2.8 Å from the oxygen atom), is on average 33.3% more accurate than the potential due to the point multipole expansion up to the octupole order. Compared to a 3 point charge approximation in which the charges are placed on the atom centers, the 3-charge OPCA is seven times more accurate, by RMS error. The maximum error at the oxygen-Na distance (2.23 Å ) is half that of the point multipole expansion up to the octupole order. PMID:23861790

Close-form expression of one-tap normalized LMS carrier phase recovery in optical communication systems

NASA Astrophysics Data System (ADS)

Xu, Tianhua; Jacobsen, Gunnar; Popov, Sergei; Li, Jie; Liu, Tiegen; Zhang, Yimo

2016-10-01

The performance of long-haul high speed coherent optical fiber communication systems is significantly degraded by the laser phase noise and the equalization enhanced phase noise (EEPN). In this paper, the analysis of the one-tap normalized least-mean-square (LMS) carrier phase recovery (CPR) is carried out and the close-form expression is investigated for quadrature phase shift keying (QPSK) coherent optical fiber communication systems, in compensating both laser phase noise and equalization enhanced phase noise. Numerical simulations have also been implemented to verify the theoretical analysis. It is found that the one-tap normalized least-mean-square algorithm gives the same analytical expression for predicting CPR bit-error-rate (BER) floors as the traditional differential carrier phase recovery, when both the laser phase noise and the equalization enhanced phase noise are taken into account.

Collisional excitation of the highly excited hydrogen atoms in the dipole form of the semiclassical impact parameter and Born approximations

NASA Technical Reports Server (NTRS)

Omidvar, K.

1971-01-01

Expressions for the excitation cross section of the highly excited states of the hydrogenlike atoms by fast charged particles have been derived in the dipole approximation of the semiclassical impact parameter and the Born approximations, making use of a formula for the asymptotic expansion of the oscillator strength of the hydrogenlike atoms given by Menzel. When only the leading term in the asymptotic expansion is retained, the expression for the cross section becomes identical to the expression obtained by the method of the classical collision and correspondence principle given by Percival and Richards. Comparisons are made between the Bethe coefficients obtained here and the Bethe coefficients of the Born approximation for transitions where the Born calculation is available. Satisfactory agreement is obtained only for n yields n + 1 transitions, with n the principal quantum number of the excited state.

Exact closed-form solutions of a fully nonlinear asymptotic two-fluid model

NASA Astrophysics Data System (ADS)

Cheviakov, Alexei F.

2018-05-01

A fully nonlinear model of Choi and Camassa (1999) describing one-dimensional incompressible dynamics of two non-mixing fluids in a horizontal channel, under a shallow water approximation, is considered. An equivalence transformation is presented, leading to a special dimensionless form of the system, involving a single dimensionless constant physical parameter, as opposed to five parameters present in the original model. A first-order dimensionless ordinary differential equation describing traveling wave solutions is analyzed. Several multi-parameter families of physically meaningful exact closed-form solutions of the two-fluid model are derived, corresponding to periodic, solitary, and kink-type bidirectional traveling waves; specific examples are given, and properties of the exact solutions are analyzed.

Propagation of sound waves through a linear shear layer: A closed form solution

NASA Technical Reports Server (NTRS)

Scott, J. N.

1978-01-01

Closed form solutions are presented for sound propagation from a line source in or near a shear layer. The analysis was exact for all frequencies and was developed assuming a linear velocity profile in the shear layer. This assumption allowed the solution to be expressed in terms of parabolic cyclinder functions. The solution is presented for a line monopole source first embedded in the uniform flow and then in the shear layer. Solutions are also discussed for certain types of dipole and quadrupole sources. Asymptotic expansions of the exact solutions for small and large values of Strouhal number gave expressions which correspond to solutions previously obtained for these limiting cases.

A High Frequency Model of Cascade Noise

NASA Technical Reports Server (NTRS)

Envia, Edmane

1998-01-01

Closed form asymptotic expressions for computing high frequency noise generated by an annular cascade in an infinite duct containing a uniform flow are presented. There are two new elements in this work. First, the annular duct mode representation does not rely on the often-used Bessel function expansion resulting in simpler expressions for both the radial eigenvalues and eigenfunctions of the duct. In particular, the new representation provides an explicit approximate formula for the radial eigenvalues obviating the need for solutions of the transcendental annular duct eigenvalue equation. Also, the radial eigenfunctions are represented in terms of exponentials eliminating the numerical problems associated with generating the Bessel functions on a computer. The second new element is the construction of an unsteady response model for an annular cascade. The new construction satisfies the boundary conditions on both the cascade and duct walls simultaneously adding a new level of realism to the noise calculations. Preliminary results which demonstrate the effectiveness of the new elements are presented. A discussion of the utility of the asymptotic formulas for calculating cascade discrete tone as well as broadband noise is also included.

Partial characterization of the lettuce infectious yellows virus genomic RNAs, identification of the coat protein gene and comparison of its amino acid sequence with those of other filamentous RNA plant viruses.

PubMed

Klaassen, V A; Boeshore, M; Dolja, V V; Falk, B W

1994-07-01

Purified virions of lettuce infectious yellows virus (LIYV), a tentative member of the closterovirus group, contained two RNAs of approximately 8500 and 7300 nucleotides (RNAs 1 and 2 respectively) and a single coat protein species with M(r) of approximately 28,000. LIYV-infected plants contained multiple dsRNAs. The two largest were the correct size for the replicative forms of LIYV virion RNAs 1 and 2. To assess the relationships between LIYV RNAs 1 and 2, cDNAs corresponding to the virion RNAs were cloned. Northern blot hybridization analysis showed no detectable sequence homology between these RNAs. A partial amino acid sequence obtained from purified LIYV coat protein was found to align in the most upstream of four complete open reading frames (ORFs) identified in a LIYV RNA 2 cDNA clone. The identity of this ORF was confirmed as the LIYV coat protein gene by immunological analysis of the gene product expressed in vitro and in Escherichia coli. Computer analysis of the LIYV coat protein amino acid sequence indicated that it belongs to a large family of proteins forming filamentous capsids of RNA plant viruses. The LIYV coat protein appears to be most closely related to the coat proteins of two closteroviruses, beet yellows virus and citrus tristeza virus.

Extension of the method of moments for population balances involving fractional moments and application to a typical agglomeration problem.

PubMed

Alexiadis, Alessio; Vanni, Marco; Gardin, Pascal

2004-08-01

The method of moment (MOM) is a powerful tool for solving population balance. Nevertheless it cannot be used in every circumstance. Sometimes, in fact, it is not possible to write the governing equations in closed form. Higher moments, for instance, could appear in the evolution of the lower ones. This obstacle has often been resolved by prescribing some functional form for the particle size distribution. Another example is the occurrence of fractional moment, usually connected with the presence of fractal aggregates. For this case we propose a procedure that does not need any assumption on the form of the distribution but it is based on the "moments generating function" (that is the Laplace transform of the distribution). An important result of probability theory is that the kth derivative of the moments generating function represents the kth moment of the original distribution. This result concerns integer moments but, taking in account the Weyl fractional derivative, could be extended to fractional orders. Approximating fractional derivative makes it possible to express the fractional moments in terms of the integer ones and so to use regularly the method of moments.

Approximate Solution to the Angular Speeds of a Nearly-Symmetric Mass-Varying Cylindrical Body

NASA Astrophysics Data System (ADS)

Nanjangud, Angadh; Eke, Fidelis

2017-06-01

This paper examines the rotational motion of a nearly axisymmetric rocket type system with uniform burn of its propellant. The asymmetry comes from a slight difference in the transverse principal moments of inertia of the system, which then results in a set of nonlinear equations of motion even when no external torque is applied to the system. It is often difficult, or even impossible, to generate analytic solutions for such equations; closed form solutions are even more difficult to obtain. In this paper, a perturbation-based approach is employed to linearize the equations of motion and generate analytic solutions. The solutions for the variables of transverse motion are analytic and a closed-form solution to the spin rate is suggested. The solutions are presented in a compact form that permits rapid computation. The approximate solutions are then applied to the torque-free motion of a typical solid rocket system and the results are found to agree with those obtained from the numerical solution of the full non-linear equations of motion of the mass varying system.

Boundary Control of Linear Uncertain 1-D Parabolic PDE Using Approximate Dynamic Programming.

PubMed

Talaei, Behzad; Jagannathan, Sarangapani; Singler, John

2018-04-01

This paper develops a near optimal boundary control method for distributed parameter systems governed by uncertain linear 1-D parabolic partial differential equations (PDE) by using approximate dynamic programming. A quadratic surface integral is proposed to express the optimal cost functional for the infinite-dimensional state space. Accordingly, the Hamilton-Jacobi-Bellman (HJB) equation is formulated in the infinite-dimensional domain without using any model reduction. Subsequently, a neural network identifier is developed to estimate the unknown spatially varying coefficient in PDE dynamics. Novel tuning law is proposed to guarantee the boundedness of identifier approximation error in the PDE domain. A radial basis network (RBN) is subsequently proposed to generate an approximate solution for the optimal surface kernel function online. The tuning law for near optimal RBN weights is created, such that the HJB equation error is minimized while the dynamics are identified and closed-loop system remains stable. Ultimate boundedness (UB) of the closed-loop system is verified by using the Lyapunov theory. The performance of the proposed controller is successfully confirmed by simulation on an unstable diffusion-reaction process.

Local approximation of a metapopulation's equilibrium.

PubMed

Barbour, A D; McVinish, R; Pollett, P K

2018-04-18

We consider the approximation of the equilibrium of a metapopulation model, in which a finite number of patches are randomly distributed over a bounded subset [Formula: see text] of Euclidean space. The approximation is good when a large number of patches contribute to the colonization pressure on any given unoccupied patch, and when the quality of the patches varies little over the length scale determined by the colonization radius. If this is the case, the equilibrium probability of a patch at z being occupied is shown to be close to [Formula: see text], the equilibrium occupation probability in Levins's model, at any point [Formula: see text] not too close to the boundary, if the local colonization pressure and extinction rates appropriate to z are assumed. The approximation is justified by giving explicit upper and lower bounds for the occupation probabilities, expressed in terms of the model parameters. Since the patches are distributed randomly, the occupation probabilities are also random, and we complement our bounds with explicit bounds on the probability that they are satisfied at all patches simultaneously.

Sparse approximation problem: how rapid simulated annealing succeeds and fails

NASA Astrophysics Data System (ADS)

Obuchi, Tomoyuki; Kabashima, Yoshiyuki

2016-03-01

Information processing techniques based on sparseness have been actively studied in several disciplines. Among them, a mathematical framework to approximately express a given dataset by a combination of a small number of basis vectors of an overcomplete basis is termed the sparse approximation. In this paper, we apply simulated annealing, a metaheuristic algorithm for general optimization problems, to sparse approximation in the situation where the given data have a planted sparse representation and noise is present. The result in the noiseless case shows that our simulated annealing works well in a reasonable parameter region: the planted solution is found fairly rapidly. This is true even in the case where a common relaxation of the sparse approximation problem, the G-relaxation, is ineffective. On the other hand, when the dimensionality of the data is close to the number of non-zero components, another metastable state emerges, and our algorithm fails to find the planted solution. This phenomenon is associated with a first-order phase transition. In the case of very strong noise, it is no longer meaningful to search for the planted solution. In this situation, our algorithm determines a solution with close-to-minimum distortion fairly quickly.

Wealth and price distribution by diffusive approximation in a repeated prediction market

NASA Astrophysics Data System (ADS)

Bottazzi, Giulio; Giachini, Daniele

2017-04-01

The approximate agents' wealth and price invariant densities of a repeated prediction market model is derived using the Fokker-Planck equation of the associated continuous-time jump process. We show that the approximation obtained from the evolution of log-wealth difference can be reliably exploited to compute all the quantities of interest in all the acceptable parameter space. When the risk aversion of the trader is high enough, we are able to derive an explicit closed-form solution for the price distribution which is asymptotically correct.

Rapid execution of fan beam image reconstruction algorithms using efficient computational techniques and special-purpose processors

NASA Astrophysics Data System (ADS)

Gilbert, B. K.; Robb, R. A.; Chu, A.; Kenue, S. K.; Lent, A. H.; Swartzlander, E. E., Jr.

1981-02-01

Rapid advances during the past ten years of several forms of computer-assisted tomography (CT) have resulted in the development of numerous algorithms to convert raw projection data into cross-sectional images. These reconstruction algorithms are either 'iterative,' in which a large matrix algebraic equation is solved by successive approximation techniques; or 'closed form'. Continuing evolution of the closed form algorithms has allowed the newest versions to produce excellent reconstructed images in most applications. This paper will review several computer software and special-purpose digital hardware implementations of closed form algorithms, either proposed during the past several years by a number of workers or actually implemented in commercial or research CT scanners. The discussion will also cover a number of recently investigated algorithmic modifications which reduce the amount of computation required to execute the reconstruction process, as well as several new special-purpose digital hardware implementations under development in laboratories at the Mayo Clinic.

Purely cubic action for string field theory

NASA Technical Reports Server (NTRS)

Horowitz, G. T.; Lykken, J.; Rohm, R.; Strominger, A.

1986-01-01

It is shown that Witten's (1986) open-bosonic-string field-theory action and a closed-string analog can be written as a purely cubic interaction term. The conventional form of the action arises by expansion around particular solutions of the classical equations of motion. The explicit background dependence of the conventional action via the Becchi-Rouet-Stora-Tyutin operator is eliminated in the cubic formulation. A closed-form expression is found for the full nonlinear gauge-transformation law.

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

Price, Morgan N.; Arkin, Adam P.; Alm, Eric J.

Operons are a major feature of all prokaryotic genomes, but how and why operon structures vary is not well understood. To elucidate the life-cycle of operons, we compared gene order between Escherichia coli K12 and its relatives and identified the recently formed and destroyed operons in E. coli. This allowed us to determine how operons form, how they become closely spaced, and how they die. Our findings suggest that operon evolution is driven by selection on gene expression patterns. First, both operon creation and operon destruction lead to large changes in gene expression patterns. For example, the removal of lysAmore » and ruvA from ancestral operons that contained essential genes allowed their expression to respond to lysine levels and DNA damage, respectively. Second, some operons have undergone accelerated evolution, with multiple new genes being added during a brief period. Third, although most operons are closely spaced because of a neutral bias towards deletion and because of selection against large overlaps, highly expressed operons tend to be widely spaced because of regulatory fine-tuning by intervening sequences. Although operon evolution seems to be adaptive, it need not be optimal: new operons often comprise functionally unrelated genes that were already in proximity before the operon formed.« less

Exact Closed-form Solutions for Lamb's Problem

NASA Astrophysics Data System (ADS)

Feng, Xi; Zhang, Haiming

2018-04-01

In this article, we report on an exact closed-form solution for the displacement at the surface of an elastic half-space elicited by a buried point source that acts at some point underneath that surface. This is commonly referred to as the 3-D Lamb's problem, for which previous solutions were restricted to sources and receivers placed at the free surface. By means of the reciprocity theorem, our solution should also be valid as a means to obtain the displacements at interior points when the source is placed at the free surface. We manage to obtain explicit results by expressing the solution in terms of elementary algebraic expression as well as elliptic integrals. We anchor our developments on Poisson's ratio 0.25 starting from Johnson's (1974) integral solutions which must be computed numerically. In the end, our closed-form results agree perfectly with the numerical results of Johnson (1974), which strongly confirms the correctness of our explicit formulas. It is hoped that in due time, these formulas may constitute a valuable canonical solution that will serve as a yardstick against which other numerical solutions can be compared and measured.

Exact closed-form solutions for Lamb's problem

NASA Astrophysics Data System (ADS)

Feng, Xi; Zhang, Haiming

2018-07-01

In this paper, we report on an exact closed-form solution for the displacement at the surface of an elastic half-space elicited by a buried point source that acts at some point underneath that surface. This is commonly referred to as the 3-D Lamb's problem for which previous solutions were restricted to sources and receivers placed at the free surface. By means of the reciprocity theorem, our solution should also be valid as a means to obtain the displacements at interior points when the source is placed at the free surface. We manage to obtain explicit results by expressing the solution in terms of elementary algebraic expression as well as elliptic integrals. We anchor our developments on Poisson's ratio 0.25 starting from Johnson's integral solutions which must be computed numerically. In the end, our closed-form results agree perfectly with the numerical results of Johnson, which strongly confirms the correctness of our explicit formulae. It is hoped that in due time, these formulae may constitute a valuable canonical solution that will serve as a yardstick against which other numerical solutions can be compared and measured.

Electromagnetic fields radiated from a lightning return stroke - Application of an exact solution to Maxwell's equations

NASA Technical Reports Server (NTRS)

Le Vine, D. M.; Meneghini, R.

1978-01-01

A solution is presented for the electromagnetic fields radiated by an arbitrarily oriented current filament over a conducting ground plane in the case where the current propagates along the filament at the speed of light, and this solution is interpreted in terms of radiation from lightning return strokes. The solution is exact in the fullest sense; no mathematical approximations are made, and the governing differential equations and boundary conditions are satisfied. The solution has the additional attribute of being specified in closed form in terms of elementary functions. This solution is discussed from the point of view of deducing lightning current wave forms from measurements of the electromagnetic fields and understanding the effects of channel tortuosity on the radiated fields. In addition, it is compared with two approximate solutions, the traditional moment approximation and the Fraunhofer approximation, and a set of criteria describing their applicability are presented and interpreted.

Partially Coherent Scattering in Stellar Chromospheres. Part 4; Analytic Wing Approximations

NASA Technical Reports Server (NTRS)

Gayley, K. G.

1993-01-01

Simple analytic expressions are derived to understand resonance-line wings in stellar chromospheres and similar astrophysical plasmas. The results are approximate, but compare well with accurate numerical simulations. The redistribution is modeled using an extension of the partially coherent scattering approximation (PCS) which we term the comoving-frame partially coherent scattering approximation (CPCS). The distinction is made here because Doppler diffusion is included in the coherent/noncoherent decomposition, in a form slightly improved from the earlier papers in this series.

A combinatorial model of malware diffusion via bluetooth connections.

PubMed

Merler, Stefano; Jurman, Giuseppe

2013-01-01

We outline here the mathematical expression of a diffusion model for cellphones malware transmitted through Bluetooth channels. In particular, we provide the deterministic formula underlying the proposed infection model, in its equivalent recursive (simple but computationally heavy) and closed form (more complex but efficiently computable) expression.

The properties of coke breeze briquettes produced by ram briquetting

NASA Astrophysics Data System (ADS)

Loginov, Yu. N.; Babailov, N. A.; Polyansky, L. I.

2017-12-01

The paper reports on the results of briquetting coke breeze with a binder in a closed cylindrical press-die. Liquid glass is used as a binder. Approximating curves for the "compaction ratio vs. compaction pressure" dependences are plotted from experimental data. The mechanical properties of the briquettes are determined, namely, drop damage resistance and breaking stress. The results are presented as approximating dependences in the form of a power function.

Vacuum Stress in Schwarzschild Spacetime

NASA Astrophysics Data System (ADS)

Howard, Kenneth Webster

Vacuum stress in the conformally invariant scalar field in the region exterior to the horizon of a Schwarzschild black hole is examined. In the Hartle-Hawking vacuum state <(phi)('2)> and are calculated. Covariant point-splitting renormalization is used, as is a mode sum expression for the Hartle-Hawking propagator. It is found that <(phi)('2)> separates naturally into two parts, a part that has a simple analytic form coinciding with the approximate expression of Whiting and Page, and a small remainder. The results of our numerical evaluation of the remainder agree with, but are more accurate than, those previously given by Fawcett. We find that also separates into two terms. The first coincides with the approximate expression obtained by Page with a Gaussian approximation to the proper time Green function. The second term, composed of sums over mode functions, is evaluated numerically. It is found that the total expression is in good qualitative agreement with Page's approximation. Our results disagree with previous numerical results given by Fawcett. The error in Fawcett's calculation is explained.

Simulation of Aluminum Micro-mirrors for Space Applications at Cryogenic Temperatures

NASA Technical Reports Server (NTRS)

Kuhn, J. L.; Dutta, S. B.; Greenhouse, M. A.; Mott, D. B.

2000-01-01

Closed form and finite element models are developed to predict the device response of aluminum electrostatic torsion micro-mirrors fabricated on silicon substrate for space applications at operating temperatures of 30K. Initially, closed form expressions for electrostatic pressure arid mechanical restoring torque are used to predict the pull-in and release voltages at room temperature. Subsequently, a detailed mechanical finite element model is developed to predict stresses and vertical beam deflection induced by the electrostatic and thermal loads. An incremental and iterative solution method is used in conjunction with the nonlinear finite element model and closed form electrostatic equations to solve. the coupled electro-thermo-mechanical problem. The simulation results are compared with experimental measurements at room temperature of fabricated micro-mirror devices.

Variational Dirac-Hartree-Fock calculation of the Breit interaction

NASA Astrophysics Data System (ADS)

Goldman, S. P.

1988-04-01

The calculation of the retarded version of the Breit interaction in the context of the VDHF method is discussed. With the use of Slater-type basis functions, all the terms involved can be calculated in closed form. The results are expressed as an expansion in powers of one-electron energy differences and linear combinations of hypergeometric functions. Convergence is fast and high accuracy is obtained with a small number of terms in the expansion even for high values of the nuclear charge. An added advantage is that the lowest order cancellations occurring in the retardation terms are accounted for exactly a priori. A comparison of the number of terms in the total expansion needed for an accuracy of 12 significant digits in the total energy, as well as a comparison of the results with an without retardation and in the local potential approximation, are presented for the carbon isoelectronic sequence.

Achievable rate degradation of ultra-wideband coherent fiber communication systems due to stimulated Raman scattering.

PubMed

Semrau, Daniel; Killey, Robert; Bayvel, Polina

2017-06-12

As the bandwidths of optical communication systems are increased to maximize channel capacity, the impact of stimulated Raman scattering (SRS) on the achievable information rates (AIR) in ultra-wideband coherent WDM systems becomes significant, and is investigated in this work, for the first time. By modifying the GN-model to account for SRS, it is possible to derive a closed-form expression that predicts the optical signal-to-noise ratio of all channels at the receiver for bandwidths of up to 15 THz, which is in excellent agreement with numerical calculations. It is shown that, with fixed modulation and coding rate, SRS leads to a drop of approximately 40% in achievable information rates for bandwidths higher than 15 THz. However, if adaptive modulation and coding rates are applied across the entire spectrum, this AIR reduction can be limited to only 10%.

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.

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

Approximate Theoretical Model for the Five Electronic States (Ω = 5/2, 3/2, 3/2, 1/2, 1/2) Arising from the Ground 3d9 Configuration in Nickel Halide Molecules and for Rotational Levels of the Two Ω = 1/2 States in that Manifold

NASA Astrophysics Data System (ADS)

Cheung, Allan S.-C.

2011-06-01

An effective Hamiltonian for a non-rotating diatomic molecule containing only crystal-field and spin-orbit operators has been set up to describe the energies of the five spin-orbit components that arise in the ground electronic configuration of the nickel monohalides. The model assumes that bonding in the nickel halides has the approximate form Ni+X-, with an electronic 3d9 configuration plus closed shells on the Ni+ moiety and a closed shell configuration on the X&- moiety. Least-squares fits of the observed five spin-orbit components of the three lowest electronic states in NiF and NiCl are then carried out in terms of the three crystal field parameters C0, C2, C4 and the spin-orbit coupling constant A. Following this, the usual effective Hamiltonian B(J-L-S)^2 for a rotating diatomic molecule is used to derive expressions for the unusually large Ω-type doubling parameter p in the two Ω = 1/2 states in the 3d9 manifold. These expressions show (for certain sign conventions) that the sum of the two p values should be -2B, but that their difference can vary between -10B and +10B. The theoretical magnitudes for p are in good agreement with the two observed p values for both NiF and NiCl, but the signs are not. The experimental signs can be brought into agreement with the theoretical signs by a fairly massive change in +/- parity assignments in the NiF and NiCl literature. The last part of the talk will focus on the theoretical and experimental implications of these parity changes.

A Combinatorial Model of Malware Diffusion via Bluetooth Connections

PubMed Central

Merler, Stefano; Jurman, Giuseppe

2013-01-01

We outline here the mathematical expression of a diffusion model for cellphones malware transmitted through Bluetooth channels. In particular, we provide the deterministic formula underlying the proposed infection model, in its equivalent recursive (simple but computationally heavy) and closed form (more complex but efficiently computable) expression. PMID:23555677

Instability of a planar expansion wave.

PubMed

Velikovich, A L; Zalesak, S T; Metzler, N; Wouchuk, J G

2005-10-01

An expansion wave is produced when an incident shock wave interacts with a surface separating a fluid from a vacuum. Such an interaction starts the feedout process that transfers perturbations from the rippled inner (rear) to the outer (front) surface of a target in inertial confinement fusion. Being essentially a standing sonic wave superimposed on a centered expansion wave, a rippled expansion wave in an ideal gas, like a rippled shock wave, typically produces decaying oscillations of all fluid variables. Its behavior, however, is different at large and small values of the adiabatic exponent gamma. At gamma > 3, the mass modulation amplitude delta(m) in a rippled expansion wave exhibits a power-law growth with time alpha(t)beta, where beta = (gamma - 3)/(gamma - 1). This is the only example of a hydrodynamic instability whose law of growth, dependent on the equation of state, is expressed in a closed analytical form. The growth is shown to be driven by a physical mechanism similar to that of a classical Richtmyer-Meshkov instability. In the opposite extreme gamma - 1 < 1, delta(m) exhibits oscillatory growth, approximately linear with time, until it reaches its peak value approximately (gamma - 1)(-1/2), and then starts to decrease. The mechanism driving the growth is the same as that of Vishniac's instability of a blast wave in a gas with low . Exact analytical expressions for the growth rates are derived for both cases and favorably compared to hydrodynamic simulation results.

A study on the achievable data rate in massive MIMO system

NASA Astrophysics Data System (ADS)

Salh, Adeeb; Audah, Lukman; Shah, Nor Shahida M.; Hamzah, Shipun A.

2017-09-01

The achievable high data rates depend on the ability of massive multi-input-multi-output (MIMO) for the fifth-generation (5G) cellular networks, where the massive MIMO systems can support very high energy and spectral efficiencies. A major challenge in mobile broadband networks is how to support the throughput in the future 5G, where the highlight of 5G expected to provide high speed internet for every user. The performance massive MIMO system increase with linear minimum mean square error (MMSE), zero forcing (ZF) and maximum ratio transmission (MRT) when the number of antennas increases to infinity, by deriving the closed-form approximation for achievable data rate expressions. Meanwhile, the high signal-to-noise ratio (SNR) can be mitigated by using MMSE, ZF and MRT, which are used to suppress the inter-cell interference signals between neighboring cells. The achievable sum rate for MMSE is improved based on the distributed users inside cell, mitigated the inter-cell interference caused when send the same signal by other cells. By contrast, MMSE is better than ZF in perfect channel state information (CSI) for approximately 20% of the achievable sum rate.

On the Problem of Bandwidth Partitioning in FDD Block-Fading Single-User MISO/SIMO Systems

NASA Astrophysics Data System (ADS)

Ivrlač, Michel T.; Nossek, Josef A.

2008-12-01

We report on our research activity on the problem of how to optimally partition the available bandwidth of frequency division duplex, multi-input single-output communication systems, into subbands for the uplink, the downlink, and the feedback. In the downlink, the transmitter applies coherent beamforming based on quantized channel information which is obtained by feedback from the receiver. As feedback takes away resources from the uplink, which could otherwise be used to transfer payload data, it is highly desirable to reserve the "right" amount of uplink resources for the feedback. Under the assumption of random vector quantization, and a frequency flat, independent and identically distributed block-fading channel, we derive closed-form expressions for both the feedback quantization and bandwidth partitioning which jointly maximize the sum of the average payload data rates of the downlink and the uplink. While we do introduce some approximations to facilitate mathematical tractability, the analytical solution is asymptotically exact as the number of antennas approaches infinity, while for systems with few antennas, it turns out to be a fairly accurate approximation. In this way, the obtained results are meaningful for practical communication systems, which usually can only employ a few antennas.

Solving the Integral of Quadratic Forms of Covariance Matrices for Applications in Polarimetric Radar Imagery

NASA Astrophysics Data System (ADS)

Marino, Armando; Hajnsek, Irena

2015-04-01

In this work, the solution of quadratic forms with special application to polarimetric and interferometric covariance matrices is investigated. An analytical solution for the integral of a single quadratic form is derived. Additionally, the integral of the Pol-InSAR coherence (expressed as combination of quadratic forms) is investigated. An approximation for such integral is proposed and defined as Trace coherence. Such approximation is tested on real data to verify that the error is acceptable. The trace coherence can be used for tackle problems related to change detection. Moreover, the use of the Trace coherence in model inversion (as for the RVoG three stage inversion) will be investigated in the future.

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.

Connections between EM2-containing terminals and GABA/μ-opioid receptor co-expressing neurons in the rat spinal trigeminal caudal nucleus

PubMed Central

Li, Meng-Ying; Wu, Zhen-Yu; Lu, Ya-Cheng; Yin, Jun-Bin; Wang, Jian; Zhang, Ting; Dong, Yu-Lin; Wang, Feng

2014-01-01

Endomorphin-2 (EM2) demonstrates a potent antinociceptive effect via the μ-opioid receptor (MOR). To provide morphological evidence for the pain control effect of EM2, the synaptic connections between EM2-immunoreactive (IR) axonal terminals and γ-amino butyric acid (GABA)/MOR co-expressing neurons in lamina II of the spinal trigeminal caudal nucleus (Vc) were investigated in the rat. Dense EM2-, MOR- and GABA-IR fibers and terminals were mainly observed in lamina II of the Vc. Within lamina II, GABA- and MOR-neuronal cell bodies were also encountered. The results of immunofluorescent histochemical triple-staining showed that approximately 14.2 or 18.9% of GABA-IR or MOR-IR neurons also showed MOR- or GABA-immunopositive staining in lamina II; approximately 45.2 and 36.1% of the GABA-IR and MOR-IR neurons, respectively, expressed FOS protein in their nuclei induced by injecting formalin into the left lower lip of the mouth. Most of the GABA/MOR, GABA/FOS, and MOR/FOS double-labeled neurons made close contacts with EM2-IR fibers and terminals. Immuno-electron microscopy confirmed that the EM2-IR terminals formed synapses with GABA-IR or MOR-IR dendritic processes and neuronal cell bodies in lamina II of the Vc. These results suggest that EM2 might participate in pain transmission and modulation by binding to MOR-IR and GABAergic inhibitory interneuron in lamina II of the Vc to exert inhibitory effect on the excitatory interneuron in lamina II and projection neurons in laminae I and III. PMID:25386121

Analytic Expressions for the Gravity Gradient Tensor of 3D Prisms with Depth-Dependent Density

NASA Astrophysics Data System (ADS)

Jiang, Li; Liu, Jie; Zhang, Jianzhong; Feng, Zhibing

2017-12-01

Variable-density sources have been paid more attention in gravity modeling. We conduct the computation of gravity gradient tensor of given mass sources with variable density in this paper. 3D rectangular prisms, as simple building blocks, can be used to approximate well 3D irregular-shaped sources. A polynomial function of depth can represent flexibly the complicated density variations in each prism. Hence, we derive the analytic expressions in closed form for computing all components of the gravity gradient tensor due to a 3D right rectangular prism with an arbitrary-order polynomial density function of depth. The singularity of the expressions is analyzed. The singular points distribute at the corners of the prism or on some of the lines through the edges of the prism in the lower semi-space containing the prism. The expressions are validated, and their numerical stability is also evaluated through numerical tests. The numerical examples with variable-density prism and basin models show that the expressions within their range of numerical stability are superior in computational accuracy and efficiency to the common solution that sums up the effects of a collection of uniform subprisms, and provide an effective method for computing gravity gradient tensor of 3D irregular-shaped sources with complicated density variation. In addition, the tensor computed with variable density is different in magnitude from that with constant density. It demonstrates the importance of the gravity gradient tensor modeling with variable density.

Stochastic analysis of unsaturated steady flows above the water table

NASA Astrophysics Data System (ADS)

Severino, Gerardo; Scarfato, Maddalena; Comegna, Alessandro

2017-08-01

Steady flow takes place into a three-dimensional partially saturated porous medium where, due to their spatial variability, the saturated conductivity Ks, and the relative conductivity Kr are modeled as random space functions (RSF)s. As a consequence, the flow variables (FVs), i.e., pressure-head and specific flux, are also RSFs. The focus of the present paper consists into quantifying the uncertainty of the FVs above the water table. The simple expressions (most of which in closed form) of the second-order moments pertaining to the FVs allow one to follow the transitional behavior from the zone close to the water table (where the FVs are nonstationary), till to their far-field limit (where the FVs become stationary RSFs). In particular, it is shown how the stationary limits (and the distance from the water table at which stationarity is attained) depend upon the statistical structure of the RSFs Ks, Kr, and the infiltrating rate. The mean pressure head ><Ψ>> has been also computed, and it is expressed as <Ψ>=Ψ0>(1+ψ>), being ψ a characteristic heterogeneity function which modifies the zero-order approximation Ψ0 of the pressure head (valid for a vadose zone of uniform soil properties) to account for the spatial variability of Ks and Kr. Two asymptotic limits, i.e., close (near field) and away (far field) from the water table, are derived into a very general manner, whereas the transitional behavior of ψ between the near/far field can be determined after specifying the shape of the various input soil properties. Besides the theoretical interest, results of the present paper are useful for practical purposes, as well. Indeed, the model is tested against to real data, and in particular it is shown how it is possible for the specific case study to grasp the behavior of the FVs within an environment (i.e., the vadose zone close to the water table) which is generally very difficult to access by direct inspection.

Optimal Mortgage Refinancing: A Closed Form Solution.

PubMed

Agarwal, Sumit; Driscoll, John C; Laibson, David I

2013-06-01

We derive the first closed-form optimal refinancing rule: Refinance when the current mortgage interest rate falls below the original rate by at least [Formula: see text] In this formula W (.) is the Lambert W -function, [Formula: see text] ρ is the real discount rate, λ is the expected real rate of exogenous mortgage repayment, σ is the standard deviation of the mortgage rate, κ/M is the ratio of the tax-adjusted refinancing cost and the remaining mortgage value, and τ is the marginal tax rate. This expression is derived by solving a tractable class of refinancing problems. Our quantitative results closely match those reported by researchers using numerical methods.

Analysis of delamination related fracture processes in composites

NASA Technical Reports Server (NTRS)

Armanios, Erian A.

1992-01-01

An anisotropic thin walled closed section beam theory was developed based on an asymptotical analysis of the shell energy functional. The displacement field is not assumed a priori and emerges as a result of the analysis. In addition to the classical out-of-plane torsional warping, two new contributions are identified namely, axial strain and bending warping. A comparison of the derived governing equations confirms the theory developed by Reissner and Tsai. Also, explicit closed form expressions for the beam stiffness coefficients, the stress and displacement fields are provided. The predictions of the present theory were validated by comparison with finite element simulation, other closed form analyses and test data.

Confocal imaging of butterfly tissue.

PubMed

Brunetti, Craig R

2014-01-01

To understand the molecular events responsible for morphological change requires the ability to examine gene expression in a wide range of organisms in addition to model systems to determine how the differences in gene expression correlate with phenotypic differences. There are approximately 12,000 species of butterflies, most, with distinct patterns on their wings. The most important tool for studying gene expression in butterflies is confocal imaging of butterfly tissue by indirect immunofluorescence using either cross-reactive antibodies from closely related species such as Drosophila or developing butterfly-specific antibodies. In this report, we describe how indirect immunofluorescence protocols can be used to visualize protein expression patterns on the butterfly wing imaginal disc and butterfly embryo.

Extinction threshold for spatial forest dynamics with height structure.

PubMed

Garcia-Domingo, Josep L; Saldaña, Joan

2011-05-07

We present a pair-approximation model for spatial forest dynamics defined on a regular lattice. The model assumes three possible states for a lattice site: empty (gap site), occupied by an immature tree, and occupied by a mature tree, and considers three nonlinearities in the dynamics associated to the processes of light interference, gap expansion, and recruitment. We obtain an expression of the basic reproduction number R(0) which, in contrast to the one obtained under the mean-field approach, uses information about the spatial arrangement of individuals close to extinction. Moreover, we analyze the corresponding survival-extinction transition of the forest and the spatial correlations among gaps, immature and mature trees close to this critical point. Predictions of the pair-approximation model are compared with those of a cellular automaton. Copyright © 2011 Elsevier Ltd. All rights reserved.

Atmospheric guidance law for planar skip trajectories

NASA Technical Reports Server (NTRS)

Mease, K. D.; Mccreary, F. A.

1985-01-01

The applicability of an approximate, closed-form, analytical solution to the equations of motion, as a basis for a deterministic guidance law for controlling the in-plane motion during a skip trajectory, is investigated. The derivation of the solution by the method of matched asymptotic expansions is discussed. Specific issues that arise in the application of the solution to skip trajectories are addressed. Based on the solution, an explicit formula for the approximate energy loss due to an atmospheric pass is derived. A guidance strategy is proposed that illustrates the use of the approximate solution. A numerical example shows encouraging performance.

Structural optimization with approximate sensitivities

NASA Technical Reports Server (NTRS)

Patnaik, S. N.; Hopkins, D. A.; Coroneos, R.

1994-01-01

Computational efficiency in structural optimization can be enhanced if the intensive computations associated with the calculation of the sensitivities, that is, gradients of the behavior constraints, are reduced. Approximation to gradients of the behavior constraints that can be generated with small amount of numerical calculations is proposed. Structural optimization with these approximate sensitivities produced correct optimum solution. Approximate gradients performed well for different nonlinear programming methods, such as the sequence of unconstrained minimization technique, method of feasible directions, sequence of quadratic programming, and sequence of linear programming. Structural optimization with approximate gradients can reduce by one third the CPU time that would otherwise be required to solve the problem with explicit closed-form gradients. The proposed gradient approximation shows potential to reduce intensive computation that has been associated with traditional structural optimization.

An Exact Form of Lilley's Equation with a Velocity Quadrupole/Temperature Dipole Source Term

NASA Technical Reports Server (NTRS)

Goldstein, Marvin E.

2001-01-01

There have been several attempts to introduce approximations into the exact form of Lilley's equation in order to express the source term as the sum of a quadrupole whose strength is quadratic in the fluctuating velocities and a dipole whose strength is proportional to the temperature fluctuations. The purpose of this note is to show that it is possible to choose the dependent (i.e., the pressure) variable so that this type of result can be derived directly from the Euler equations without introducing any additional approximations.

Approximate analytic expression for the Skyrmions crystal

NASA Astrophysics Data System (ADS)

Grandi, Nicolás; Sturla, Mauricio

2018-01-01

We find approximate solutions for the two-dimensional nonlinear Σ-model with Dzyalioshinkii-Moriya term, representing magnetic Skyrmions. They are built in an analytic form, by pasting different approximate solutions found in different regions of space. We verify that our construction reproduces the phenomenology known from numerical solutions and Monte Carlo simulations, giving rise to a Skyrmion lattice at an intermediate range of magnetic field, flanked by spiral and spin-polarized phases for low and high magnetic fields, respectively.

CC, CS, and IOS generalized phenomenological cross sections for atom--diatom mixtures

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

Fitz, D.E.; Kouri, D.J.; Evans, D.

1981-05-01

Close coupled expressions for phenomenological cross sections which describe transport properties of atom--diatom mixtures are obtained in the total-J coupling scheme and are related to the bracket integrals of kinetic theory. Coupled states and infinite order sudden expressions for the generalized phenomenological cross sections using initial, final, and average l-labeling are also given. Particular care is taken to use a phase convention for the CS and IOS approximations which is consistent with the Arthurs--Dalgarno formalism and which gives the correct behavior of degeneracy averaged differential cross sections.

A polymorphic DNA marker that represents a conserved expressed sequence in the region of the Huntington disease gene.

PubMed Central

Hayden, M R; Hewitt, J; Wasmuth, J J; Kastelein, J J; Langlois, S; Conneally, M; Haines, J; Smith, B; Hilbert, C; Allard, D

1988-01-01

A polymorphic marker (D4S62) that is genetically closely linked to D4S10 and is in the region of the gene for Huntington disease is described. A four-allele polymorphism is detected when HincII-digested DNA is hybridized with D4S62. D4S62 maps, by Southern blot analysis using somatic-cell hybrids, to 4p16.1 closer to the centromere than does D4S10. The use of the polymorphisms detected by D4S62 increases the informativeness of markers close to the gene for Huntington disease and will be useful for preclinical diagnosis. D4S62 detects transcripts of approximately 6,000 nucleotides in rat, mouse, and monkey liver and brain. This represents the first demonstration of conserved expressed sequences close to the gene for Huntington disease. Images Figure 1 Figure 2 Figure 3 Figure 4 Figure 6 PMID:2892395

76 FR 40987 - Medicare Program; Home Health Prospective Payment System Rate Update for Calendar Year 2012

Federal Register 2010, 2011, 2012, 2013, 2014

2011-07-12

... comments to be received before the close of the comment period. 3. By express or overnight mail. You may... they are received, generally beginning approximately 3 weeks after publication of a document, at the.... Background 2. Regulatory Update 3. Statutory Update 4. Loss-Sharing Ratio and Fixed Dollar Loss (FDL) Ratio 5...

Enhanced expression of rat hepatic CYP2B1/2B2 and 2E1 by pyridine: differential induction kinetics and molecular basis of expression.

PubMed

Kim, H; Putt, D; Reddy, S; Hollenberg, P F; Novak, R F

1993-11-01

Expression of the cytochrome P450 (CYP) 2B subfamily in rat and rabbit hepatic tissues after pyridine (PY) treatment has been examined, and the molecular basis for enhanced 2B1/2B2 expression has been determined. P450 expression was monitored using metabolic activity, sodium dodecyl sulfate-polyacrylamide gel electrophoresis and immunoblot analyses, and the identity of the proteins was confirmed through N-terminus microsequence analysis. PY caused a dose-dependent elevation of hepatic CYP2B1/B2B levels in rats, which ranged from 4- to 22-fold over the dosing regimen of 100 to 400 mg PY/kg/day, for 3 days, respectively. PY at low dose failed to induce CYP2B in rabbit hepatic tissue, suggesting a species-dependent response in 2B expression. Anti-2B1 IgG addition to PY-induced microsomes inhibited benzphetamine N-demethylase activity by only approximately 15%, in sharp contrast to the approximately 73% inhibition observed for phenobarbital-induced microsomes, suggesting the induction of other form(s) of P450 having benzphetamine N-demethylase activity. Northern blot analysis revealed that PY treatment increased 2B1 and 2B2 poly(A)+ RNA levels approximately 69- and approximately 34-fold, respectively, whereas the 2E1 poly(A)+ RNA levels failed to increase. The results of this study show that PY induces CYP2B1/2B2 and that induction is species-dependent and kinetically distinguishable from 2E1 induction. Moreover, 2B1/2B2 induction occurs as a result of elevated mRNA levels associated with either transcriptional activation or mRNA stabilization, and it differs from the mechanism of hepatic 2E1 induction by PY.

Joint Symbol Timing and CFO Estimation for OFDM/OQAM Systems in Multipath Channels

NASA Astrophysics Data System (ADS)

Fusco, Tilde; Petrella, Angelo; Tanda, Mario

2009-12-01

The problem of data-aided synchronization for orthogonal frequency division multiplexing (OFDM) systems based on offset quadrature amplitude modulation (OQAM) in multipath channels is considered. In particular, the joint maximum-likelihood (ML) estimator for carrier-frequency offset (CFO), amplitudes, phases, and delays, exploiting a short known preamble, is derived. The ML estimators for phases and amplitudes are in closed form. Moreover, under the assumption that the CFO is sufficiently small, a closed form approximate ML (AML) CFO estimator is obtained. By exploiting the obtained closed form solutions a cost function whose peaks provide an estimate of the delays is derived. In particular, the symbol timing (i.e., the delay of the first multipath component) is obtained by considering the smallest estimated delay. The performance of the proposed joint AML estimator is assessed via computer simulations and compared with that achieved by the joint AML estimator designed for AWGN channel and that achieved by a previously derived joint estimator for OFDM systems.

Color moiré simulations in contact-type 3-D displays.

PubMed

Lee, B-R; Son, J-Y; Chernyshov, O O; Lee, H; Jeong, I-K

2015-06-01

A new method of color moiré fringe simulation in the contact-type 3-D displays is introduced. The method allows simulating color moirés appearing in the displays, which cannot be approximated by conventional cosine approximation of a line grating. The color moirés are mainly introduced by the line width of the boundary lines between the elemental optics in and plate thickness of viewing zone forming optics. This is because the lines are hiding some parts of pixels under the viewing zone forming optics, and the plate thickness induces a virtual contraction of the pixels. The simulated color moiré fringes are closely matched with those appearing at the displays.

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.

ROCOPT: A user friendly interactive code to optimize rocket structural components

NASA Technical Reports Server (NTRS)

Rule, William K.

1989-01-01

ROCOPT is a user-friendly, graphically-interfaced, microcomputer-based computer program (IBM compatible) that optimizes rocket components by minimizing the structural weight. The rocket components considered are ring stiffened truncated cones and cylinders. The applied loading is static, and can consist of any combination of internal or external pressure, axial force, bending moment, and torque. Stress margins are calculated by means of simple closed form strength of material type equations. Stability margins are determined by approximate, orthotropic-shell, closed-form equations. A modified form of Powell's method, in conjunction with a modified form of the external penalty method, is used to determine the minimum weight of the structure subject to stress and stability margin constraints, as well as user input constraints on the structural dimensions. The graphical interface guides the user through the required data prompts, explains program options and graphically displays results for easy interpretation.

Computation of Stability Derivatives of an oscillating cone for specific heat ratio = 1.66

NASA Astrophysics Data System (ADS)

Shabana, Aysha; Monis, Renita Sharon; Crasta, Asha; Khan, S. A.

2018-05-01

In this paper the expressions for stiffness and Damping derivatives are obtained in a closed form for perfect gas where the flow is quasi-steady and axi-axisymmetric, and the nose semi angle of the cone is such that the Mach number M 2 behind the shock M 2 ≥ 2.5. Results are presented for an oscillating cone for gas with = 1.666, at different Mach numbers and semi cone angles. The Stiffness derivative decreases with pivot position and also with semi vertex angle, there is substantial change in the stiffness derivative when semi-vertex has been increased from 5 degrees to ten degrees, further increase in the semi-vertex angle results in marginal change in the stiffness derivative. Due the marginal change in the Mach number level there is marginal increase in the magnitude of the stability and with further increase in the inertia level the stability derivative conform to the Mach number independence principle. The present theory for Oscillating cone is restricted to quasi-steady case. Viscous effects have been neglected. The expressions so obtained for stability derivative in pitch are valid for a slender ogive which often approximates to the whole fuselage of an aircraft.

BAKABLE ULTRA-HIGH VACUUM VALVE

DOEpatents

Mark, J.T.; Gantz, I.H.

1962-07-10

S>This patent relates to a valve useful in applications involving successively closing and opening a communication between a chamber evacuated to an ultra-high vacuum condition of the order of 10/sup -10/ millimeters of mercury and another chamber or the ambient. The valve is capable of withstanding extended baking at 450 deg C and repeated opening and closing without repiacement of the valve seat (approximately 200 cycle limit). The seal is formed by mutual interdiffusion weld, coerced by a pneumatic actuator. (AEC)

Effect of damage on elastically tailored composite laminates

NASA Technical Reports Server (NTRS)

Armanios, Erian; Badir, Ashraf; Berdichevsky, Victor

1991-01-01

A variationally consistent theory is derived in order to predict the response of anisotropic thin-walled closed sections subjected to axial load, torsion and bending. The theory is valid for arbitrary cross-sections made of laminated composite materials with variable thickness and stiffness. Closed form expressions for the stiffness coefficients are provided as integrals in terms of lay-ups parameters and cross-sectional geometry. A comparison of stiffness coefficients and response with finite element predictions and a closed form solution is performed. The theory is applied to the investigation of the effect of damage on the extension-twist coupling in a thin-walled closed section beam. The damage is simulated as a progressive ply-by-ply failure. Results show that damage can have a significant effect on the extension-twist coupling.

Novel harmonic regularization approach for variable selection in Cox's proportional hazards model.

PubMed

Chu, Ge-Jin; Liang, Yong; Wang, Jia-Xuan

2014-01-01

Variable selection is an important issue in regression and a number of variable selection methods have been proposed involving nonconvex penalty functions. In this paper, we investigate a novel harmonic regularization method, which can approximate nonconvex Lq  (1/2 < q < 1) regularizations, to select key risk factors in the Cox's proportional hazards model using microarray gene expression data. The harmonic regularization method can be efficiently solved using our proposed direct path seeking approach, which can produce solutions that closely approximate those for the convex loss function and the nonconvex regularization. Simulation results based on the artificial datasets and four real microarray gene expression datasets, such as real diffuse large B-cell lymphoma (DCBCL), the lung cancer, and the AML datasets, show that the harmonic regularization method can be more accurate for variable selection than existing Lasso series methods.

The decay widths, the decay constants, and the branching fractions of a resonant state

NASA Astrophysics Data System (ADS)

de la Madrid, Rafael

2015-08-01

We introduce the differential and the total decay widths of a resonant (Gamow) state decaying into a continuum of stable states. When the resonance has several decay modes, we introduce the corresponding partial decay widths and branching fractions. In the approximation that the resonance is sharp, the expressions for the differential, partial and total decay widths of a resonant state bear a close resemblance with the Golden Rule. In such approximation, the branching fractions of a resonant state are the same as the standard branching fractions obtained by way of the Golden Rule. We also introduce dimensionless decay constants along with their associated differential decay constants, and we express experimentally measurable quantities such as the branching fractions and the energy distributions of decay events in terms of those dimensionless decay constants.

An Extension of the Krieger-Li-Iafrate Approximation to the Optimized-Effective-Potential Method

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

Wilson, B.G.

1999-11-11

The Krieger-Li-Iafrate approximation can be expressed as the zeroth order result of an unstable iterative method for solving the integral equation form of the optimized-effective-potential method. By pre-conditioning the iterate a first order correction can be obtained which recovers the bulk of quantal oscillations missing in the zeroth order approximation. A comparison of calculated total energies are given with Krieger-Li-Iafrate, Local Density Functional, and Hyper-Hartree-Fock results for non-relativistic atoms and ions.

Asymptotic Effect of Misspecification in the Random Part of the Multilevel Model

ERIC Educational Resources Information Center

Berkhof, Johannes; Kampen, Jarl Kennard

2004-01-01

The authors examine the asymptotic effect of omitting a random coefficient in the multilevel model and derive expressions for the change in (a) the variance components estimator and (b) the estimated variance of the fixed effects estimator. They apply the method of moments, which yields a closed form expression for the omission effect. In…

1,2-Diiodo-4,5-dimethyl­benzene

PubMed Central

Hathaway, Bruce A.; Kilgore, Uriah J.; Bond, Marcus R.

2009-01-01

The structure of the title compound, C8H8I2, conforms closely to the mm2 symmetry expected for the free mol­ecule and is the first reported structure of a diiodo­dimethyl­benzene. Repulsion by neighboring I atoms and the neighboring methyl groups opposite to them results in a slight elongation of the mol­ecule along the approximate twofold rotation axis that bis­ects the ring between the two I atoms. In the extended structure, the mol­ecules form inversion-related pairs which are organized in approximately hexa­gonal close-packed layers and the layers then stacked so that mol­ecules in neighboring layers abut head-to-tail in a manner that optimizes dipole–dipole inter­actions. PMID:21583089

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM.

PubMed

Singh, Brajesh K; Srivastava, Vineet K

2015-04-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations.

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM

PubMed Central

Singh, Brajesh K.; Srivastava, Vineet K.

2015-01-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations. PMID:26064639

Approximations to Joint Distributions of Definite Quadratic Forms

DTIC Science & Technology

1989-11-21

with To and 1 [ in partitioned form, we obtain T -i . =1 UOtu2tai23 . t V (A .3) where s’ = s - 1 and the expression inside brackets is the typical (u,v...errors in cephalometric measurement of three-dimensional distances on the maxilla." Angle Orthodont ., 36, 169-175. [27] Pearson, K. (1900). "On a

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.

Differential equation based method for accurate approximations in optimization

NASA Technical Reports Server (NTRS)

Pritchard, Jocelyn I.; Adelman, Howard M.

1990-01-01

This paper describes a method to efficiently and accurately approximate the effect of design changes on structural response. The key to this new method is to interpret sensitivity equations as differential equations that may be solved explicitly for closed form approximations, hence, the method is denoted the Differential Equation Based (DEB) method. Approximations were developed for vibration frequencies, mode shapes and static displacements. The DEB approximation method was applied to a cantilever beam and results compared with the commonly-used linear Taylor series approximations and exact solutions. The test calculations involved perturbing the height, width, cross-sectional area, tip mass, and bending inertia of the beam. The DEB method proved to be very accurate, and in msot cases, was more accurate than the linear Taylor series approximation. The method is applicable to simultaneous perturbation of several design variables. Also, the approximations may be used to calculate other system response quantities. For example, the approximations for displacement are used to approximate bending stresses.

Differential equation based method for accurate approximations in optimization

NASA Technical Reports Server (NTRS)

Pritchard, Jocelyn I.; Adelman, Howard M.

1990-01-01

A method to efficiently and accurately approximate the effect of design changes on structural response is described. The key to this method is to interpret sensitivity equations as differential equations that may be solved explicitly for closed form approximations, hence, the method is denoted the Differential Equation Based (DEB) method. Approximations were developed for vibration frequencies, mode shapes and static displacements. The DEB approximation method was applied to a cantilever beam and results compared with the commonly-used linear Taylor series approximations and exact solutions. The test calculations involved perturbing the height, width, cross-sectional area, tip mass, and bending inertia of the beam. The DEB method proved to be very accurate, and in most cases, was more accurate than the linear Taylor series approximation. The method is applicable to simultaneous perturbation of several design variables. Also, the approximations may be used to calculate other system response quantities. For example, the approximations for displacements are used to approximate bending stresses.

Structural features of a close homologue of L1 (CHL1) in the mouse: a new member of the L1 family of neural recognition molecules.

PubMed

Holm, J; Hillenbrand, R; Steuber, V; Bartsch, U; Moos, M; Lübbert, H; Montag, D; Schachner, M

1996-08-01

We have identified a close homologue of L1 (CHL1) in the mouse. CHL1 comprises an N-terminal signal sequence, six immunoglobulin (Ig)-like domains, 4.5 fibronectin type III (FN)-like repeats, a transmembrane domain and a C-terminal, most likely intracellular domain of approximately 100 amino acids. CHL1 is most similar in its extracellular domain to chicken Ng-CAM (approximately 40% amino acid identity), followed by mouse L1, chicken neurofascin, chicken Nr-CAM, Drosophila neuroglian and zebrafish L1.1 (37-28% amino acid identity), and mouse F3, rat TAG-1 and rat BIG-1 (approximately 27% amino acid identity). The similarity with other members of the Ig superfamily [e.g. neural cell adhesion molecule (N-CAM), DCC, HLAR, rse] is 16-11%. The intracellular domain is most similar to mouse and chicken Nr-CAM, mouse and rat neurofascin (approximately 60% amino acid identity) followed by chicken neurofascin and Ng-CAM, Drosophila neuroglian and zebrafish L1.1 and L1.2 (approximately 40% amino acid identity). Besides the high overall homology and conserved modular structure among previously recognized members of the L1 family (mouse/human L1/rat NILE; chicken Ng-CAM; chicken/mouse Nr-CAM; Drosophila neuroglian; zebrafish L1.1 and L1.2; chicken/mouse neurofascin/rat ankyrin-binding glycoprotein), criteria characteristic of L1 were identified with regard to the number of amino acids between positions of conserved amino acid residues defining distances within and between two adjacent Ig-like domains and FN-like repeats. These show a collinearity in the six Ig-like domains and four adjacent FN-like repeats that is remarkably conserved between L1 and molecules containing these modules (designated the L1 family cassette), including the GPI-linked forms of the F3 subgroup (mouse F3/chicken F11/human CNTN1; rat BIG-1/mouse PANG; rat TAG-1/mouse TAX-1/chicken axonin-1). The colorectal cancer molecule (DCC), previously introduced as an N-CAM-like molecule, conforms to the L1 family cassette. Other structural features of CHL 1 shared between members of the L1 family are a high degree of N-glycosidically linked carbohydrates (approximately 20% of its molecular mass), which include the HNK-1 carbohydrate structure, and a pattern of protein fragments comprising a major 185 kDa band and smaller fragments of 165 and 125 kDa. As for the other L1 family members, predominant expression of CHL1 is observed in the nervous system and at later developmental stages. In the central nervous system CHL1 is expressed by neurons, but, in contrast to L1, also by glial cells. Our findings suggest a common ancestral L1-like molecule which evolved via gene duplication to generate a diversity of structurally and functionally distinct yet similar molecules.

Delay in polling systems in heavy traffic

NASA Astrophysics Data System (ADS)

van der Mei, Robert D.

1998-10-01

We study the delay in asymmetric cyclic polling systems with general mixtures of gated and exhaustive service, with generally distributed service times and switch-over times, in heavy traffic. We obtain closed-form expressions for all moments of the delay incurred at each of the queues. The expressions are strikingly simple and can even be expressed as finite products of known factors. The results provide new insights into the heavy-traffic behavior of polling systems.

Optimal CCD readout by digital correlated double sampling

NASA Astrophysics Data System (ADS)

Alessandri, C.; Abusleme, A.; Guzman, D.; Passalacqua, I.; Alvarez-Fontecilla, E.; Guarini, M.

2016-01-01

Digital correlated double sampling (DCDS), a readout technique for charge-coupled devices (CCD), is gaining popularity in astronomical applications. By using an oversampling ADC and a digital filter, a DCDS system can achieve a better performance than traditional analogue readout techniques at the expense of a more complex system analysis. Several attempts to analyse and optimize a DCDS system have been reported, but most of the work presented in the literature has been experimental. Some approximate analytical tools have been presented for independent parameters of the system, but the overall performance and trade-offs have not been yet modelled. Furthermore, there is disagreement among experimental results that cannot be explained by the analytical tools available. In this work, a theoretical analysis of a generic DCDS readout system is presented, including key aspects such as the signal conditioning stage, the ADC resolution, the sampling frequency and the digital filter implementation. By using a time-domain noise model, the effect of the digital filter is properly modelled as a discrete-time process, thus avoiding the imprecision of continuous-time approximations that have been used so far. As a result, an accurate, closed-form expression for the signal-to-noise ratio at the output of the readout system is reached. This expression can be easily optimized in order to meet a set of specifications for a given CCD, thus providing a systematic design methodology for an optimal readout system. Simulated results are presented to validate the theory, obtained with both time- and frequency-domain noise generation models for completeness.

Analytical approximations for effective relative permeability in the capillary limit

NASA Astrophysics Data System (ADS)

Rabinovich, Avinoam; Li, Boxiao; Durlofsky, Louis J.

2016-10-01

We present an analytical method for calculating two-phase effective relative permeability, krjeff, where j designates phase (here CO2 and water), under steady state and capillary-limit assumptions. These effective relative permeabilities may be applied in experimental settings and for upscaling in the context of numerical flow simulations, e.g., for CO2 storage. An exact solution for effective absolute permeability, keff, in two-dimensional log-normally distributed isotropic permeability (k) fields is the geometric mean. We show that this does not hold for krjeff since log normality is not maintained in the capillary-limit phase permeability field (Kj=k·krj) when capillary pressure, and thus the saturation field, is varied. Nevertheless, the geometric mean is still shown to be suitable for approximating krjeff when the variance of ln⁡k is low. For high-variance cases, we apply a correction to the geometric average gas effective relative permeability using a Winsorized mean, which neglects large and small Kj values symmetrically. The analytical method is extended to anisotropically correlated log-normal permeability fields using power law averaging. In these cases, the Winsorized mean treatment is applied to the gas curves for cases described by negative power law exponents (flow across incomplete layers). The accuracy of our analytical expressions for krjeff is demonstrated through extensive numerical tests, using low-variance and high-variance permeability realizations with a range of correlation structures. We also present integral expressions for geometric-mean and power law average krjeff for the systems considered, which enable derivation of closed-form series solutions for krjeff without generating permeability realizations.

Analytical approximation of the InGaZnO thin-film transistors surface potential

NASA Astrophysics Data System (ADS)

Colalongo, Luigi

2016-10-01

Surface-potential-based mathematical models are among the most accurate and physically based compact models of thin-film transistors, and in turn of indium gallium zinc oxide TFTs, available today. However, the need of iterative computations of the surface potential limits their computational efficiency and diffusion in CAD applications. The existing closed-form approximations of the surface potential are based on regional approximations and empirical smoothing functions that could result not accurate enough in particular to model transconductances and transcapacitances. In this work we present an extremely accurate (in the range of nV) and computationally efficient non-iterative approximation of the surface potential that can serve as a basis for advanced surface-potential-based indium gallium zinc oxide TFTs models.

Thermodynamics of Quantum Gases for the Entire Range of Temperature

ERIC Educational Resources Information Center

Biswas, Shyamal; Jana, Debnarayan

2012-01-01

We have analytically explored the thermodynamics of free Bose and Fermi gases for the entire range of temperature, and have extended the same for harmonically trapped cases. We have obtained approximate chemical potentials for the quantum gases in closed forms of temperature so that the thermodynamic properties of the quantum gases become…

The Influence of Technological Literacy on Students' Writing

ERIC Educational Resources Information Center

Turner, Kristen H.; Katic, Elvira K.

2009-01-01

Many forms of technological communication exist in non-linear environments and there is potential for new approaches to learning and teaching which may more closely approximate naturalistic and authentic approaches to learning. The following study examined the ways in which high school students were influenced by technology as they wrote and how…

Asymptotic Poincare lemma and its applications

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

Ziolkowski, R.W.; Deschamps, G.A.

1984-05-01

An asymptotic version of Poincare's lemma is defined and solutions are obtained with the calculus of exterior differential forms. They are used to construct the asymptotic approximations of multidimensional oscillatory integrals whose forms are commonly encountered, for example, in electromagnetic problems. In particular, the boundary and stationary point evaluations of these integrals are considered. The former is applied to the Kirchhoff representation of a scalar field diffracted through an aperture and simply recovers the Maggi-Rubinowicz-Miyamoto-Wolf results. Asymptotic approximations in the presence of other (standard) critical points are also discussed. Techniques developed for the asymptotic Poincare lemma are used to generatemore » a general representation of the Leray form. All of the (differential form) expressions presented are generalizations of known (vector calculus) results. 14 references, 4 figures.« less

Ensemble-based virtual screening reveals dual-inhibitors for the p53-MDM2/MDMX interactions.

PubMed

Barakat, Khaled; Mane, Jonathan; Friesen, Douglas; Tuszynski, Jack

2010-02-26

The p53 protein, a guardian of the genome, is inactivated by mutations or deletions in approximately half of human tumors. While in the rest of human tumors, p53 is expressed in wild-type form, yet it is inhibited by over-expression of its cellular regulators MDM2 and MDMX proteins. Although the p53-binding sites within the MDMX and MDM2 proteins are closely related, known MDM2 small-molecule inhibitors have been shown experimentally not to bind to its homolog, MDMX. As a result, the activity of these inhibitors including Nutlin3 is compromised in tumor cells over-expressing MDMX, preventing these compounds from fully activating the p53 protein. Here, we applied the relaxed complex scheme (RCS) to allow for the full receptor flexibility in screening for dual-inhibitors that can mutually antagonize the two p53-regulator proteins. First, we filtered the NCI diversity set, DrugBank compounds and a derivative library for MDM2-inhibitors against 28 dominant MDM2-conformations. Then, we screened the MDM2 top hits against the binding site of p53 within the MDMX target. Results described herein identify a set of compounds that have been computationally predicted to ultimately activate the p53 pathway in tumor cells retaining the wild-type protein. Crown Copyright 2009. Published by Elsevier Inc. All rights reserved.

Linear approximations of nonlinear systems

NASA Technical Reports Server (NTRS)

Hunt, L. R.; Su, R.

1983-01-01

The development of a method for designing an automatic flight controller for short and vertical take off aircraft is discussed. This technique involves transformations of nonlinear systems to controllable linear systems and takes into account the nonlinearities of the aircraft. In general, the transformations cannot always be given in closed form. Using partial differential equations, an approximate linear system called the modified tangent model was introduced. A linear transformation of this tangent model to Brunovsky canonical form can be constructed, and from this the linear part (about a state space point x sub 0) of an exact transformation for the nonlinear system can be found. It is shown that a canonical expansion in Lie brackets about the point x sub 0 yields the same modified tangent model.

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

Surface expression of the Chicxulub crater

PubMed

Pope, K O; Ocampo, A C; Kinsland, G L; Smith, R

1996-06-01

Analyses of geomorphic, soil, and topographic data from the northern Yucatan Peninsula, Mexico, confirm that the buried Chicxulub impact crater has a distinct surface expression and that carbonate sedimentation throughout the Cenozoic has been influenced by the crater. Late Tertiary sedimentation was mostly restricted to the region within the buried crater, and a semicircular moat existed until at least Pliocene time. The topographic expression of the crater is a series of features concentric with the crater. The most prominent is an approximately 83-km-radius trough or moat containing sinkholes (the Cenote ring). Early Tertiary surfaces rise abruptly outside the moat and form a stepped topography with an outer trough and ridge crest at radii of approximately 103 and approximately 129 km, respectively. Two discontinuous troughs lie within the moat at radii of approximately 41 and approximately 62 km. The low ridge between the inner troughs corresponds to the buried peak ring. The moat corresponds to the outer edge of the crater floor demarcated by a major ring fault. The outer trough and the approximately 62-km-radius inner trough also mark buried ring faults. The ridge crest corresponds to the topographic rim of the crater as modified by postimpact processes. These interpretations support previous findings that the principal impact basin has a diameter of approximately 180 km, but concentric, low-relief slumping extends well beyond this diameter and the eroded crater rim may extend to a diameter of approximately 260 km.

Minimal-Approximation-Based Distributed Consensus Tracking of a Class of Uncertain Nonlinear Multiagent Systems With Unknown Control Directions.

PubMed

Choi, Yun Ho; Yoo, Sung Jin

2017-03-28

A minimal-approximation-based distributed adaptive consensus tracking approach is presented for strict-feedback multiagent systems with unknown heterogeneous nonlinearities and control directions under a directed network. Existing approximation-based consensus results for uncertain nonlinear multiagent systems in lower-triangular form have used multiple function approximators in each local controller to approximate unmatched nonlinearities of each follower. Thus, as the follower's order increases, the number of the approximators used in its local controller increases. However, the proposed approach employs only one function approximator to construct the local controller of each follower regardless of the order of the follower. The recursive design methodology using a new error transformation is derived for the proposed minimal-approximation-based design. Furthermore, a bounding lemma on parameters of Nussbaum functions is presented to handle the unknown control direction problem in the minimal-approximation-based distributed consensus tracking framework and the stability of the overall closed-loop system is rigorously analyzed in the Lyapunov sense.

Fast-slow asymptotic for semi-analytical ignition criteria in FitzHugh-Nagumo system.

PubMed

Bezekci, B; Biktashev, V N

2017-09-01

We study the problem of initiation of excitation waves in the FitzHugh-Nagumo model. Our approach follows earlier works and is based on the idea of approximating the boundary between basins of attraction of propagating waves and of the resting state as the stable manifold of a critical solution. Here, we obtain analytical expressions for the essential ingredients of the theory by singular perturbation using two small parameters, the separation of time scales of the activator and inhibitor and the threshold in the activator's kinetics. This results in a closed analytical expression for the strength-duration curve.

Molecular cloning and expression analysis of sea bass (Dicentrarchus labrax L.) tumor necrosis factor-alpha (TNF-alpha).

PubMed

Nascimento, Diana S; Pereira, Pedro J B; Reis, Marta I R; do Vale, Ana; Zou, Jun; Silva, Manuel T; Secombes, Christopher J; dos Santos, Nuno M S

2007-09-01

In the search for pro-inflammatory genes in sea bass a TNF-alpha gene was cloned and sequenced. The sea bass TNF-alpha (sbTNF-alpha) putative protein conserves the TNF-alpha family signature, as well as the two cysteines usually involved in the formation of a disulfide bond. The mouse TNF-alpha Thr-Leu cleavage sequence and a potential transmembrane domain were also found, suggesting that sbTNF-alpha exists as two forms: a approximately 28 kDa membrane-bound form and a approximately 18.4 kDa soluble protein. The single copy sbTNF-alpha gene contains a four exon-three intron structure similar to other known TNF-alpha genes. Homology modeling of sbTNF-alpha is compatible with the trimeric quaternary architecture of its mammalian counterparts. SbTNF-alpha is constitutively expressed in several unstimulated tissues, and was not up-regulated in the spleen and head-kidney, in response to UV-killed Photobacterium damselae subsp. piscicida. However, an increase of sbTNF-alpha expression was detected in the head-kidney during an experimental infection using the same pathogen.

Closed Form Solutions for Unsteady Free Convection Flow of a Second Grade Fluid over an Oscillating Vertical Plate

PubMed Central

Ali, Farhad; Khan, Ilyas; Shafie, Sharidan

2014-01-01

Closed form solutions for unsteady free convection flows of a second grade fluid near an isothermal vertical plate oscillating in its plane using the Laplace transform technique are established. Expressions for velocity and temperature are obtained and displayed graphically for different values of Prandtl number Pr, thermal Grashof number Gr, viscoelastic parameter α, phase angle ωτ and time τ. Numerical values of skin friction τ 0 and Nusselt number Nu are shown in tables. Some well-known solutions in literature are reduced as the limiting cases of the present solutions. PMID:24551033

Novel Harmonic Regularization Approach for Variable Selection in Cox's Proportional Hazards Model

PubMed Central

Chu, Ge-Jin; Liang, Yong; Wang, Jia-Xuan

2014-01-01

Variable selection is an important issue in regression and a number of variable selection methods have been proposed involving nonconvex penalty functions. In this paper, we investigate a novel harmonic regularization method, which can approximate nonconvex Lq  (1/2 < q < 1) regularizations, to select key risk factors in the Cox's proportional hazards model using microarray gene expression data. The harmonic regularization method can be efficiently solved using our proposed direct path seeking approach, which can produce solutions that closely approximate those for the convex loss function and the nonconvex regularization. Simulation results based on the artificial datasets and four real microarray gene expression datasets, such as real diffuse large B-cell lymphoma (DCBCL), the lung cancer, and the AML datasets, show that the harmonic regularization method can be more accurate for variable selection than existing Lasso series methods. PMID:25506389

Formation of nanooctahedra in molybdenum disulfide and molybdenum diselenide using pulsed laser vaporization.

PubMed

Parilla, Philip A; Dillon, Anne C; Parkinson, Bruce A; Jones, Kim M; Alleman, Jeff; Riker, Gerald; Ginley, David S; Heben, Michael J

2004-05-20

Pulsed laser vaporization has been used to produce nanooctahedra of MoS2 and MoSe2. The nanooctahedra primarily form in two- or three-layer nested octahedra, although nesting up to five layers has been observed. Tilting the TEM sample stage and mapping how the images of single particles transformed provided the evidence to verify their octahedral geometry. Analysis of 30 two- and three-layered octahedra showed that their outer edge lengths clustered at approximately 3.8 nm and approximately 5.1 nm, respectively. This discreet sizing and the high symmetry of these closed nanooctahedra represent the closest inorganic analogy yet to the carbon fullerenes. The geometrical implications for forming octahedra from these layered compounds are investigated by considering different atomic arrangements assuming either trigonal prismatic or octahedral coordination around the Mo atom and yields two possible configurations for the actual structure of the nanooctahedra. A preliminary survey of pulsed laser vaporization of other layered metal chalcogenides shows that these dichalcogenides differ in their tendency to form small closed layered fullerene-like structures. These materials can be ranked from highest tendency to lowest as follows: NbSe2, WS2, WSe2, SnS2, TaS2, GaS, ReS2, and MoTe2.

On the closed form mechanistic modeling of milling: Specific cutting energy, torque, and power

NASA Astrophysics Data System (ADS)

Bayoumi, A. E.; Yücesan, G.; Hutton, D. V.

1994-02-01

Specific energy in metal cutting, defined as the energy expended in removing a unit volume of workpiece material, is formulated and determined using a previously developed closed form mechanistic force model for milling operations. Cutting power is computed from the cutting torque, cutting force, kinematics of the cutter, and the volumetric material removal rate. Closed form expressions for specific cutting energy were formulated and found to be functions of the process parameters: pressure and friction for both rake and flank surfaces and chip flow angle at the rake face of the tool. Friction is found to play a very important role in cutting torque and power. Experiments were carried out to determine the effects of feedrate, cutting speed, workpiece material, and flank wear land width on specific cutting energy. It was found that the specific cutting energy increases with a decrease in the chip thickness and with an increase in flank wear land.

Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard

NASA Astrophysics Data System (ADS)

Roquet, F.; Madec, G.; McDougall, Trevor J.; Barker, Paul M.

2015-06-01

A new set of approximations to the standard TEOS-10 equation of state are presented. These follow a polynomial form, making it computationally efficient for use in numerical ocean models. Two versions are provided, the first being a fit of density for Boussinesq ocean models, and the second fitting specific volume which is more suitable for compressible models. Both versions are given as the sum of a vertical reference profile (6th-order polynomial) and an anomaly (52-term polynomial, cubic in pressure), with relative errors of ∼0.1% on the thermal expansion coefficients. A 75-term polynomial expression is also presented for computing specific volume, with a better accuracy than the existing TEOS-10 48-term rational approximation, especially regarding the sound speed, and it is suggested that this expression represents a valuable approximation of the TEOS-10 equation of state for hydrographic data analysis. In the last section, practical aspects about the implementation of TEOS-10 in ocean models are discussed.

Optimum allocation of redundancy among subsystems connected in series. Ph.D. Thesis - Case Western Reserve Univ., Sep. 1970

NASA Technical Reports Server (NTRS)

Bien, D. D.

1973-01-01

This analysis considers the optimum allocation of redundancy in a system of serially connected subsystems in which each subsystem is of the k-out-of-n type. Redundancy is optimally allocated when: (1) reliability is maximized for given costs; or (2) costs are minimized for given reliability. Several techniques are presented for achieving optimum allocation and their relative merits are discussed. Approximate solutions in closed form were attainable only for the special case of series-parallel systems and the efficacy of these approximations is discussed.

Approximate solutions to Mathieu's equation

NASA Astrophysics Data System (ADS)

Wilkinson, Samuel A.; Vogt, Nicolas; Golubev, Dmitry S.; Cole, Jared H.

2018-06-01

Mathieu's equation has many applications throughout theoretical physics. It is especially important to the theory of Josephson junctions, where it is equivalent to Schrödinger's equation. Mathieu's equation can be easily solved numerically, however there exists no closed-form analytic solution. Here we collect various approximations which appear throughout the physics and mathematics literature and examine their accuracy and regimes of applicability. Particular attention is paid to quantities relevant to the physics of Josephson junctions, but the arguments and notation are kept general so as to be of use to the broader physics community.

Oligomeric state of purified transient receptor potential melastatin-1 (TRPM1), a protein essential for dim light vision.

PubMed

Agosto, Melina A; Zhang, Zhixian; He, Feng; Anastassov, Ivan A; Wright, Sara J; McGehee, Jennifer; Wensel, Theodore G

2014-09-26

Transient receptor potential melastatin-1 (TRPM1) is essential for the light-induced depolarization of retinal ON bipolar cells. TRPM1 likely forms a multimeric channel complex, although almost nothing is known about the structure or subunit composition of channels formed by TRPM1 or any of its close relatives. Recombinant TRPM1 was robustly expressed in insect cells, but only a small fraction was localized to the plasma membrane. Similar intracellular localization was observed when TRPM1 was heterologously expressed in mammalian cells. TRPM1 was affinity-purified from Sf9 cells and complexed with amphipol, followed by detergent removal. In blue native gels and size exclusion chromatography, TRPM1 migrated with a mobility consistent with detergent- or amphipol-bound dimers. Cross-linking experiments were also consistent with a dimeric subunit stoichiometry, and cryoelectron microscopy and single particle analysis without symmetry imposition yielded a model with approximate 2-fold symmetrical features. Finally, electron microscopy of TRPM1-antibody complexes revealed a large particle that can accommodate TRPM1 and two antibody molecules. Taken together, these data indicate that purified TRPM1 is mostly dimeric. The three-dimensional structure of TRPM1 dimers is characterized by a small putative transmembrane domain and a larger domain with a hollow cavity. Blue native gels of solubilized mouse retina indicate that TRPM1 is present in two distinct complexes: one similar in size to the recombinant protein and one much larger. Because dimers are likely not functional ion channels, these results suggest that additional partner subunits participate in forming the transduction channel required for dim light vision and the ON pathway. © 2014 by The American Society for Biochemistry and Molecular Biology, Inc.

Spectral simplicity of apparent complexity. II. Exact complexities and complexity spectra

NASA Astrophysics Data System (ADS)

Riechers, Paul M.; Crutchfield, James P.

2018-03-01

The meromorphic functional calculus developed in Part I overcomes the nondiagonalizability of linear operators that arises often in the temporal evolution of complex systems and is generic to the metadynamics of predicting their behavior. Using the resulting spectral decomposition, we derive closed-form expressions for correlation functions, finite-length Shannon entropy-rate approximates, asymptotic entropy rate, excess entropy, transient information, transient and asymptotic state uncertainties, and synchronization information of stochastic processes generated by finite-state hidden Markov models. This introduces analytical tractability to investigating information processing in discrete-event stochastic processes, symbolic dynamics, and chaotic dynamical systems. Comparisons reveal mathematical similarities between complexity measures originally thought to capture distinct informational and computational properties. We also introduce a new kind of spectral analysis via coronal spectrograms and the frequency-dependent spectra of past-future mutual information. We analyze a number of examples to illustrate the methods, emphasizing processes with multivariate dependencies beyond pairwise correlation. This includes spectral decomposition calculations for one representative example in full detail.

Effects of the target aspect ratio and intrinsic reactivity onto diffusive search in bounded domains

NASA Astrophysics Data System (ADS)

Grebenkov, Denis S.; Metzler, Ralf; Oshanin, Gleb

2017-10-01

We study the mean first passage time (MFPT) to a reaction event on a specific site in a cylindrical geometry—characteristic, for instance, for bacterial cells, with a concentric inner cylinder representing the nuclear region of the bacterial cell. A similar problem emerges in the description of a diffusive search by a transcription factor protein for a specific binding region on a single strand of DNA. We develop a unified theoretical approach to study the underlying boundary value problem which is based on a self-consistent approximation of the mixed boundary condition. Our approach permits us to derive explicit, novel, closed-form expressions for the MFPT valid for a generic setting with an arbitrary relation between the system parameters. We analyse this general result in the asymptotic limits appropriate for the above-mentioned biophysical problems. Our investigation reveals the crucial role of the target aspect ratio and of the intrinsic reactivity of the binding region, which were disregarded in previous studies. Theoretical predictions are confirmed by numerical simulations.

Exact simulation of max-stable processes.

PubMed

Dombry, Clément; Engelke, Sebastian; Oesting, Marco

2016-06-01

Max-stable processes play an important role as models for spatial extreme events. Their complex structure as the pointwise maximum over an infinite number of random functions makes their simulation difficult. Algorithms based on finite approximations are often inexact and computationally inefficient. We present a new algorithm for exact simulation of a max-stable process at a finite number of locations. It relies on the idea of simulating only the extremal functions, that is, those functions in the construction of a max-stable process that effectively contribute to the pointwise maximum. We further generalize the algorithm by Dieker & Mikosch (2015) for Brown-Resnick processes and use it for exact simulation via the spectral measure. We study the complexity of both algorithms, prove that our new approach via extremal functions is always more efficient, and provide closed-form expressions for their implementation that cover most popular models for max-stable processes and multivariate extreme value distributions. For simulation on dense grids, an adaptive design of the extremal function algorithm is proposed.

Heterologous expression of Trametes versicolor laccase in Saccharomyces cerevisiae.

PubMed

Iimura, Yosuke; Sonoki, Tomonori; Habe, Hiroshi

2018-01-01

Laccase is used in various industrial fields, and it has been the subject of numerous studies. Trametes versicolor laccase has one of the highest redox potentials among the various forms of this enzyme. In this study, we optimized the expression of laccase in Saccharomyces cerevisiae. Optimizing the culture conditions resulted in an improvement in the expression level, and approximately 45 U/L of laccase was functionally secreted in the culture. The recombinant laccase was found to be a heavily hypermannosylated glycoprotein, and the molecular weight of the carbohydrate chain was approximately 60 kDa. These hypermannosylated glycans lowered the substrate affinity, but the optimum pH and thermo-stability were not changed by these hypermannosylated glycans. This functional expression system described here will aid in molecular evolutionary studies conducted to generate new variants of laccase. Copyright © 2017 Elsevier Inc. All rights reserved.

Light-induced cross transport phenomena in a single-component gas

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

Chermyaninov, I. V.; Chernyak, V. G., E-mail: Vladimir.Chernyak@usu.ru

2013-07-15

The cross transport processes that occur in a single-component gas in a capillary and are caused by resonance laser radiation and pressure and temperature gradients are studied. An expression for entropy production is derived using a system of kinetic Boltzmann equations in a linear approximation. The kinetic coefficients that determine the transport processes are shown to satisfy the Onsager reciprocal relations at any Knudsen numbers and any character of the elastic interaction of gas particles with the capillary surface. The light-induced baro- and thermoeffects that take place in a closed heat-insulated system in the field of resonance laser radiation aremore » considered. Analytical expressions are obtained for the Onsager coefficients in an almost free-molecular regime. The light-induced pressure and temperature gradients that appear in a closed heat-insulated capillary under typical experimental conditions are numerically estimated.« less

Radiation Pattern of Chair Armed Microstrip Antenna

NASA Astrophysics Data System (ADS)

Mishra, Rabindra Kishore; Sahu, Kumar Satyabrat

2016-12-01

This work analyzes planar antenna conformable to chair arm shaped surfaces for WLAN application. Closed form expressions for its radiation pattern are developed and validated using measurements on prototype and commercial EM code at 2.4 GHz.

Note on use of slope diffraction coefficients for aperture antennas on finite ground planes

NASA Technical Reports Server (NTRS)

Cockrell, C. R.; Beck, F. B.

1995-01-01

The use of slope diffraction coefficients along with regular diffraction coefficients for calculating the radiation patterns of aperture antennas in a finite ground plane is investigated. Explicit expressions for regular diffraction coefficients and slope diffraction coefficients are presented. The expressions for the incident magnetic field in terms of the magnetic current in the aperture are given. The slope of the incident magnetic field is calculated and closed form expressions are presented.

Adaptive Neural Network Based Control of Noncanonical Nonlinear Systems.

PubMed

Zhang, Yanjun; Tao, Gang; Chen, Mou

2016-09-01

This paper presents a new study on the adaptive neural network-based control of a class of noncanonical nonlinear systems with large parametric uncertainties. Unlike commonly studied canonical form nonlinear systems whose neural network approximation system models have explicit relative degree structures, which can directly be used to derive parameterized controllers for adaptation, noncanonical form nonlinear systems usually do not have explicit relative degrees, and thus their approximation system models are also in noncanonical forms. It is well-known that the adaptive control of noncanonical form nonlinear systems involves the parameterization of system dynamics. As demonstrated in this paper, it is also the case for noncanonical neural network approximation system models. Effective control of such systems is an open research problem, especially in the presence of uncertain parameters. This paper shows that it is necessary to reparameterize such neural network system models for adaptive control design, and that such reparameterization can be realized using a relative degree formulation, a concept yet to be studied for general neural network system models. This paper then derives the parameterized controllers that guarantee closed-loop stability and asymptotic output tracking for noncanonical form neural network system models. An illustrative example is presented with the simulation results to demonstrate the control design procedure, and to verify the effectiveness of such a new design method.

Efficient secretory expression of the sweet-tasting protein brazzein in the yeast Kluyveromyces lactis.

PubMed

Jo, Hyun-Joo; Noh, Jin-Seok; Kong, Kwang-Hoon

2013-08-01

Brazzein is an intensely sweet-tasting protein with high water solubility, heat stability, and taste properties resembling those of carbohydrate sweeteners. In the present study, we describe the expression of the synthetic gene encoding brazzein, a sweet protein in the yeast Kluyveromyces lactis. The synthetic brazzein gene was designed based on the biased codons of the yeast, so as to optimize its expression, as well as on the extracellular secretion for expression in an active, soluble form. The synthesized brazzein gene was cloned into the secretion vector pKLAC2, which contains the yeast prepropeptide signal from the Saccharomycescerevisiae α-mating factor. The constructed plasmid pKLAC2-des-pE1M-brazzein was introduced into the yeast K. lactis GG799. The yeast transformants were cultured for high-yield secretion of the recombinant des-pE1M-brazzein in YPGal medium for 96 h at 30°C. The expressed recombinant des-pE1M-brazzein was purified by CM-Sepharose column chromatography and approximately 104 mg/L was obtained. The purity and conformational state of the recombinant des-pE1M-brazzein were confirmed using SDS-PAGE, HPLC, and circular dichroism. The identity of the recombinant protein was also confirmed by N-terminal amino acid analysis and taste testing. The purified recombinant des-pE1M-brazzein had an intrinsic sweetness in its minor form, approximately 2130 times sweeter than sucrose on a weight basis. These results demonstrate that the K. lactis expression system is useful for producing the recombinant brazzein in active form at a high yield with attributes useful in the food industry. Copyright © 2013 Elsevier Inc. All rights reserved.

Too hot to handle? Analytic solutions for massive neutrino or warm dark matter cosmologies

NASA Astrophysics Data System (ADS)

Slepian, Zachary; Portillo, Stephen K. N.

2018-05-01

We obtain novel closed-form solutions to the Friedmann equation for cosmological models containing a component whose equation of state is that of radiation (w = 1/3) at early times and that of cold pressureless matter (w = 0) at late times. The equation of state smoothly transitions from the early to late-time behavior and exactly describes the evolution of a species with a Dirac Delta function distribution in momentum magnitudes |p_0| (i.e. all particles have the same |p_0|). Such a component, here termed "hot matter", is an approximate model for both neutrinos and warm dark matter. We consider it alone and in combination with cold matter and with radiation, also obtaining closed-form solutions for the growth of super-horizon perturbations in each case. The idealized model recovers t(a) to better than 1.5% accuracy for all a relative to a Fermi-Dirac distribution (as describes neutrinos). We conclude by adding the second moment of the distribution to our exact solution and then generalizing to include all moments of an arbitrary momentum distribution in a closed-form solution.

Too hot to handle? Analytic solutions for massive neutrino or warm dark matter cosmologies

NASA Astrophysics Data System (ADS)

Slepian, Zachary; Portillo, Stephen K. N.

2018-07-01

We obtain novel closed-form solutions to the Friedmann equation for cosmological models containing a component whose equation of state is that of radiation (w = 1/3) at early times and that of cold pressureless matter (w= 0) at late times. The equation of state smoothly transitions from the early- to late-time behaviour and exactly describes the evolution of a species with a Dirac delta function distribution in momentum magnitudes |{p}_0| (i.e. all particles have the same |{p}_0|). Such a component, here termed `hot matter', is an approximate model for both neutrinos and warm dark matter. We consider it alone and in combination with cold matter and with radiation, also obtaining closed-form solutions for the growth of superhorizon perturbations in each case. The idealized model recovers t(a) to better than 1.5 per cent accuracy for all a relative to a Fermi-Dirac distribution (as describes neutrinos). We conclude by adding the second moment of the distribution to our exact solution and then generalizing to include all moments of an arbitrary momentum distribution in a closed-form solution.

Correlation Energies from the Two-Component Random Phase Approximation.

PubMed

Kühn, Michael

2014-02-11

The correlation energy within the two-component random phase approximation accounting for spin-orbit effects is derived. The resulting plasmon equation is rewritten-analogously to the scalar relativistic case-in terms of the trace of two Hermitian matrices for (Kramers-restricted) closed-shell systems and then represented as an integral over imaginary frequency using the resolution of the identity approximation. The final expression is implemented in the TURBOMOLE program suite. The code is applied to the computation of equilibrium distances and vibrational frequencies of heavy diatomic molecules. The efficiency is demonstrated by calculation of the relative energies of the Oh-, D4h-, and C5v-symmetric isomers of Pb6. Results within the random phase approximation are obtained based on two-component Kohn-Sham reference-state calculations, using effective-core potentials. These values are finally compared to other two-component and scalar relativistic methods, as well as experimental data.

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 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.

A simple closed-form solution for assessing concentration uncertainty

NASA Astrophysics Data System (ADS)

de Barros, F. P. J.; Fiori, Aldo; Bellin, Alberto

2011-12-01

We propose closed-form approximate solutions for the moments of a nonreactive tracer that can be used in applications, such as risk analysis. This is in line with the tenet that analytical solutions provide useful information, with minimum cost, during initial site characterization efforts and can serve as a preliminary screening tool when used with prior knowledge. We show that with the help of a few assumptions, the first-order solutions of the concentration moments proposed by Fiori and Dagan (2000) can be further simplified to assume a form similar to well-known deterministic solutions, therefore facilitating their use in applications. A highly anisotropic formation is assumed, and we neglect the transverse components of the two-particle correlation trajectory. The proposed solution compares well with the work of Fiori and Dagan while presenting the same simplicity of use of existing solutions for homogeneous porous media.

Amphotericin B channels in phospholipid membrane-coated nanoporous silicon surfaces: implications for photovoltaic driving of ions across membranes.

PubMed

Yilma, Solomon; Liu, Nangou; Samoylov, Alexander; Lo, Ting; Brinker, C Jeffrey; Vodyanoy, Vitaly

2007-03-15

The antimycotic agent amphotericin B (AmB) functions by forming complexes with sterols to form ion channels that cause membrane leakage. When AmB and cholesterol mixed at 2:1 ratio were incorporated into phospholipid bilayer membranes formed on the tip of patch pipettes, ion channel current fluctuations with characteristic open and closed states were observed. These channels were also functional in phospholipid membranes formed on nanoporous silicon surfaces. Electrophysiological studies of AmB-cholesterol mixtures that were incorporated into phospholipid membranes formed on the surface of nanoporous (6.5 nm pore diameter) silicon plates revealed large conductance ion channels ( approximately 300 pS) with distinct open and closed states. Currents through the AmB-cholesterol channels on nanoporous silicon surfaces can be driven by voltage applied via conventional electrical circuits or by photovoltaic electrical potential entirely generated when the nanoporous silicon surface is illuminated with a narrow laser beam. Electrical recordings made during laser illumination of AmB-cholesterol containing membrane-coated nanoporous silicon surfaces revealed very large conductance ion channels with distinct open and closed states. Our findings indicate that nanoporous silicon surfaces can serve as mediums for ion-channel-based biosensors. The photovoltaic properties of nanoporous silicon surfaces show great promise for making such biosensors addressable via optical technologies.

Close Up of Monochromatic Aberrations Using Snell's Law: An Undergraduate Computational Experiment

ERIC Educational Resources Information Center

Levesque, L.

2009-01-01

Images formed from light rays refracting a spherical surface are often introduced in textbooks using the paraxial approximation. Incoming rays propagating from the object meeting the surface of a transparent medium at a given point for which the angle is larger than 15 degrees with respect to the normal are not described accurately from the…

Molecular cloning and functional characterization of peptidoglycan recognition protein 6 in grass carp Ctenopharyngodon idella.

PubMed

Li, Jun Hua; Yu, Zhang Long; Xue, Na Na; Zou, Peng Fei; Hu, Jing Yu; Nie, P; Chang, Ming Xian

2014-02-01

Peptidoglycan recognition proteins (PGRPs) are pattern recognition molecules of innate immunity. In this study, a long-form PGRP, designated as gcPGRP6, was identified from grass carp Ctenopharyngodon idella. The deduced amino acid sequence of gcPGRP6 is composed of 464 residues with a conserved PGRP domain at the C-terminus. The gcPGRP6 gene consists of four exons and three introns, spacing approximately 2.7 kb of genomic sequence. Phylogenetic analysis demonstrated that gcPGRP6 is clustered closely with zebrafish PGLYRP6, and formed a long-type PGRP subfamily together with PGLYRP2 members identified in teleosts and mammals. Real-time PCR and Western blotting analyses revealed that gcPGRP6 is constitutively expressed in organs/tissues examined, and its expression was significantly induced in liver and intestine of grass carp in response to PGN stimulation and in CIK cells treated with lipoteichoic acid (LTA), polyinosinic polycytidylic acid (Poly I:C) and peptidoglycan (PGN). Immunofluorescence microscopy and Western blotting analyses revealed that gcPGRP6 is effectively secreted to the exterior of CIK cells. The over-expression of gcPGRP6 in CIK cells leads to the activation of NF-κB and the inhibition of intracellular bacterial growth. Moreover, cell lysates from CIK cells transfected with pTurbo-gcPGRP6-GFP plasmid display the binding activity towards Lys-type PGN from Staphylococcus aureus and DAP-type PGN from Bacillus subtilis. Furthermore, proinflammatory cytokine IL-2 and intracellular PGN receptor NOD2 had a significantly increased expression in CIK cells overexpressed with gcPGRP6. It is demonstrated that the PGRP6 in grass carp has a role in binding PGN, in inhibiting the growth of intracellular bacteria, and in activating NF-κB, as well as in regulating innate immune genes. Copyright © 2013 Elsevier Ltd. All rights reserved.

Calculation of the detection limit in radiation measurements with systematic uncertainties

NASA Astrophysics Data System (ADS)

Kirkpatrick, J. M.; Russ, W.; Venkataraman, R.; Young, B. M.

2015-06-01

The detection limit (LD) or Minimum Detectable Activity (MDA) is an a priori evaluation of assay sensitivity intended to quantify the suitability of an instrument or measurement arrangement for the needs of a given application. Traditional approaches as pioneered by Currie rely on Gaussian approximations to yield simple, closed-form solutions, and neglect the effects of systematic uncertainties in the instrument calibration. These approximations are applicable over a wide range of applications, but are of limited use in low-count applications, when high confidence values are required, or when systematic uncertainties are significant. One proposed modification to the Currie formulation attempts account for systematic uncertainties within a Gaussian framework. We have previously shown that this approach results in an approximation formula that works best only for small values of the relative systematic uncertainty, for which the modification of Currie's method is the least necessary, and that it significantly overestimates the detection limit or gives infinite or otherwise non-physical results for larger systematic uncertainties where such a correction would be the most useful. We have developed an alternative approach for calculating detection limits based on realistic statistical modeling of the counting distributions which accurately represents statistical and systematic uncertainties. Instead of a closed form solution, numerical and iterative methods are used to evaluate the result. Accurate detection limits can be obtained by this method for the general case.

An Analytic Approach to Projectile Motion in a Linear Resisting Medium

ERIC Educational Resources Information Center

Stewart, Sean M.

2006-01-01

The time of flight, range and the angle which maximizes the range of a projectile in a linear resisting medium are expressed in analytic form in terms of the recently defined Lambert W function. From the closed-form solutions a number of results characteristic to the motion of the projectile in a linear resisting medium are analytically confirmed,…

Closed-form expressions for flip angle variation that maximize total signal in T1-weighted rapid gradient echo MRI.

PubMed

Drobnitzky, Matthias; Klose, Uwe

2017-03-01

Magnetization-prepared rapid gradient-echo (MPRAGE) sequences are commonly employed for T1-weighted structural brain imaging. Following a contrast preparation radiofrequency (RF) pulse, the data acquisition proceeds under nonequilibrium conditions of the relaxing longitudinal magnetization. Variation of the flip angle can be used to maximize total available signal. Simulated annealing or greedy algorithms have so far been published to numerically solve this problem, with signal-to-noise ratios optimized for clinical imaging scenarios by adhering to a predefined shape of the signal evolution. We propose an unconstrained optimization of the MPRAGE experiment that employs techniques from resource allocation theory. A new dynamic programming solution is introduced that yields closed-form expressions for optimal flip angle variation. Flip angle series are proposed that maximize total transverse magnetization (Mxy) for a range of physiologic T1 values. A 3D MPRAGE sequence is modified to allow for a controlled variation of the excitation angle. Experiments employing a T1 contrast phantom are performed at 3T. 1D acquisitions without phase encoding permit measurement of the temporal development of Mxy. Image mean signal and standard deviation for reference flip angle trains are compared in 2D measurements. Signal profiles at sharp phantom edges are acquired to access image blurring related to nonuniform Mxy development. A novel closed-form expression for flip angle variation is found that constitutes the optimal policy to reach maximum total signal. It numerically equals previously published results of other authors when evaluated under their simplifying assumptions. Longitudinal magnetization (Mz) is exhaustively used without causing abrupt changes in the measured MR signal, which is a prerequisite for artifact free images. Phantom experiments at 3T verify the expected benefit for total accumulated k-space signal when compared with published flip angle series. Describing the MR signal collection in MPRAGE sequences as a Bellman problem is a new concept. By means of recursively solving a series of overlapping subproblems, this leads to an elegant solution for the problem of maximizing total available MR signal in k-space. A closed-form expression for flip angle variation avoids the complexity of numerical optimization and eases access to controlled variation in an attempt to identify potential clinical applications. © 2017 American Association of Physicists in Medicine.

Analytical expressions for the log-amplitude correlation function of a plane wave through anisotropic atmospheric refractive turbulence.

PubMed

Gudimetla, V S Rao; Holmes, Richard B; Smith, Carey; Needham, Gregory

2012-05-01

The effect of anisotropic Kolmogorov turbulence on the log-amplitude correlation function for plane-wave fields is investigated using analysis, numerical integration, and simulation. A new analytical expression for the log-amplitude correlation function is derived for anisotropic Kolmogorov turbulence. The analytic results, based on the Rytov approximation, agree well with a more general wave-optics simulation based on the Fresnel approximation as well as with numerical evaluations, for low and moderate strengths of turbulence. The new expression reduces correctly to previously published analytic expressions for isotropic turbulence. The final results indicate that, as asymmetry becomes greater, the Rytov variance deviates from that given by the standard formula. This deviation becomes greater with stronger turbulence, up to moderate turbulence strengths. The anisotropic effects on the log-amplitude correlation function are dominant when the separation of the points is within the Fresnel length. In the direction of stronger turbulence, there is an enhanced dip in the correlation function at a separation close to the Fresnel length. The dip is diminished in the weak-turbulence axis, suggesting that energy redistribution via focusing and defocusing is dominated by the strong-turbulence axis. The new analytical expression is useful when anisotropy is observed in relevant experiments. © 2012 Optical Society of America

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.

Theory of rotational transition in atom-diatom chemical reaction

NASA Astrophysics Data System (ADS)

Nakamura, Masato; Nakamura, Hiroki

1989-05-01

Rotational transition in atom-diatom chemical reaction is theoretically studied. A new approximate theory (which we call IOS-DW approximation) is proposed on the basis of the physical idea that rotational transition in reaction is induced by the following two different mechanisms: rotationally inelastic half collision in both initial and final arrangement channels, and coordinate transformation in the reaction zone. This theory gives a fairy compact expression for the state-to-state transition probability. Introducing the additional physically reasonable assumption that reaction (particle rearrangement) takes place in a spatially localized region, we have reduced this expression into a simpler analytical form which can explicitly give overall rotational state distribution in reaction. Numerical application was made to the H+H2 reaction and demonstrated its effectiveness for the simplicity. A further simplified most naive approximation, i.e., independent events approximation was also proposed and demonstrated to work well in the test calculation of H+H2. The overall rotational state distribution is expressed simply by a product sum of the transition probabilities for the three consecutive processes in reaction: inelastic transition in the initial half collision, transition due to particle rearrangement, and inelastic transition in the final half collision.

Hamiltonian BFV-BRST theory of closed quantum cosmological models

NASA Astrophysics Data System (ADS)

Kamenshchik, A. Yu.; Lyakhovich, S. L.

1997-02-01

We introduce and study a new discrete basis of gravity constraints by making use of harmonic expansion for closed cosmological models. The full set of constraints is split into area-preserving spatial diffeomorphisms, forming closed subalgebra, and Virasoro-like generators. Operational Hamiltonian BFV-BRST quantization is performed in the framework of perturbative expansion in the dimensionless parameter, which is a positive power of the ratio of Planckian volume to the volume of the Universe. For the (N + 1)-dimensional generalization of stationary closed Bianchi-I cosmology the nilpotency condition for the BRST operator is examined in the first quantum approximation. It turns out that a certain relationship between the dimensionality of the space and the spectrum of matter fields emerges from the requirement of quantum consistency of the model.

Hamiltonian BFV-BRST theory of closed quantum cosmological models

NASA Astrophysics Data System (ADS)

Kamenshchik, A. Yu.; Lyakhovich, S. L.

1997-08-01

We introduce and study a new discrete basis of gravity constraints by making use of the harmonic expansion for closed cosmological models. The full set of constraints is split into area-preserving spatial diffeomorphisms, forming a closed subalgebra, and Virasoro-like generators. The operatorial Hamiltonian BFV-BRST quantization is performed in the framework of a perturbative expansion in the dimensionless parameter which is a positive power of the ratio of the Planck volume to the volume of the Universe. For the (N + 1) - dimensional generalization of a stationary closed Bianchi-I cosmology the nilpotency condition for the BRST operator is examined in the first quantum approximation. It turns out that a relationship between the dimensionality of the space and the spectrum of matter fields emerges from the requirement of quantum consistency of the model.

The asymptotic form of non-global logarithms, black disc saturation, and gluonic deserts

NASA Astrophysics Data System (ADS)

Neill, Duff

2017-01-01

We develop an asymptotic perturbation theory for the large logarithmic behavior of the non-linear integro-differential equation describing the soft correlations of QCD jet measurements, the Banfi-Marchesini-Smye (BMS) equation. This equation captures the late-time evolution of radiating color dipoles after a hard collision. This allows us to prove that at large values of the control variable (the non-global logarithm, a function of the infra-red energy scales associated with distinct hard jets in an event), the distribution has a gaussian tail. We compute the decay width analytically, giving a closed form expression, and find it to be jet geometry independent, up to the number of legs of the dipole in the active jet. Enabling the asymptotic expansion is the correct perturbative seed, where we perturb around an anzats encoding formally no real emissions, an intuition motivated by the buffer region found in jet dynamics. This must be supplemented with the correct application of the BFKL approximation to the BMS equation in collinear limits. Comparing to the asymptotics of the conformally related evolution equation encountered in small-x physics, the Balitisky-Kovchegov (BK) equation, we find that the asymptotic form of the non-global logarithms directly maps to the black-disc unitarity limit of the BK equation, despite the contrasting physical pictures. Indeed, we recover the equations of saturation physics in the final state dynamics of QCD.

Optimal Mortgage Refinancing: A Closed Form Solution

PubMed Central

Agarwal, Sumit; Driscoll, John C.; Laibson, David I.

2013-01-01

We derive the first closed-form optimal refinancing rule: Refinance when the current mortgage interest rate falls below the original rate by at least 1ψ[ϕ+W(−exp(−ϕ))]. In this formula W(.) is the Lambert W-function, ψ=2(ρ+λ)σ,ϕ=1+ψ(ρ+λ)κ∕M(1−τ), ρ is the real discount rate, λ is the expected real rate of exogenous mortgage repayment, σ is the standard deviation of the mortgage rate, κ/M is the ratio of the tax-adjusted refinancing cost and the remaining mortgage value, and τ is the marginal tax rate. This expression is derived by solving a tractable class of refinancing problems. Our quantitative results closely match those reported by researchers using numerical methods. PMID:25843977

Nonviral transfection of suspension cells in ultrasound standing wave fields.

PubMed

Lee, Yu-Hsiang; Peng, Ching-An

2007-05-01

Ultrasound-induced cavitation has been widely used for delivering DNA vectors into cells. However, this approach may seriously disrupt cell membranes and cause lethal damage when cells are exposed to the inertial cavitation field. In this study, instead of using sonoporation, ultrasound standing wave fields (USWF) were explored for nonviral transfection of suspension cells. Acoustic resonance in a tubular chamber was generated from the interference of waves emitted from a piezoelectric transducer and consequently reflected from a borosilicate glass coverslip. The suspended K562 erythroleukemia cells were transfected by polyethyleneimine (PEI)/DNA complexes with and without exposure to 1-MHz USWF for 5 min. During USWF exposure, K562 cells moved to the pressure nodal planes first and formed cell bands by the primary radiation force. Nanometer-sized PEI/DNA complexes, circulated between nodal planes by acoustic microstreaming, then used the cell agglomerates as the nucleating sites on which to attach. After incubation at 37 degrees C for 48 h, the efficiency of nonviral transfection based on EGFP transgene expression was determined by fluorescent microscopy and fluorometry. Both studies showed that USWF brought suspended K562 cells and PEI/DNA complexes into close contact at the pressure nodal planes, yielding an approximately 10-fold increment of EGFP transgene expression compared with the group without ultrasonic treatment.

Expression and purification of recombinant tung tree diacylglycerol acyltransferase 2

USDA-ARS?s Scientific Manuscript database

Diacylglycerol acyltransferases (DGATs) are responsible for the last step of triacylglycerol (TAG) biosynthesis in eukaryotic organisms. Different forms of DGATs have nonredundant functions in TAG biosynthesis in species such as tung tree (Vernicia fordii), which contains approximately 80% high-valu...

MODELING STREAM-AQUIFIER INTERACTIONS WITH LINEAR RESPONSE FUNCTIONS

EPA Science Inventory

The problem of stream-aquifer interactions is pertinent to conjunctive-use management of water resources and riparian zone hydrology. Closed form solutions are derived for stream-aquifer interactions in rates and volumes expressed as convolution integrals of impulse response and ...

Nonequilibrium itinerant-electron magnetism: A time-dependent mean-field theory

NASA Astrophysics Data System (ADS)

Secchi, A.; Lichtenstein, A. I.; Katsnelson, M. I.

2016-08-01

We study the dynamical magnetic susceptibility of a strongly correlated electronic system in the presence of a time-dependent hopping field, deriving a generalized Bethe-Salpeter equation that is valid also out of equilibrium. Focusing on the single-orbital Hubbard model within the time-dependent Hartree-Fock approximation, we solve the equation in the nonequilibrium adiabatic regime, obtaining a closed expression for the transverse magnetic susceptibility. From this, we provide a rigorous definition of nonequilibrium (time-dependent) magnon frequencies and exchange parameters, expressed in terms of nonequilibrium single-electron Green's functions and self-energies. In the particular case of equilibrium, we recover previously known results.

A Local Approximation of Fundamental Measure Theory Incorporated into Three Dimensional Poisson-Nernst-Planck Equations to Account for Hard Sphere Repulsion Among Ions

NASA Astrophysics Data System (ADS)

Qiao, Yu; Liu, Xuejiao; Chen, Minxin; Lu, Benzhuo

2016-04-01

The hard sphere repulsion among ions can be considered in the Poisson-Nernst-Planck (PNP) equations by combining the fundamental measure theory (FMT). To reduce the nonlocal computational complexity in 3D simulation of biological systems, a local approximation of FMT is derived, which forms a local hard sphere PNP (LHSPNP) model. In the derivation, the excess chemical potential from hard sphere repulsion is obtained with the FMT and has six integration components. For the integrands and weighted densities in each component, Taylor expansions are performed and the lowest order approximations are taken, which result in the final local hard sphere (LHS) excess chemical potential with four components. By plugging the LHS excess chemical potential into the ionic flux expression in the Nernst-Planck equation, the three dimensional LHSPNP is obtained. It is interestingly found that the essential part of free energy term of the previous size modified model (Borukhov et al. in Phys Rev Lett 79:435-438, 1997; Kilic et al. in Phys Rev E 75:021502, 2007; Lu and Zhou in Biophys J 100:2475-2485, 2011; Liu and Eisenberg in J Chem Phys 141:22D532, 2014) has a very similar form to one term of the LHS model, but LHSPNP has more additional terms accounting for size effects. Equation of state for one component homogeneous fluid is studied for the local hard sphere approximation of FMT and is proved to be exact for the first two virial coefficients, while the previous size modified model only presents the first virial coefficient accurately. To investigate the effects of LHS model and the competitions among different counterion species, numerical experiments are performed for the traditional PNP model, the LHSPNP model, the previous size modified PNP (SMPNP) model and the Monte Carlo simulation. It's observed that in steady state the LHSPNP results are quite different from the PNP results, but are close to the SMPNP results under a wide range of boundary conditions. Besides, in both LHSPNP and SMPNP models the stratification of one counterion species can be observed under certain bulk concentrations.

Oral Interpretation of C.S. Lewis'"Narnia Tales": A Refracting of "Pictures."

ERIC Educational Resources Information Center

Keefe, Carolyn

"The Chronicles of Narnia" are a series of seven fairy tales written by C.S. Lewis that have become popular with both children and adults. Lewis points to five aspects of the fairy tale form that made the form suitable for expressing the images he saw. The aspects are: (1) no love interest; (2) no close psychology; (3) severe restraints…

78 FR 59394 - Self-Regulatory Organizations; The NASDAQ Stock Market LLC; Notice of Filing of Proposed Rule...

Federal Register 2010, 2011, 2012, 2013, 2014

2013-09-26

.... exchange-traded covered call options on the Index in order to seek additional cash flow in the form of... more closely approximate those of the markets in which it invests), to manage cash flows or to preserve... Creation Units for cash, the Fund may incur additional costs associated with the acquisition of Deposit...

Secondary Education in Austria, 1918-38. Bulletin, 1941, No. 9

ERIC Educational Resources Information Center

Lederer, Max

1941-01-01

Between the close of the first World War and the beginning of the second, approximately two decades, several European nations that had not previously done so maintained democratic forms of government. In that period they tried to arrange their school systems in such a way as to educate their children for life in democracies. Their moves in that…

Design equations for the assessment and FRP-strengthening of reinforced rectangular concrete columns under combined biaxial bending and axial loads

NASA Astrophysics Data System (ADS)

Alessandri, S.; Monti, G.

2008-05-01

A simple procedure is proposed for the assessment of reinforced rectangular concrete columns under combined biaxial bending and axial loads and for the design of a correct amount of FRP-strengthening for underdesigned concrete sections. Approximate closed-form equations are developed based on the load contour method originally proposed by Bresler for reinforced concrete sections. The 3D failure surface is approximated along its contours, at a constant axial load, by means of equations given as the sum of the acting/resisting moment ratio in the directions of principal axes of the sections, raised to a power depending on the axial load, the steel reinforcement ratio, and the section shape. The method is extended to FRP-strengthened sections. Moreover, to make it possible to apply the load contour method in a more practical way, simple closed-form equations are developed for rectangular reinforced concrete sections with a two-way steel reinforcement and FRP strengthenings on each side. A comparison between the approach proposed and the fiber method (which is considered exact) shows that the simplified equations correctly represent the section interaction diagram.

Characterization of local thermodynamic equilibrium in a laser-induced aluminum alloy plasma.

PubMed

Zhang, Yong; Zhao, Zhenyang; Xu, Tao; Niu, GuangHui; Liu, Ying; Duan, Yixiang

2016-04-01

The electron temperature was evaluated using the line-to-continuum ratio method, and whether the plasma was close to the local thermodynamic equilibrium (LTE) state was investigated in detail. The results showed that approximately 5 μs after the plasma formed, the changes in the electron and excitation temperatures, which were determined using a Boltzmann plot, overlapped in the 15% error range, which indicated that the LTE state was reached. The recombination of electrons and ions and the free electron expansion process led to the deviation from the LTE state. The plasma's expansion rate slowed over time, and when the expansion time was close to the ionization equilibrium time, the LTE state was almost reached. The McWhirter criterion was adopted to calculate the threshold electron density for different species, and the results showed that experimental electron density was greater than the threshold electron density, which meant that the LTE state may have existed. However, for the nonmetal element N, the threshold electron density was greater than the value experimental value approximately 0.8 μs after the plasma formed, which meant that LTE state did not exist for N.

The gravitational potential due to uniform disks and rings

NASA Astrophysics Data System (ADS)

Lass, H.; Blitzer, L.

1983-07-01

The gravitational potential of bodies possessing axial symmetry can be expressed as a power series in distance, with the Legendre polynomials as coefficients. Such series, however, converge so slowly in the neighborhood of thin, uniform disks and rings that too many series terms must be summed in order to obtain an accurate field measure. A gravitational potential expression is presently obtained in closed form, in terms of complete elliptic integrals.

Moving to continuous facial expression space using the MPEG-4 facial definition parameter (FDP) set

NASA Astrophysics Data System (ADS)

Karpouzis, Kostas; Tsapatsoulis, Nicolas; Kollias, Stefanos D.

2000-06-01

Research in facial expression has concluded that at least six emotions, conveyed by human faces, are universally associated with distinct expressions. Sadness, anger, joy, fear, disgust and surprise are categories of expressions that are recognizable across cultures. In this work we form a relation between the description of the universal expressions and the MPEG-4 Facial Definition Parameter Set (FDP). We also investigate the relation between the movement of basic FDPs and the parameters that describe emotion-related words according to some classical psychological studies. In particular Whissel suggested that emotions are points in a space, which seem to occupy two dimensions: activation and evaluation. We show that some of the MPEG-4 Facial Animation Parameters (FAPs), approximated by the motion of the corresponding FDPs, can be combined by means of a fuzzy rule system to estimate the activation parameter. In this way variations of the six archetypal emotions can be achieved. Moreover, Plutchik concluded that emotion terms are unevenly distributed through the space defined by dimensions like Whissel's; instead they tend to form an approximately circular pattern, called 'emotion wheel,' modeled using an angular measure. The 'emotion wheel' can be defined as a reference for creating intermediate expressions from the universal ones, by interpolating the movement of dominant FDP points between neighboring basic expressions. By exploiting the relation between the movement of the basic FDP point and the activation and angular parameters we can model more emotions than the primary ones and achieve efficient recognition in video sequences.

The Temporal Dynamics of Two Response-Focused Forms of Emotion Regulation: Experiential, Expressive, and Autonomic Consequences

PubMed Central

Dan-Glauser, Elise S.; Gross, James J.

2011-01-01

This study examines the early affective consequences of two close forms of suppression. Participants (N=37) were shown negative, positive, and neutral pictures and cued either to attend to the pictures, or to perform expressive or physiological suppression (i.e. reduce body reactions). Continuous measures of experience, expressivity, and autonomic responses showed that both suppression strategies produced rapid response modulation. Common effects of the two strategies included a transient increase in negative feeling, a durable decrease in positive feeling, and a decrease in expressivity, cardiovascular activity, and oxygenation. The two strategies were significantly different only in response to positive stimuli, with physiological suppression showing a larger decrease in experience intensity and blood pressure. These results suggest a strong overlap between the two suppression strategies in terms of their early impact on emotional responses. PMID:21361967

A general method for the derivation of the functional forms of the effective energy terms in coarse-grained energy functions of polymers. I. Backbone potentials of coarse-grained polypeptide chains

NASA Astrophysics Data System (ADS)

Sieradzan, Adam K.; Makowski, Mariusz; Augustynowicz, Antoni; Liwo, Adam

2017-03-01

A general and systematic method for the derivation of the functional expressions for the effective energy terms in coarse-grained force fields of polymer chains is proposed. The method is based on the expansion of the potential of mean force of the system studied in the cluster-cumulant series and expanding the all-atom energy in the Taylor series in the squares of interatomic distances about the squares of the distances between coarse-grained centers, to obtain approximate analytical expressions for the cluster cumulants. The primary degrees of freedom to average about are the angles for collective rotation of the atoms contained in the coarse-grained interaction sites about the respective virtual-bond axes. The approach has been applied to the revision of the virtual-bond-angle, virtual-bond-torsional, and backbone-local-and-electrostatic correlation potentials for the UNited RESidue (UNRES) model of polypeptide chains, demonstrating the strong dependence of the torsional and correlation potentials on virtual-bond angles, not considered in the current UNRES. The theoretical considerations are illustrated with the potentials calculated from the ab initio potential-energy surface of terminally blocked alanine by numerical integration and with the statistical potentials derived from known protein structures. The revised torsional potentials correctly indicate that virtual-bond angles close to 90° result in the preference for the turn and helical structures, while large virtual-bond angles result in the preference for polyproline II and extended backbone geometry. The revised correlation potentials correctly reproduce the preference for the formation of β-sheet structures for large values of virtual-bond angles and for the formation of α-helical structures for virtual-bond angles close to 90°.

Choice of phase in the CS and IOS approximation

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

Snider, R.F.

1982-04-01

With the recognition that the angular momentum representations of unit position and momentum directional states must have different but uniquely related phases, the previously presented expression of scattering amplitude in terms of IOS angle dependent phase shifts must be modified. This resolves a major disagreement between IOS and close coupled degeneracy averaged differential cross sections. It is found that the phase factors appearing in the differential cross section have nothing to do with any particular choice of decoupling parameter. As a consequence, the differential cross section is relatively insensitive to the choice of CS decoupling parameter. The phase relations obtainedmore » are also in agreement with those deduced from the Born approximation.« less

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

Lie algebraic approach to the time-dependent quantum general harmonic oscillator and the bi-dimensional charged particle in time-dependent electromagnetic fields

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

Ibarra-Sierra, V.G.; Sandoval-Santana, J.C.; Cardoso, J.L.

We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra ismore » later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai–Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators. -- Highlights: •We deal with the general quadratic Hamiltonian and a particle in electromagnetic fields. •The evolution operator is worked out through the Lie algebraic approach. •We also obtain the propagator and Heisenberg picture position and momentum operators. •Analytical expressions for a rotating quadrupole field ion trap are presented. •Exact solutions for magneto-transport in variable electromagnetic fields are shown.« less

Evidence for a major retinitis pigmentosa locus on 19q13.4 (RP11), and association with a unique bimodal expressivity phenotype

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

Al-Maghtheh, M.; Vithana, E.; Tarttelin, E.

Retinitis pigmentosa (RP) is the name given to a heterogeneous group of retinal degenerations mapping to at least 16 loci. The autosomal dominant form (adRP), accounting for {approximately}25% of cases, can be caused by mutations in two genes, rhodopsin and peripherin/RDS, and by at least six other loci identified by linkage analysis. The RP11 locus for adRP has previously been mapped to chromosome 19q13.4 in a large English family. This linkage has been independently confirmed in a Japanese family, and we now report three additional unrelated linked U.K. families, suggesting that this is a major locus for RP. Linkage analysismore » in the U.K. families refines the RP11 interval to 5 cM between markers D19S180 and AFMc001yb1. All linked families exhibit incomplete penetrance; some obligate gene carriers remain asymptomatic throughout their lives, whereas symptomatic individuals experience night blindness and visual field loss in their teens and are generally registered as blind by their 30s. This {open_quotes}bimodal expressivity{close_quotes} contrasts with the variable-expressivity RP mapping to chromosome 7p (RP9) in another family, which has implications for diagnosis and counseling of RP11 families. These results may also imply that a proportion of sporadic RP, previously assumed to be recessive, might result from mutations at this locus. 27 refs., 3 figs., 1 tab.« less

Microplastic interactions with freshwater microalgae: Hetero-aggregation and changes in plastic density appear strongly dependent on polymer type.

PubMed

Lagarde, Fabienne; Olivier, Ophélie; Zanella, Marie; Daniel, Philippe; Hiard, Sophie; Caruso, Aurore

2016-08-01

In this study, the interactions between microplastics, chosen among the most widely used in industry such as polypropylene (PP) and high-density polyethylene (HDPE), and a model freshwater microalgae, Chlamydomas reinhardtii, were investigated. It was shown that the presence of high concentrations of microplastics with size >400 μm did not directly impact the growth of microalgae in the first days of contact and that the expression of three genes involved in the stress response was not modified after 78 days. In parallel, a similar colonization was observed for the two polymers. However, after 20 days of contact, in the case of PP only, hetero-aggregates constituted of microalgae, microplastics and exopolysaccharides were formed. An estimation of the hetero-aggregates composition was approximately 50% of PP fragments and 50% of microalgae, which led to a final density close to 1.2. Such hetero-aggregates appear as an important pathway for the vertical transport of PP microplastics from the water surface to sediment. Moreover, after more than 70 days of contact with microplastics, the microalgae genes involved in the sugar biosynthesis pathways were strongly over-expressed compared to control conditions. The levels of over-expression were higher in the case of HDPE than in PP condition. This work presents the first evidence that depending on their chemical nature, microplastics will follow different fates in the environment. Copyright © 2016 Elsevier Ltd. All rights reserved.

Localization and functional analysis of the insect-specific RabX4 in the brain of Bombyx mori.

PubMed

Uno, Tomohide; Furutani, Masayuki; Sakamoto, Katsuhiko; Uno, Yuichi; Kanamaru, Kengo; Mizoguchi, Akira; Hiragaki, Susumu; Takeda, Makio

2017-09-01

Rab proteins are small monomeric GTPases/GTP-binding proteins, which form the largest branch of the Ras superfamily. The different Rab GTPases are localized to the cytosolic face of specific intracellular membranes, where they function as regulators of distinct steps in membrane trafficking. RabX4 is an insect-specific Rab protein that has no close homolog in vertebrates. There is little information about insect-specific Rab proteins. RabX4 was expressed in Escherichia coli and subsequently purified. Antibodies against Bombyx mori RabX4 were produced in rabbits for western immunoblotting and immunohistochemistry. Western blotting of neural tissues revealed a single band, at approximately 26 kD. RabX4-like immunohistochemical reactivity was restricted to neurons of the pars intercerebralis and dorsolateral protocerebrum in the brain. Further immunohistochemical analysis revealed that RabX4 colocalized with Rab6 and bombyxin in the corpus allatum, a neuronal organ that secretes neuropeptides synthesized in the brain into the hemolymph. RabX4 expression in the frontal ganglion, part of the insect stomatogastric nervous system that is found in most insect orders, was restricted to two neurons on the outer region and did not colocalize with allatotropin or Rab6. Furthermore, RNA interference of RabX4 decreased bombyxin expression levels in the brain. These findings suggest that RabX4 is involved in the neurosecretion of a secretory organ in Bombyx mori. © 2017 Wiley Periodicals, Inc.

Alternative splicing of class Ib major histocompatibility complex transcripts in vivo leads to the expression of soluble Qa-2 molecules in murine blood.

PubMed Central

Tabaczewski, P; Shirwan, H; Lewis, K; Stroynowski, I

1994-01-01

Class Ib Qa-2 molecules are expressed in tissue culture cells as approximately 40-kDa membrane-bound, glycophosphatidylinositol-linked antigens and as approximately 39-kDa soluble polypeptides. Recently, alternative splicing events which delete exon 5 from a portion of Qa-2 transcripts were demonstrated to give rise to truncated secreted Qa-2 molecules in transfected cell lines. To determine whether this mechanism operates in vivo and to find out whether Qa-2 can be detected in soluble form in circulation, murine blood samples were analyzed. Critical to these experiments was preparation of an anti-peptide antiserum against an epitope encoded by a junction of exon 4 and exon 6. We find that supernatants of splenocytes cultured in vitro as well as serum or plasma contain two forms of soluble Qa-2 molecules. One form corresponds to a secreted molecule translated from transcripts from which exon 5 has been deleted; the other is derived from membrane-bound antigens or their precursors. The levels of both soluble forms of Qa-2 are inducible upon stimulation of the immune system, suggesting an immunoregulatory role for these molecules or for the mechanism leading to the reduction of cell-associated Qa-2 antigens in vivo. Images PMID:8127900

Feynman perturbation expansion for the price of coupon bond options and swaptions in quantum finance. I. Theory

NASA Astrophysics Data System (ADS)

Baaquie, Belal E.

2007-01-01

European options on coupon bonds are studied in a quantum field theory model of forward interest rates. Swaptions are briefly reviewed. An approximation scheme for the coupon bond option price is developed based on the fact that the volatility of the forward interest rates is a small quantity. The field theory for the forward interest rates is Gaussian, but when the payoff function for the coupon bond option is included it makes the field theory nonlocal and nonlinear. A perturbation expansion using Feynman diagrams gives a closed form approximation for the price of coupon bond option. A special case of the approximate bond option is shown to yield the industry standard one-factor HJM formula with exponential volatility.

Oscillatory Reduction in Option Pricing Formula Using Shifted Poisson and Linear Approximation

NASA Astrophysics Data System (ADS)

Nur Rachmawati, Ro'fah; Irene; Budiharto, Widodo

2014-03-01

Option is one of derivative instruments that can help investors improve their expected return and minimize the risks. However, the Black-Scholes formula is generally used in determining the price of the option does not involve skewness factor and it is difficult to apply in computing process because it produces oscillation for the skewness values close to zero. In this paper, we construct option pricing formula that involve skewness by modified Black-Scholes formula using Shifted Poisson model and transformed it into the form of a Linear Approximation in the complete market to reduce the oscillation. The results are Linear Approximation formula can predict the price of an option with very accurate and successfully reduce the oscillations in the calculation processes.

Feynman perturbation expansion for the price of coupon bond options and swaptions in quantum finance. I. Theory.

PubMed

Baaquie, Belal E

2007-01-01

European options on coupon bonds are studied in a quantum field theory model of forward interest rates. Swaptions are briefly reviewed. An approximation scheme for the coupon bond option price is developed based on the fact that the volatility of the forward interest rates is a small quantity. The field theory for the forward interest rates is Gaussian, but when the payoff function for the coupon bond option is included it makes the field theory nonlocal and nonlinear. A perturbation expansion using Feynman diagrams gives a closed form approximation for the price of coupon bond option. A special case of the approximate bond option is shown to yield the industry standard one-factor HJM formula with exponential volatility.

Covariance approximation for fast and accurate computation of channelized Hotelling observer statistics

NASA Astrophysics Data System (ADS)

Bonetto, P.; Qi, Jinyi; Leahy, R. M.

2000-08-01

Describes a method for computing linear observer statistics for maximum a posteriori (MAP) reconstructions of PET images. The method is based on a theoretical approximation for the mean and covariance of MAP reconstructions. In particular, the authors derive here a closed form for the channelized Hotelling observer (CHO) statistic applied to 2D MAP images. The theoretical analysis models both the Poission statistics of PET data and the inhomogeneity of tracer uptake. The authors show reasonably good correspondence between these theoretical results and Monte Carlo studies. The accuracy and low computational cost of the approximation allow the authors to analyze the observer performance over a wide range of operating conditions and parameter settings for the MAP reconstruction algorithm.

Closed-form solution for Eshelby's elliptic inclusion in antiplane elasticity using complex variable

NASA Astrophysics Data System (ADS)

Chen, Y. Z.

2013-12-01

This paper provides a closed-form solution for the Eshelby's elliptic inclusion in antiplane elasticity. In the formulation, the prescribed eigenstarins are not only for the uniform distribution, but also for the linear form. After using the complex variable and the conformal mapping, the continuation condition for the traction and displacement along the interface in the physical plane can be reduced to a condition along the unit circle. The relevant complex potentials defined in the inclusion and the matrix can be separated from the continuation conditions of the traction and displacement along the interface. The expressions of the real strains and stresses in the inclusion from the assumed eigenstrains are presented. Results for the case of linear distribution of eigenstrain are first obtained in the paper.

Vector fields and nilpotent Lie algebras

NASA Technical Reports Server (NTRS)

Grayson, Matthew; Grossman, Robert

1987-01-01

An infinite-dimensional family of flows E is described with the property that the associated dynamical system: x(t) = E(x(t)), where x(0) is a member of the set R to the Nth power, is explicitly integrable in closed form. These flows E are of the form E = E1 + E2, where E1 and E2 are the generators of a nilpotent Lie algebra, which is either free, or satisfies some relations at a point. These flows can then be used to approximate the flows of more general types of dynamical systems.

Wounding coordinately induces cell wall protein, cell cycle and pectin methyl esterase genes involved in tuber closing layer and wound periderm development.

PubMed

Neubauer, Jonathan D; Lulai, Edward C; Thompson, Asunta L; Suttle, Jeffrey C; Bolton, Melvin D

2012-04-15

Little is known about the coordinate induction of genes that may be involved in agriculturally important wound-healing events. In this study, wound-healing events were determined together with wound-induced expression profiles of selected cell cycle, cell wall protein, and pectin methyl esterase genes using two diverse potato genotypes and two harvests (NDTX4271-5R and Russet Burbank tubers; 2008 and 2009 harvests). By 5 d after wounding, the closing layer and a nascent phellogen had formed. Phellogen cell divisions generated phellem layers until cessation of cell division at 28 d after wounding for both genotypes and harvests. Cell cycle genes encoding epidermal growth factor binding protein (StEBP), cyclin-dependent kinase B (StCDKB) and cyclin-dependent kinase regulatory subunit (StCKS1At) were induced by 1 d after wounding; these expressions coordinated with related phellogen formation and the induction and cessation of phellem cell formation. Genes encoding the structural cell wall proteins extensin (StExt1) and extensin-like (StExtlk) were dramatically up-regulated by 1-5 d after wounding, suggesting involvement with closing layer and later phellem cell layer formation. Wounding up-regulated pectin methyl esterase genes (StPME and StPrePME); StPME expression increased during closing layer and phellem cell formation, whereas maximum expression of StPrePME occurred at 5-14 d after wounding, implicating involvement in later modifications for closing layer and phellem cell formation. The coordinate induction and expression profile of StTLRP, a gene encoding a cell wall strengthening "tyrosine-and lysine-rich protein," suggested a role in the formation of the closing layer followed by phellem cell generation and maturation. Collectively, the genes monitored were wound-inducible and their expression profiles markedly coordinated with closing layer formation and the index for phellogen layer meristematic activity during wound periderm development; results were more influenced by harvest than genotype. Importantly, StTLRP was the only gene examined that may be involved in phellogen cell wall thickening after cessation of phellogen cell division. Published by Elsevier GmbH.

Segmented strings and the McMillan map

DOE PAGES

Gubser, Steven S.; Parikh, Sarthak; Witaszczyk, Przemek

2016-07-25

We present new exact solutions describing motions of closed segmented strings in AdS 3 in terms of elliptic functions. The existence of analytic expressions is due to the integrability of the classical equations of motion, which in our examples reduce to instances of the McMillan map. Here, we also obtain a discrete evolution rule for the motion in AdS 3 of arbitrary bound states of fundamental strings and D1-branes in the test approximation.

APPROXIMATION OF ROTATIONAL STRENGTHS FROM MOLAR ROTATION DATA AND GENERATION OF ROTATORY DISPERSION CURVES FOR D-CAMPHOR-10-SULFONATE

PubMed Central

Urry, Dan W.

1969-01-01

Starting with the expression for optical rotatory dispersion in the absorption region that was arrived at by Condon, two series were considered for the purpose of achieving the experimentally observed, steeper wavelength dependence in the absorption region while retaining the established 1/λ2 law in regions removed from absorption. The first two terms of one series in which the second term exhibits a 1/λ6 wavelength dependence were found to calculate satisfactorily the optical rotatory dispersion curve of d-camphor-10-sulfonate from 400 mμ to 190 mμ when only three bands were considered. Evaluated at the extrema, the two-term expression can be approximated by a simple equation which allows calculation of the rotational strength of a nonoverlapping band by using only the wavelength and molar rotation of the extrema and the index of refraction of the solution. The rotational strengths calculated from optical rotatory dispersion data in this manner closely agree with those calculated from corresponding circular dichroism data. Thus when position and magnitude of rotatory dispersion extrema alone are reported for carbonyls, it is suggested that such published data may be converted to approximate rotational strengths. PMID:5257123

A high capacity data recording device based on a digital audio processor and a video cassette recorder.

PubMed

Bezanilla, F

1985-03-01

A modified digital audio processor, a video cassette recorder, and some simple added circuitry are assembled into a recording device of high capacity. The unit converts two analog channels into digital form at 44-kHz sampling rate and stores the information in digital form in a common video cassette. Bandwidth of each channel is from direct current to approximately 20 kHz and the dynamic range is close to 90 dB. The total storage capacity in a 3-h video cassette is 2 Gbytes. The information can be retrieved in analog or digital form.

A high capacity data recording device based on a digital audio processor and a video cassette recorder.

PubMed Central

Bezanilla, F

1985-01-01

A modified digital audio processor, a video cassette recorder, and some simple added circuitry are assembled into a recording device of high capacity. The unit converts two analog channels into digital form at 44-kHz sampling rate and stores the information in digital form in a common video cassette. Bandwidth of each channel is from direct current to approximately 20 kHz and the dynamic range is close to 90 dB. The total storage capacity in a 3-h video cassette is 2 Gbytes. The information can be retrieved in analog or digital form. PMID:3978213

Localized surface plasmon mediated energy transfer in the vicinity of core-shell nanoparticle

NASA Astrophysics Data System (ADS)

Shishodia, Manmohan Singh; Juneja, Soniya

2016-05-01

Multipole spectral expansion based theory of energy transfer interactions between a donor and an acceptor molecule in the vicinity of a core-shell (nanoshell or core@shell) based plasmonic nanostructure is developed. In view of the diverse applications and rich plasmonic features such as tuning capability of surface plasmon (SP) frequencies, greater sensitivity to the change of dielectric environment, controllable redirection of electromagnetic radiation, closed form expressions for Energy Transfer Rate Enhancement Factor (ETREF) near core-shell particle are reported. The dependence of ETREF on different parameters is established through fitting equations, perceived to be of key importance for developing appropriate designs. The theoretical approach developed in the present work is capable of treating higher order multipoles, which, in turn, are also shown to play a crucial role in the present context. Moreover, closed form expressions derived in the present work can directly be used as formula, e.g., for designing SP based biosensors and estimating energy exchange between proteins and excitonic interactions in quantum dots.

Effect of non-Kolmogorov turbulence on BER performance in uplink ground-to-satellite laser communication

NASA Astrophysics Data System (ADS)

Wang, Yi; Zhang, Ao; Ma, Jing; Guo, Qiang

2016-12-01

Based on the non-Kolmogorov turbulence model of the stratosphere, a theoretical model for the influence of the angle of arrival (AOA) fluctuations on the performance of the bit error rate (BER) is established. A closed form expression of BER is then derived based on this model. Then, considering the combined effect of scintillation, beam wander and AOA fluctuations, the probability density function of the received intensity and the closed form expressions of BER for uplink are derived. Coherent detection of Circle Polarization Shift Keying modulation which is suitable for ground-to-satellite laser communication is employed. For an uplink, the BER performance is emulation analyzed and compared to the condition without taking AOA fluctuations into account. And the variation of BER as a function of AOA fluctuations has also been researched. The influence of intensity scintillation, beam wander and AOA fluctuations on BER has been analyzed based on laser transmit power restrictions.

Frequency response of a supported thermocouple wire: Effects of axial conduction

NASA Technical Reports Server (NTRS)

Forney, L. J.; Meeks, E. L.; Fralick, G. C.

1991-01-01

Theoretical expressions are derived for the steady-state frequency response of a supported thermocouple wire. In particular, the effects of axial heat conduction are demonstrated for both a supported one material wire and a two material wire with unequal material properties across the junction. For the case of a one material supported wire, an exact solution is derived which compares favorably with an approximate expression that only matches temperatures at the support junction. Moreover, for the case of a two material supported wire, an analytical expression is derived that closely correlates numerical results. Experimental data were taken with a type K supported thermocouple. The test thermocouple was constructed with dimensions to demonstrate the effects of axial heat conduction assuming constant physical properties across the junction.

Non-Parabolic Hydrodynamic Formulations for the Simulation of Inhomogeneous Semiconductor Devices

NASA Technical Reports Server (NTRS)

Smith, A. W.; Brennan, K. F.

1996-01-01

Hydrodynamic models are becoming prevalent design tools for small scale devices and other devices in which high energy effects can dominate transport. Most current hydrodynamic models use a parabolic band approximation to obtain fairly simple conservation equations. Interest in accounting for band structure effects in hydrodynamic device simulation has begun to grow since parabolic models cannot fully describe the transport in state of the art devices due to the distribution populating non-parabolic states within the band. This paper presents two different non-parabolic formulations or the hydrodynamic model suitable for the simulation of inhomogeneous semiconductor devices. The first formulation uses the Kane dispersion relationship ((hk)(exp 2)/2m = W(1 + alphaW). The second formulation makes use of a power law ((hk)(exp 2)/2m = xW(exp y)) for the dispersion relation. Hydrodynamic models which use the first formulation rely on the binomial expansion to obtain moment equations with closed form coefficients. This limits the energy range over which the model is valid. The power law formulation readily produces closed form coefficients similar to those obtained using the parabolic band approximation. However, the fitting parameters (x,y) are only valid over a limited energy range. The physical significance of the band non-parabolicity is discussed as well as the advantages/disadvantages and approximations of the two non-parabolic models. A companion paper describes device simulations based on the three dispersion relationships; parabolic, Kane dispersion and power law dispersion.

Non-parabolic hydrodynamic formulations for the simulation of inhomogeneous semiconductor devices

NASA Technical Reports Server (NTRS)

Smith, Arlynn W.; Brennan, Kevin F.

1995-01-01

Hydrodynamic models are becoming prevalent design tools for small scale devices and other devices in which high energy effects can dominate transport. Most current hydrodynamic models use a parabolic band approximation to obtain fairly simple conservation equations. Interest in accounting for band structure effects in hydrodynamic device simulation has begun to grow since parabolic models can not fully describe the transport in state of the art devices due to the distribution populating non-parabolic states within the band. This paper presents two different non-parabolic formulations of the hydrodynamic model suitable for the simulation of inhomogeneous semiconductor devices. The first formulation uses the Kane dispersion relationship (hk)(exp 2)/2m = W(1 + alpha(W)). The second formulation makes use of a power law ((hk)(exp 2)/2m = xW(sup y)) for the dispersion relation. Hydrodynamic models which use the first formulation rely on the binomial expansion to obtain moment equations with closed form coefficients. This limits the energy range over which the model is valid. The power law formulation readily produces closed form coefficients similar to those obtained using the parabolic band approximation. However, the fitting parameters (x,y) are only valid over a limited energy range. The physical significance of the band non-parabolicity is discussed as well as the advantages/disadvantages and approximations of the two non-parabolic models. A companion paper describes device simulations based on the three dispersion relationships: parabolic, Kane dispersion, and power low dispersion.

Three-dimensional microscopy of the Rad51 recombination protein during meiotic prophase.

PubMed Central

Franklin, A E; McElver, J; Sunjevaric, I; Rothstein, R; Bowen, B; Cande, W Z

1999-01-01

An open question in meiosis is whether the Rad51 recombination protein functions solely in meiotic recombination or whether it is also involved in the chromosome homology search. To address this question, we have performed three-dimensional high-resolution immunofluorescence microscopy to visualize native Rad51 structures in maize male meiocytes. Maize has two closely related RAD51 genes that are expressed at low levels in differentiated tissues and at higher levels in mitotic and meiotic tissues. Cells and nuclei were specially fixed and embedded in polyacrylamide to maintain both native chromosome structure and the three dimensionality of the specimens. Analysis of Rad51 in maize meiocytes revealed that when chromosomes condense during leptotene, Rad51 is diffuse within the nucleus. Rad51 foci form on the chromosomes at the beginning of zygotene and rise to approximately 500 per nucleus by mid-zygotene when chromosomes are pairing and synapsing. During chromosome pairing, we consistently found two contiguous Rad51 foci on paired chromosomes. These paired foci may identify the sites where DNA sequence homology is being compared. During pachytene, the number of Rad51 foci drops to seven to 22 per nucleus. This higher number corresponds approximately to the number of chiasmata in maize meiosis. These observations are consistent with a role for Rad51 in the homology search phase of chromosome pairing in addition to its known role in meiotic recombination. PMID:10330467

Modulation of nucleotide sensitivity of ATP-sensitive potassium channels by phosphatidylinositol-4-phosphate 5-kinase.

PubMed

Shyng, S L; Barbieri, A; Gumusboga, A; Cukras, C; Pike, L; Davis, J N; Stahl, P D; Nichols, C G

2000-01-18

ATP-sensitive potassium channels (K(ATP) channels) regulate cell excitability in response to metabolic changes. K(ATP) channels are formed as a complex of a sulfonylurea receptor (SURx), a member of the ATP-binding cassette protein family, and an inward rectifier K(+) channel subunit (Kir6.x). Membrane phospholipids, in particular phosphatidylinositol (PI) 4,5-bisphosphate (PIP(2)), activate K(ATP) channels and antagonize ATP inhibition of K(ATP) channels when applied to inside-out membrane patches. To examine the physiological relevance of this regulatory mechanism, we manipulated membrane PIP(2) levels by expressing either the wild-type or an inactive form of PI-4-phosphate 5-kinase (PIP5K) in COSm6 cells and examined the ATP sensitivity of coexpressed K(ATP) channels. Channels from cells expressing the wild-type PIP5K have a 6-fold lower ATP sensitivity (K(1/2), the half maximal inhibitory concentration, approximately 60 microM) than the sensitivities from control cells (K(1/2) approximately 10 microM). An inactive form of the PIP5K had little effect on the K(1/2) of wild-type channels but increased the ATP-sensitivity of a mutant K(ATP) channel that has an intrinsically lower ATP sensitivity (from K(1/2) approximately 450 microM to K(1/2) approximately 100 microM), suggesting a decrease in membrane PIP(2) levels as a consequence of a dominant-negative effect of the inactive PIP5K. These results show that PIP5K activity, which regulates PIP(2) and PI-3,4,5-P(3) levels, is a significant determinant of the physiological nucleotide sensitivity of K(ATP) channels.

Male reproductive development: gene expression profiling of maize anther and pollen ontogeny

PubMed Central

Ma, Jiong; Skibbe, David S; Fernandes, John; Walbot, Virginia

2008-01-01

Background During flowering, central anther cells switch from mitosis to meiosis, ultimately forming pollen containing haploid sperm. Four rings of surrounding somatic cells differentiate to support first meiosis and later pollen dispersal. Synchronous development of many anthers per tassel and within each anther facilitates dissection of carefully staged maize anthers for transcriptome profiling. Results Global gene expression profiles of 7 stages representing 29 days of anther development are analyzed using a 44 K oligonucleotide array querying approximately 80% of maize protein-coding genes. Mature haploid pollen containing just two cell types expresses 10,000 transcripts. Anthers contain 5 major cell types and express >24,000 transcript types: each anther stage expresses approximately 10,000 constitutive and approximately 10,000 or more transcripts restricted to one or a few stages. The lowest complexity is present during meiosis. Large suites of stage-specific and co-expressed genes are identified through Gene Ontology and clustering analyses as functional classes for pre-meiotic, meiotic, and post-meiotic anther development. MADS box and zinc finger transcription factors with constitutive and stage-limited expression are identified. Conclusions We propose that the extensive gene expression of anther cells and pollen represents the key test of maize genome fitness, permitting strong selection against deleterious alleles in diploid anthers and haploid pollen. Because flowering plants show a substantial bias for male-sterile compared to female-sterile mutations, we propose that this fitness test is general. Because both somatic and germinal cells are transcriptionally quiescent during meiosis, we hypothesize that successful completion of meiosis is required to trigger maturation of anther somatic cells. PMID:19099579

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.

Compartmental hollow fiber capillary membrane-based bioreactor technology for in vitro studies on red blood cell lineage direction of hematopoietic stem cells.

PubMed

Housler, Greggory J; Miki, Toshio; Schmelzer, Eva; Pekor, Christopher; Zhang, Xiaokui; Kang, Lin; Voskinarian-Berse, Vanessa; Abbot, Stewart; Zeilinger, Katrin; Gerlach, Jörg C

2012-02-01

Continuous production of red blood cells (RBCs) in an automated closed culture system using hematopoietic stem cell (HSC) progenitor cell populations is of interest for clinical application because of the high demand for blood transfusions. Previously, we introduced a four-compartment bioreactor that consisted of two bundles of hollow fiber microfiltration membranes for transport of culture medium (forming two medium compartments), interwoven with one bundle of hollow fiber membranes for transport of oxygen (O(2)), carbon dioxide (CO(2)), and other gases (forming one gas compartment). Small-scale prototypes were developed of the three-dimensional (3D) perfusion cell culture systems, which enable convection-based mass transfer and integral oxygenation in the cell compartment. CD34(+) HSC were isolated from human cord blood units using a magnetic separation procedure. Cells were inoculated into 2- or 8-mL scaled-down versions of the previously designed 800-mL cell compartment devices and perfused with erythrocyte proliferation and differentiation medium. First, using the small-scale 2-mL analytical scale bioreactor, with an initial seeding density of 800,000 cells/mL, we demonstrated approximately 100-fold cell expansion and differentiation after 7 days of culture. An 8-mL laboratory-scale bioreactor was then used to show pseudocontinuous production by intermediately harvesting cells. Subsequently, we were able to use a model to demonstrate semicontinuous production with up to 14,288-fold expansion using seeding densities of 800,000 cells/mL. The down-scaled culture technology allows for expansion of CD34(+) cells and stimulating these progenitors towards RBC lineage, expressing approximately 40% CD235(+) and enucleation. The 3D perfusion technology provides an innovative tool for studies on RBC production, which is scalable.

Compartmental Hollow Fiber Capillary Membrane–Based Bioreactor Technology for In Vitro Studies on Red Blood Cell Lineage Direction of Hematopoietic Stem Cells

PubMed Central

Housler, Greggory J.; Miki, Toshio; Schmelzer, Eva; Pekor, Christopher; Zhang, Xiaokui; Kang, Lin; Voskinarian-Berse, Vanessa; Abbot, Stewart; Zeilinger, Katrin

2012-01-01

Continuous production of red blood cells (RBCs) in an automated closed culture system using hematopoietic stem cell (HSC) progenitor cell populations is of interest for clinical application because of the high demand for blood transfusions. Previously, we introduced a four-compartment bioreactor that consisted of two bundles of hollow fiber microfiltration membranes for transport of culture medium (forming two medium compartments), interwoven with one bundle of hollow fiber membranes for transport of oxygen (O2), carbon dioxide (CO2), and other gases (forming one gas compartment). Small-scale prototypes were developed of the three-dimensional (3D) perfusion cell culture systems, which enable convection-based mass transfer and integral oxygenation in the cell compartment. CD34+ HSC were isolated from human cord blood units using a magnetic separation procedure. Cells were inoculated into 2- or 8-mL scaled-down versions of the previously designed 800-mL cell compartment devices and perfused with erythrocyte proliferation and differentiation medium. First, using the small-scale 2-mL analytical scale bioreactor, with an initial seeding density of 800,000 cells/mL, we demonstrated approximately 100-fold cell expansion and differentiation after 7 days of culture. An 8-mL laboratory-scale bioreactor was then used to show pseudocontinuous production by intermediately harvesting cells. Subsequently, we were able to use a model to demonstrate semicontinuous production with up to 14,288-fold expansion using seeding densities of 800,000 cells/mL. The down-scaled culture technology allows for expansion of CD34+ cells and stimulating these progenitors towards RBC lineage, expressing approximately 40% CD235+ and enucleation. The 3D perfusion technology provides an innovative tool for studies on RBC production, which is scalable. PMID:21933020

An iterative analytical technique for the design of interplanetary direct transfer trajectories including perturbations

NASA Astrophysics Data System (ADS)

Parvathi, S. P.; Ramanan, R. V.

2018-06-01

An iterative analytical trajectory design technique that includes perturbations in the departure phase of the interplanetary orbiter missions is proposed. The perturbations such as non-spherical gravity of Earth and the third body perturbations due to Sun and Moon are included in the analytical design process. In the design process, first the design is obtained using the iterative patched conic technique without including the perturbations and then modified to include the perturbations. The modification is based on, (i) backward analytical propagation of the state vector obtained from the iterative patched conic technique at the sphere of influence by including the perturbations, and (ii) quantification of deviations in the orbital elements at periapsis of the departure hyperbolic orbit. The orbital elements at the sphere of influence are changed to nullify the deviations at the periapsis. The analytical backward propagation is carried out using the linear approximation technique. The new analytical design technique, named as biased iterative patched conic technique, does not depend upon numerical integration and all computations are carried out using closed form expressions. The improved design is very close to the numerical design. The design analysis using the proposed technique provides a realistic insight into the mission aspects. Also, the proposed design is an excellent initial guess for numerical refinement and helps arrive at the four distinct design options for a given opportunity.

The frequency-dependent response of single aerosol particles to vapour phase oscillations and its application in measuring diffusion coefficients

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

Preston, Thomas C.; Davies, James F.; Wilson, Kevin R.

A new method for measuring diffusion in the condensed phase of single aerosol particles is proposed and demonstrated. The technique is based on the frequency-dependent response of a binary particle to oscillations in the vapour phase of one of its chemical components. Here, we discuss how this physical situation allows for what would typically be a non-linear boundary value problem to be approximately reduced to a linear boundary value problem. For the case of aqueous aerosol particles, we investigate the accuracy of the closed-form analytical solution to this linear problem through a comparison with the numerical solution of the fullmore » problem. Then, using experimentally measured whispering gallery modes to track the frequency-dependent response of aqueous particles to relative humidity oscillations, we determine diffusion coefficients as a function of water activity. The measured diffusion coefficients are compared to previously reported values found using the two common experiments: (i) the analysis of the sorption/desorption of water from a particle after a step-wise change to the surrounding relative humidity and (ii) the isotopic exchange of water between a particle and the vapour phase. The technique presented here has two main strengths: first, when compared to the sorption/desorption experiment, it does not require the numerical evaluation of a boundary value problem during the fitting process as a closed-form expression is available. Second, when compared to the isotope exchange experiment, it does not require the use of labeled molecules. Therefore, the frequency-dependent experiment retains the advantages of these two commonly used methods but does not suffer from their drawbacks.« less

The frequency-dependent response of single aerosol particles to vapour phase oscillations and its application in measuring diffusion coefficients

DOE PAGES

Preston, Thomas C.; Davies, James F.; Wilson, Kevin R.

2017-01-13

A new method for measuring diffusion in the condensed phase of single aerosol particles is proposed and demonstrated. The technique is based on the frequency-dependent response of a binary particle to oscillations in the vapour phase of one of its chemical components. Here, we discuss how this physical situation allows for what would typically be a non-linear boundary value problem to be approximately reduced to a linear boundary value problem. For the case of aqueous aerosol particles, we investigate the accuracy of the closed-form analytical solution to this linear problem through a comparison with the numerical solution of the fullmore » problem. Then, using experimentally measured whispering gallery modes to track the frequency-dependent response of aqueous particles to relative humidity oscillations, we determine diffusion coefficients as a function of water activity. The measured diffusion coefficients are compared to previously reported values found using the two common experiments: (i) the analysis of the sorption/desorption of water from a particle after a step-wise change to the surrounding relative humidity and (ii) the isotopic exchange of water between a particle and the vapour phase. The technique presented here has two main strengths: first, when compared to the sorption/desorption experiment, it does not require the numerical evaluation of a boundary value problem during the fitting process as a closed-form expression is available. Second, when compared to the isotope exchange experiment, it does not require the use of labeled molecules. Therefore, the frequency-dependent experiment retains the advantages of these two commonly used methods but does not suffer from their drawbacks.« less

Facial dynamics and emotional expressions in facial aging treatments.

PubMed

Michaud, Thierry; Gassia, Véronique; Belhaouari, Lakhdar

2015-03-01

Facial expressions convey emotions that form the foundation of interpersonal relationships, and many of these emotions promote and regulate our social linkages. Hence, the facial aging symptomatological analysis and the treatment plan must of necessity include knowledge of the facial dynamics and the emotional expressions of the face. This approach aims to more closely meet patients' expectations of natural-looking results, by correcting age-related negative expressions while observing the emotional language of the face. This article will successively describe patients' expectations, the role of facial expressions in relational dynamics, the relationship between facial structures and facial expressions, and the way facial aging mimics negative expressions. Eventually, therapeutic implications for facial aging treatment will be addressed. © 2015 Wiley Periodicals, Inc.

The soil water characteristic as new class of closed-form parametric expressions for the flow duration curve

NASA Astrophysics Data System (ADS)

Sadegh, M.; Vrugt, J. A.; Gupta, H. V.; Xu, C.

2016-04-01

The flow duration curve is a signature catchment characteristic that depicts graphically the relationship between the exceedance probability of streamflow and its magnitude. This curve is relatively easy to create and interpret, and is used widely for hydrologic analysis, water quality management, and the design of hydroelectric power plants (among others). Several mathematical expressions have been proposed to mimic the FDC. Yet, these efforts have not been particularly successful, in large part because available functions are not flexible enough to portray accurately the functional shape of the FDC for a large range of catchments and contrasting hydrologic behaviors. Here, we extend the work of Vrugt and Sadegh (2013) and introduce several commonly used models of the soil water characteristic as new class of closed-form parametric expressions for the flow duration curve. These soil water retention functions are relatively simple to use, contain between two to three parameters, and mimic closely the empirical FDCs of 430 catchments of the MOPEX data set. We then relate the calibrated parameter values of these models to physical and climatological characteristics of the watershed using multivariate linear regression analysis, and evaluate the regionalization potential of our proposed models against those of the literature. If quality of fit is of main importance then the 3-parameter van Genuchten model is preferred, whereas the 2-parameter lognormal, 3-parameter GEV and generalized Pareto models show greater promise for regionalization.

Differential expression of non-coding RNAs and continuous evolution of the X chromosome in testicular transcriptome of two mouse species.

PubMed

Homolka, David; Ivanek, Robert; Forejt, Jiri; Jansa, Petr

2011-02-14

Tight regulation of testicular gene expression is a prerequisite for male reproductive success, while differentiation of gene activity in spermatogenesis is important during speciation. Thus, comparison of testicular transcriptomes between closely related species can reveal unique regulatory patterns and shed light on evolutionary constraints separating the species. Here, we compared testicular transcriptomes of two closely related mouse species, Mus musculus and Mus spretus, which diverged more than one million years ago. We analyzed testicular expression using tiling arrays overlapping Chromosomes 2, X, Y and mitochondrial genome. An excess of differentially regulated non-coding RNAs was found on Chromosome 2 including the intronic antisense RNAs, intergenic RNAs and premature forms of Piwi-interacting RNAs (piRNAs). Moreover, striking difference was found in the expression of X-linked G6pdx gene, the parental gene of the autosomal retrogene G6pd2. The prevalence of non-coding RNAs among differentially expressed transcripts indicates their role in species-specific regulation of spermatogenesis. The postmeiotic expression of G6pdx in Mus spretus points towards the continuous evolution of X-chromosome silencing and provides an example of expression change accompanying the out-of-the X-chromosomal retroposition.

Increased expression and processing of caspase-12 after traumatic brain injury in rats.

PubMed

Larner, Stephen F; Hayes, Ronald L; McKinsey, Deborah M; Pike, Brian R; Wang, Kevin K W

2004-01-01

Traumatic brain injury (TBI) disrupts tissue homeostasis resulting in pathological apoptotic activation. Recently, caspase-12 was reported to be induced and activated by the unfolded protein response following excess endoplasmic reticulum (ER) stress. This study examined rat caspase-12 expression using the controlled cortical impact TBI model. Immunoblots of fractionalized cell lysates found elevated caspase-12 proform (approximately 60 kDa) and processed form (approximately 12 kDa), with peak induction observed within 24 h post-injury in the cortex (418% and 503%, respectively). Hippocampus caspase-12 proform induction peaked at 24 h post-injury (641%), while processed form induction peaked at 6 h (620%). Semi-quantitative reverse transcriptase-polymerase chain reaction (RT-PCR) analysis confirmed elevated caspase-12 mRNA levels after TBI. Injury severity (1.0, 1.2 or 1.6 mm compression) was associated with increased caspase-12 mRNA expression, peaking at 5 days in the cortex (657%, 651% and 1259%, respectively) and 6 h in the hippocampus (435%, 451% and 460%, respectively). Immunohistochemical analysis revealed caspase-12 induction in neurons in both the cortex and hippocampus as well as in astrocytes at the contusion site. This is the first report of increased expression of caspase-12 following TBI. Our results suggest that the caspase-12-mediated ER apoptotic pathway may play a role in rat TBI pathology independent of the receptor- or mitochondria-mediated apoptotic pathways.

SU-F-T-144: Analytical Closed Form Approximation for Carbon Ion Bragg Curves in Water

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

Tuomanen, S; Moskvin, V; Farr, J

2016-06-15

Purpose: Semi-empirical modeling is a powerful computational method in radiation dosimetry. A set of approximations exist for proton ion depth dose distribution (DDD) in water. However, the modeling is more complicated for carbon ions due to fragmentation. This study addresses this by providing and evaluating a new methodology for DDD modeling of carbon ions in water. Methods: The FLUKA, Monte Carlo (MC) general-purpose transport code was used for simulation of carbon DDDs for energies of 100–400 MeV in water as reference data model benchmarking. Based on Thomas Bortfeld’s closed form equation approximating proton Bragg Curves as a basis, we derivedmore » the critical constants for a beam of Carbon ions by applying models of radiation transport by Lee et. al. and Geiger to our simulated Carbon curves. We hypothesized that including a new exponential (κ) residual distance parameter to Bortfeld’s fluence reduction relation would improve DDD modeling for carbon ions. We are introducing an additional term to be added to Bortfeld’s equation to describe fragmentation tail. This term accounts for the pre-peak dose from nuclear fragments (NF). In the post peak region, the NF transport will be treated as new beams utilizing the Glauber model for interaction cross sections and the Abrasion- Ablation fragmentation model. Results: The carbon beam specific constants in the developed model were determined to be : p= 1.75, β=0.008 cm-1, γ=0.6, α=0.0007 cm MeV, σmono=0.08, and the new exponential parameter κ=0.55. This produced a close match for the plateau part of the curve (max deviation 6.37%). Conclusion: The derived semi-empirical model provides an accurate approximation of the MC simulated clinical carbon DDDs. This is the first direct semi-empirical simulation for the dosimetry of therapeutic carbon ions. The accurate modeling of the NF tail in the carbon DDD will provide key insight into distal edge dose deposition formation.« less

Analytical Phase Equilibrium Function for Mixtures Obeying Raoult's and Henry's Laws

NASA Astrophysics Data System (ADS)

Hayes, Robert

When a mixture of two substances exists in both the liquid and gas phase at equilibrium, Raoults and Henry's laws (ideal solution and ideal dilute solution approximations) can be used to estimate the gas and liquid mole fractions at the extremes of either very little solute or solvent. By assuming that a cubic polynomial can reasonably approximate the intermediate values to these extremes as a function of mole fraction, the cubic polynomial is solved and presented. A closed form equation approximating the pressure dependence on mole fraction of the constituents is thereby obtained. As a first approximation, this is a very simple and potentially useful means to estimate gas and liquid mole fractions of equilibrium mixtures. Mixtures with an azeotrope require additional attention if this type of approach is to be utilized. This work supported in part by federal Grant NRC-HQ-84-14-G-0059.

Numerical Approximation of Elasticity Tensor Associated With Green-Naghdi Rate.

PubMed

Liu, Haofei; Sun, Wei

2017-08-01

Objective stress rates are often used in commercial finite element (FE) programs. However, deriving a consistent tangent modulus tensor (also known as elasticity tensor or material Jacobian) associated with the objective stress rates is challenging when complex material models are utilized. In this paper, an approximation method for the tangent modulus tensor associated with the Green-Naghdi rate of the Kirchhoff stress is employed to simplify the evaluation process. The effectiveness of the approach is demonstrated through the implementation of two user-defined fiber-reinforced hyperelastic material models. Comparisons between the approximation method and the closed-form analytical method demonstrate that the former can simplify the material Jacobian evaluation with satisfactory accuracy while retaining its computational efficiency. Moreover, since the approximation method is independent of material models, it can facilitate the implementation of complex material models in FE analysis using shell/membrane elements in abaqus.

Thermal ionization of Cs Rydberg states

NASA Astrophysics Data System (ADS)

Glukhov, I. L.; Ovsiannikov, V. D.

2009-01-01

Rates Pnl of photoionization from Rydberg ns-, np-, nd-states of a valence electron in Cs, induced by black-body radiation, were calculated on the basis of the modified Fues model potential method. The numerical data were approximated with a three-term expression which reproduces in a simple analytical form the dependence of Pnl on the ambient temperature T and on the principal quantum number n. The comparison between approximate and exactly calculated values of the thermal ionization rate demonstrates the applicability of the proposed approximation for highly excited states with n from 20 to 100 in a wide temperature range of T from 100 to 10,000 K. We present coefficients of this approximation for the s-, p- and d-series of Rydberg states.

Approximate Bayesian evaluations of measurement uncertainty

NASA Astrophysics Data System (ADS)

Possolo, Antonio; Bodnar, Olha

2018-04-01

The Guide to the Expression of Uncertainty in Measurement (GUM) includes formulas that produce an estimate of a scalar output quantity that is a function of several input quantities, and an approximate evaluation of the associated standard uncertainty. This contribution presents approximate, Bayesian counterparts of those formulas for the case where the output quantity is a parameter of the joint probability distribution of the input quantities, also taking into account any information about the value of the output quantity available prior to measurement expressed in the form of a probability distribution on the set of possible values for the measurand. The approximate Bayesian estimates and uncertainty evaluations that we present have a long history and illustrious pedigree, and provide sufficiently accurate approximations in many applications, yet are very easy to implement in practice. Differently from exact Bayesian estimates, which involve either (analytical or numerical) integrations, or Markov Chain Monte Carlo sampling, the approximations that we describe involve only numerical optimization and simple algebra. Therefore, they make Bayesian methods widely accessible to metrologists. We illustrate the application of the proposed techniques in several instances of measurement: isotopic ratio of silver in a commercial silver nitrate; odds of cryptosporidiosis in AIDS patients; height of a manometer column; mass fraction of chromium in a reference material; and potential-difference in a Zener voltage standard.

Biocompatibility of Synthetic Poly(ester urethane)/Polyhedral Oligomeric Silsesquioxane Matrices with Embryonic Stem Cell Proliferation and Differentiation

PubMed Central

Guo, Yan-Lin; Wang, Wenshou; Otaigbe, Joshua U.

2010-01-01

Incorporation of polyhedral oligomeric silsesquioxanes (POSS) into poly (ester urethane)s (PEU) as a building block results in a PEU/POSS hybrid polymer with increased mechanical strength and thermostability. An attractive feature of the new polymer is that it forms a porous matrix when cast in the form of a thin film, making it potentially useful in tissue engineering. In this study, we present detailed microscopic analysis of the PEU/POSS matrix and demonstrate its biocompatibility with cell culture. The PEU/POSS polymer forms a continuous porous matrix with open pores and interconnected grooves. From SEM image analysis, it is calculated that there are about 950 pores per mm2 of the matrix area with pore size ranging from 1 to 15 μm in diameter. The area occupied by the pores represents approximately 7.6 % of matrix area. Using mouse embryonic stem cells (ESCs), we demonstrate that the PEU/POSS matrix provides excellent support for cell proliferation and differentiation. Under the cell culture condition optimized to maintain self-renewal, ESCs grown on a PEU/POSS matrix exhibit undifferentiated morphology, express pluripotency markers, and have similar growth rate to cells grown on gelatin. When induced for differentiation, ESCs underwent dramatic morphological change, characterized by the loss of clonogenecity and increased cell size with well-expanded cytoskeleton networks. Differentiated cells are able to form a continuous monolayer that is closely embedded on the matrix. The excellent compatibility between the PEU/POSS matrix and ESC proliferation/differentiation demonstrates the potential of using PEU/POSS polymers in future ESC-based tissue engineering. PMID:20213627

Crystal structure of the cysteine protease inhibitor 2 from Entamoeba histolytica: Functional convergence of a common protein fold

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

Casados-Vázquez, Luz E.; Lara-González, Samuel; Brieb, Luis G.

Cysteine proteases (CP) are key pathogenesis and virulence determinants of protozoan parasites. Entamoeba histolytica contains at least 50 cysteine proteases; however, only three (EhCP1, EhCP2 and EhCP5) are responsible for approximately 90% of the cysteine protease activity in this parasite. CPs are expressed as inactive zymogens. Because the processed proteases are potentially cytotoxic, protozoan parasites have developed mechanisms to regulate their activity. Inhibitors of cysteine proteases (ICP) of the chagasin-like inhibitor family (MEROPS family I42) were recently identified in bacteria and protozoan parasites. E. histolytica contains two ICP-encoding genes of the chagasin-like inhibitor family. EhICP1 localizes to the cytosol, whereasmore » EhICP2 is targeted to phagosomes. Herein, we report two crystal structures of EhICP2. The overall structure of EhICP2 consists of eight {beta}-strands and closely resembles the immunoglobulin fold. A comparison between the two crystal forms of EhICP2 indicates that the conserved BC, DE and FG loops form a flexible wedge that may block the active site of CPs. The positively charged surface of the wedge-forming loops in EhICP2 contrasts with the neutral surface of the wedge-forming loops in chagasin. We postulate that the flexibility and positive charge observed in the DE and FG loops of EhICP2 may be important to facilitate the initial binding of this inhibitor to the battery of CPs present in E. histolytica.« less

Strong shock implosion, approximate solution

NASA Astrophysics Data System (ADS)

Fujimoto, Y.; Mishkin, E. A.; Alejaldre, C.

1983-01-01

The self-similar, center-bound motion of a strong spherical, or cylindrical, shock wave moving through an ideal gas with a constant, γ= cp/ cv, is considered and a linearized, approximate solution is derived. An X, Y phase plane of the self-similar solution is defined and the representative curved of the system behind the shock front is replaced by a straight line connecting the mappings of the shock front with that of its tail. The reduced pressure P(ξ), density R(ξ) and velocity U1(ξ) are found in closed, quite accurate, form. Comparison with numerically obtained results, for γ= {5}/{3} and γ= {7}/{5}, is shown.

Constructing analytic solutions on the Tricomi equation

NASA Astrophysics Data System (ADS)

Ghiasi, Emran Khoshrouye; Saleh, Reza

2018-04-01

In this paper, homotopy analysis method (HAM) and variational iteration method (VIM) are utilized to derive the approximate solutions of the Tricomi equation. Afterwards, the HAM is optimized to accelerate the convergence of the series solution by minimizing its square residual error at any order of the approximation. It is found that effect of the optimal values of auxiliary parameter on the convergence of the series solution is not negligible. Furthermore, the present results are found to agree well with those obtained through a closed-form equation available in the literature. To conclude, it is seen that the two are effective to achieve the solution of the partial differential equations.

A continued fraction resummation form of bath relaxation effect in the spin-boson model

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

Gong, Zhihao; Tang, Zhoufei; Wu, Jianlan, E-mail: jianlanwu@zju.edu.cn

2015-02-28

In the spin-boson model, a continued fraction form is proposed to systematically resum high-order quantum kinetic expansion (QKE) rate kernels, accounting for the bath relaxation effect beyond the second-order perturbation. In particular, the analytical expression of the sixth-order QKE rate kernel is derived for resummation. With higher-order correction terms systematically extracted from higher-order rate kernels, the resummed quantum kinetic expansion approach in the continued fraction form extends the Pade approximation and can fully recover the exact quantum dynamics as the expansion order increases.

Nonlinear Schrödinger equations with single power nonlinearity and harmonic potential

NASA Astrophysics Data System (ADS)

Cipolatti, R.; de Macedo Lira, Y.; Trallero-Giner, C.

2018-03-01

We consider a generalized nonlinear Schrödinger equation (GNLS) with a single power nonlinearity of the form λ ≤ft\\vert \\varphi \\right\\vert p , with p  >  0 and λ\\in{R} , in the presence of a harmonic confinement. We report the conditions that p and λ must fulfill for the existence and uniqueness of ground states of the GNLS. We discuss the Cauchy problem and summarize which conditions are required for the nonlinear term λ ≤ft\\vert \\varphi \\right\\vert p to render the ground state solutions orbitally stable. Based on a new variational method we provide exact formulæ for the minimum energy for each index p and the changing range of values of the nonlinear parameter λ. Also, we report an approximate close analytical expression for the ground state energy, performing a comparative analysis of the present variational calculations with those obtained by a generalized Thomas-Fermi approach, and soliton solutions for the respective ranges of p and λ where these solutions can be implemented to describe the minimum energy.

Moderately nonlinear ultrasound propagation in blood-mimicking fluid.

PubMed

Kharin, Nikolay A; Vince, D Geoffrey

2004-04-01

In medical diagnostic ultrasound (US), higher than-in-water nonlinearity of body fluids and tissue usually does not produce strong nonlinearly distorted waves because of the high absorption. The relative influence of absorption and nonlinearity can be characterized by the Gol'dberg number Gamma. There are two limiting cases in nonlinear acoustics: weak waves (Gamma < 1) or strong waves (Gamma > 1). However, at diagnostic frequencies in tissue and body fluids, the nonlinear effects and effects of absorption more likely are comparable (Gol'dberg number Gamma approximately 1). The aim of this work was to study the nonlinear propagation of a moderately nonlinear US second harmonic signal in a blood-mimicking fluid. Quasilinear solutions to the KZK equation are presented, assuming radiation from a flat and geometrically focused circular Gaussian source. The solutions are expressed in a new simplified closed form and are in very good agreement with those of previous studies measuring and modeling Gaussian beams. The solutions also show good agreement with the measurements of the beams produced by commercially available transducers, even without special Gaussian shading.

Effects of solid-propellant temperature gradients on the internal ballistics of the Space Shuttle

NASA Technical Reports Server (NTRS)

Sforzini, R. H.; Foster, W. A., Jr.; Shackelford, B. W., Jr.

1978-01-01

The internal ballistic effects of combined radial and circumferential grain temperature gradients are evaluated theoretically for the Space Shuttle solid rocket motors (SRMs). A simplified approach is devised for representing with closed-form mathematical expressions the temperature distribution resulting from the anticipated thermal history prior to launch. The internal ballistic effects of the gradients are established by use of a mathematical model which permits the propellant burning rate to vary circumferentially. Comparative results are presented for uniform and axisymmetric temperature distributions and the anticipated gradients based on an earlier two-dimensional analysis of the center SRM segment. The thrust imbalance potential of the booster stage is also assessed based on the difference in the thermal loading of the individual SRMs of the motor pair which may be encountered in both summer and winter environments at the launch site. Results indicate that grain temperature gradients could cause the thrust imbalance to be approximately 10% higher in the Space Shuttle than the imbalance caused by SRM manufacturing and propellant physical property variability alone.

Kinematics and dynamics of robotic systems with multiple closed loops

NASA Astrophysics Data System (ADS)

Zhang, Chang-De

The kinematics and dynamics of robotic systems with multiple closed loops, such as Stewart platforms, walking machines, and hybrid manipulators, are studied. In the study of kinematics, focus is on the closed-form solutions of the forward position analysis of different parallel systems. A closed-form solution means that the solution is expressed as a polynomial in one variable. If the order of the polynomial is less than or equal to four, the solution has analytical closed-form. First, the conditions of obtaining analytical closed-form solutions are studied. For a Stewart platform, the condition is found to be that one rotational degree of freedom of the output link is decoupled from the other five. Based on this condition, a class of Stewart platforms which has analytical closed-form solution is formulated. Conditions of analytical closed-form solution for other parallel systems are also studied. Closed-form solutions of forward kinematics for walking machines and multi-fingered grippers are then studied. For a parallel system with three three-degree-of-freedom subchains, there are 84 possible ways to select six independent joints among nine joints. These 84 ways can be classified into three categories: Category 3:3:0, Category 3:2:1, and Category 2:2:2. It is shown that the first category has no solutions; the solutions of the second category have analytical closed-form; and the solutions of the last category are higher order polynomials. The study is then extended to a nearly general Stewart platform. The solution is a 20th order polynomial and the Stewart platform has a maximum of 40 possible configurations. Also, the study is extended to a new class of hybrid manipulators which consists of two serially connected parallel mechanisms. In the study of dynamics, a computationally efficient method for inverse dynamics of manipulators based on the virtual work principle is developed. Although this method is comparable with the recursive Newton-Euler method for serial manipulators, its advantage is more noteworthy when applied to parallel systems. An approach of inverse dynamics of a walking machine is also developed, which includes inverse dynamic modeling, foot force distribution, and joint force/torque allocation.

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

NASA Astrophysics Data System (ADS)

Niazy, Pedram; Abbassi, Amir H.

2018-03-01

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