Wire in the Cable-Driven System of Surgical Robot

NASA Astrophysics Data System (ADS)

Wang, X. F.; Lv, N.; Mu, H. Z.; Xue, L. J.

2017-07-01

During the evolution of the surgical robot, cable plays an important role. It translates motion and force precisely from surgeon’s hand to the tool’s tips. In the paper, the vertical wires, the composition of cable, are mathematically modeled from a geometric point of view. The cable structure and tension are analyzed according to the characteristics of wire screw twist. The structural equations of the wires in different positions are derived for both non-bent cable and bent cable, respectively. The bending moment formula of bent cable is also obtained. This will help researchers find suitable cable and design more matched pulley.

A multiscale approach to modelling electrochemical processes occurring across the cell membrane with application to transmission of action potentials.

PubMed

Richardson, G

2009-09-01

By application of matched asymptotic expansions, a simplified partial differential equation (PDE) model for the dynamic electrochemical processes occurring in the vicinity of a membrane, as ions selectively permeate across it, is formally derived from the Poisson-Nernst-Planck equations of electrochemistry. It is demonstrated that this simplified model reduces itself, in the limit of a long thin axon, to the cable equation used by Hodgkin and Huxley to describe the propagation of action potentials in the unmyelinated squid giant axon. The asymptotic reduction from the simplified PDE model to the cable equation leads to insights that are not otherwise apparent; these include an explanation of why the squid giant axon attains a diameter in the region of 1 mm. The simplified PDE model has more general application than the Hodgkin-Huxley cable equation and can, e.g. be used to describe action potential propagation in myelinated axons and neuronal cell bodies.

Numerical study of signal propagation in corrugated coaxial cables

DOE PAGES

Li, Jichun; Machorro, Eric A.; Shields, Sidney

2017-01-01

Our article focuses on high-fidelity modeling of signal propagation in corrugated coaxial cables. Taking advantage of the axisymmetry, the authors reduce the 3-D problem to a 2-D problem by solving time-dependent Maxwell's equations in cylindrical coordinates.They then develop a nodal discontinuous Galerkin method for solving their model equations. We prove stability and error analysis for the semi-discrete scheme. We we present our numerical results, we demonstrate that our algorithm not only converges as our theoretical analysis predicts, but it is also very effective in solving a variety of signal propagation problems in practical corrugated coaxial cables.

Equations of motion of slung load systems with results for dual lift

NASA Technical Reports Server (NTRS)

Cicolani, Luigi S.; Kanning, Gerd

1990-01-01

General simulation equations are derived for the rigid body motion of slung load systems. These systems are viewed as consisting of several rigid bodies connected by straight-line cables or links. The suspension can be assumed to be elastic or inelastic, both cases being of interest in simulation and control studies. Equations for the general system are obtained via D'Alembert's principle and the introduction of generalized velocity coordinates. Three forms are obtained. Two of these generalize previous case-specific results for single helicopter systems with elastic or inelastic suspensions. The third is a new formulation for inelastic suspensions. It is derived from the elastic suspension equations by choosing the generalized coordinates so as to separate motion due to cable stretching from motion with invariant cable lengths. The result is computationally more efficient than the conventional formulation, and is readily integrated with the elastic suspension formulation and readily applied to the complex dual lift and multilift systems. Equations are derived for dual lift systems. Three proposed suspension arrangements can be integrated in a single equation set. The equations are given in terms of the natural vectors and matrices of three-dimensional rigid body mechanics and are tractable for both analysis and programming.

The Discrete Hanging Cable

ERIC Educational Resources Information Center

Peters, James V.

2004-01-01

Using the methods of finite difference equations the discrete analogue of the parabolic and catenary cable are analysed. The fibonacci numbers and the golden ratio arise in the treatment of the catenary.

Multi-modal vibration amplitudes of taut inclined cables due to direct and/or parametric excitation

NASA Astrophysics Data System (ADS)

Macdonald, J. H. G.

2016-02-01

Cables are often prone to potentially damaging large amplitude vibrations. The dynamic excitation may be from external loading or motion of the cable ends, the latter including direct excitation, normally from components of end motion transverse to the cable, and parametric excitation induced by axial components of end motion causing dynamic tension variations. Geometric nonlinearity can be important, causing stiffening behaviour and nonlinear modal coupling. Previous analyses of the vibrations, often neglecting sag, have generally dealt with direct and parametric excitation separately or have reverted to numerical solutions of the responses. Here a nonlinear cable model is adopted, applicable to taut cables such as on cable-stayed bridges, that allows for cable inclination, small sag (such that the vibration modes are similar to those of a taut string), multiple modes in both planes and end motion and/or external forcing close to any natural frequency. Based on the method of scaling and averaging it is found that, for sinusoidal inputs and positive damping, non-zero steady state responses can only occur in the modes in each plane with natural frequencies close to the excitation frequency and those with natural frequencies close to half this frequency. Analytical solutions, in the form of non-dimensional polynomial equations, are derived for the steady state vibration amplitudes in up to three modes simultaneously: the directly excited mode, the corresponding nonlinearly coupled mode in the orthogonal plane and a parametrically excited mode with half the natural frequency. The stability of the solutions is also identified. The outputs of the equations are consistent with previous results, where available. Example results from the analytical solutions are presented for a typical inclined bridge cable subject to vertical excitation of the lower end, and they are validated by numerical integration of the equations of motion and against some previous experimental results. It is shown that the modal interactions and sag (although very small) affect the responses significantly.

Fractional cable equation for general geometry: A model of axons with swellings and anomalous diffusion.

PubMed

López-Sánchez, Erick J; Romero, Juan M; Yépez-Martínez, Huitzilin

2017-09-01

Different experimental studies have reported anomalous diffusion in brain tissues and notably this anomalous diffusion is expressed through fractional derivatives. Axons are important to understand neurodegenerative diseases such as multiple sclerosis, Alzheimer's disease, and Parkinson's disease. Indeed, abnormal accumulation of proteins and organelles in axons is a hallmark of these diseases. The diffusion in the axons can become anomalous as a result of this abnormality. In this case the voltage propagation in axons is affected. Another hallmark of different neurodegenerative diseases is given by discrete swellings along the axon. In order to model the voltage propagation in axons with anomalous diffusion and swellings, in this paper we propose a fractional cable equation for a general geometry. This generalized equation depends on fractional parameters and geometric quantities such as the curvature and torsion of the cable. For a cable with a constant radius we show that the voltage decreases when the fractional effect increases. In cables with swellings we find that when the fractional effect or the swelling radius increases, the voltage decreases. Similar behavior is obtained when the number of swellings and the fractional effect increase. Moreover, we find that when the radius swelling (or the number of swellings) and the fractional effect increase at the same time, the voltage dramatically decreases.

Fractional cable equation for general geometry: A model of axons with swellings and anomalous diffusion

NASA Astrophysics Data System (ADS)

López-Sánchez, Erick J.; Romero, Juan M.; Yépez-Martínez, Huitzilin

2017-09-01

Different experimental studies have reported anomalous diffusion in brain tissues and notably this anomalous diffusion is expressed through fractional derivatives. Axons are important to understand neurodegenerative diseases such as multiple sclerosis, Alzheimer's disease, and Parkinson's disease. Indeed, abnormal accumulation of proteins and organelles in axons is a hallmark of these diseases. The diffusion in the axons can become anomalous as a result of this abnormality. In this case the voltage propagation in axons is affected. Another hallmark of different neurodegenerative diseases is given by discrete swellings along the axon. In order to model the voltage propagation in axons with anomalous diffusion and swellings, in this paper we propose a fractional cable equation for a general geometry. This generalized equation depends on fractional parameters and geometric quantities such as the curvature and torsion of the cable. For a cable with a constant radius we show that the voltage decreases when the fractional effect increases. In cables with swellings we find that when the fractional effect or the swelling radius increases, the voltage decreases. Similar behavior is obtained when the number of swellings and the fractional effect increase. Moreover, we find that when the radius swelling (or the number of swellings) and the fractional effect increase at the same time, the voltage dramatically decreases.

Analysis of the cable equation with non-local and non-singular kernel fractional derivative

NASA Astrophysics Data System (ADS)

Karaagac, Berat

2018-02-01

Recently a new concept of differentiation was introduced in the literature where the kernel was converted from non-local singular to non-local and non-singular. One of the great advantages of this new kernel is its ability to portray fading memory and also well defined memory of the system under investigation. In this paper the cable equation which is used to develop mathematical models of signal decay in submarine or underwater telegraphic cables will be analysed using the Atangana-Baleanu fractional derivative due to the ability of the new fractional derivative to describe non-local fading memory. The existence and uniqueness of the more generalized model is presented in detail via the fixed point theorem. A new numerical scheme is used to solve the new equation. In addition, stability, convergence and numerical simulations are presented.

User's guide for a computer program to analyze the LRC 16 ft transonic dynamics tunnel cable mount system

NASA Technical Reports Server (NTRS)

Barbero, P.; Chin, J.

1973-01-01

The theoretical derivation of the set of equations is discussed which is applicable to modeling the dynamic characteristics of aeroelastically-scaled models flown on the two-cable mount system in a 16 ft transonic dynamics tunnel. The computer program provided for the analysis is also described. The program calculates model trim conditions as well as 3 DOF longitudinal and lateral/directional dynamic conditions for various flying cable and snubber cable configurations. Sample input and output are included.

Catenary-induced geometric nonlinearity effects on cable linear vibrations

NASA Astrophysics Data System (ADS)

Mansour, Achref; Mekki, Othman Ben; Montassar, Sami; Rega, Giuseppe

2018-01-01

This paper investigates the free undamped vibrations of cables of arbitrary sag and inclination according to the catenary theory. The proposed approach accounts for the catenary effect on the static profile around which the cable motion is defined. Considering first order geometric nonlinearities, exact expression of the curvature is obtained along with the ensuing correction of the well known Irvine parameter. Taking into account the new characterization, different regions of shallow and non-shallow profiles are identified for various inclinations. In view of such classification, the analysis carried out on cable linear modal properties shows the emergence of new dynamic features such as additional hybrid modes and internal resonances. Analytical and numerical results reduce to those obtained by classic formulations in the cases of both horizontal and inclined shallow/non-shallow cables.

Optimal energy harvesting from vortex-induced vibrations of cables.

PubMed

Antoine, G O; de Langre, E; Michelin, S

2016-11-01

Vortex-induced vibrations (VIV) of flexible cables are an example of flow-induced vibrations that can act as energy harvesting systems by converting energy associated with the spontaneous cable motion into electricity. This work investigates the optimal positioning of the harvesting devices along the cable, using numerical simulations with a wake oscillator model to describe the unsteady flow forcing. Using classical gradient-based optimization, the optimal harvesting strategy is determined for the generic configuration of a flexible cable fixed at both ends, including the effect of flow forces and gravity on the cable's geometry. The optimal strategy is found to consist systematically in a concentration of the harvesting devices at one of the cable's ends, relying on deformation waves along the cable to carry the energy towards this harvesting site. Furthermore, we show that the performance of systems based on VIV of flexible cables is significantly more robust to flow velocity variations, in comparison with a rigid cylinder device. This results from two passive control mechanisms inherent to the cable geometry: (i) the adaptability to the flow velocity of the fundamental frequencies of cables through the flow-induced tension and (ii) the selection of successive vibration modes by the flow velocity for cables with gravity-induced tension.

Optimal energy harvesting from vortex-induced vibrations of cables

NASA Astrophysics Data System (ADS)

Antoine, G. O.; de Langre, E.; Michelin, S.

2016-11-01

Vortex-induced vibrations (VIV) of flexible cables are an example of flow-induced vibrations that can act as energy harvesting systems by converting energy associated with the spontaneous cable motion into electricity. This work investigates the optimal positioning of the harvesting devices along the cable, using numerical simulations with a wake oscillator model to describe the unsteady flow forcing. Using classical gradient-based optimization, the optimal harvesting strategy is determined for the generic configuration of a flexible cable fixed at both ends, including the effect of flow forces and gravity on the cable's geometry. The optimal strategy is found to consist systematically in a concentration of the harvesting devices at one of the cable's ends, relying on deformation waves along the cable to carry the energy towards this harvesting site. Furthermore, we show that the performance of systems based on VIV of flexible cables is significantly more robust to flow velocity variations, in comparison with a rigid cylinder device. This results from two passive control mechanisms inherent to the cable geometry: (i) the adaptability to the flow velocity of the fundamental frequencies of cables through the flow-induced tension and (ii) the selection of successive vibration modes by the flow velocity for cables with gravity-induced tension.

Non-rocket Earth-Moon transport system

NASA Astrophysics Data System (ADS)

Bolonkin, Alexander

2003-06-01

This paper proposes a new transportation system for travel between Earth and Moon. This transportation system uses mechanical energy transfer and requires only minimal energy, using an engine located on Earth. A cable directly connects a pole of the Earth through a drive station to the lunar surface_ The equation for an optimal equal stress cable for complex gravitational field of Earth-Moon has been derived that allows significantly lower cable masses. The required strength could be provided by cables constructed of carbon nanotubes or carbon whiskers. Some of the constraints on such a system are discussed.

Non-classical and potential symmetry analysis of Richard's equation for moisture flow in soil

NASA Astrophysics Data System (ADS)

Wiltshire, Ron; El-Kafri, Manal

2004-01-01

This paper focuses upon the derivation of the non-classical symmetries of Bluman and Cole as they apply to Richard's equation for water flow in an unsaturated uniform soil. It is shown that the determining equations for the non-classical case lead to four highly non-linear equations which have been solved in five particular cases. In each case the corresponding similarity ansatz has been derived and Richard's equation is reduced to an ordinary differential equation. Explicit solutions are produced when possible. Richard's equation is also expressed as a potential system and in reviewing the classical Lie solutions a new symmetry is derived together with its similarity ansatz. Determining equations are then produced for the potential system using the non-classical algorithm. This results in an under-determined set of equations and an example symmetry that reveals a missing classical case is presented. An example of a classical and a non-classical symmetry reduction applied to the infiltration of moisture in soil is presented. The condition for surface invariance is used to demonstrate the equivalence of a classical Lie and a potential symmetry.

Optimal energy harvesting from vortex-induced vibrations of cables

PubMed Central

de Langre, E.; Michelin, S.

2016-01-01

Vortex-induced vibrations (VIV) of flexible cables are an example of flow-induced vibrations that can act as energy harvesting systems by converting energy associated with the spontaneous cable motion into electricity. This work investigates the optimal positioning of the harvesting devices along the cable, using numerical simulations with a wake oscillator model to describe the unsteady flow forcing. Using classical gradient-based optimization, the optimal harvesting strategy is determined for the generic configuration of a flexible cable fixed at both ends, including the effect of flow forces and gravity on the cable’s geometry. The optimal strategy is found to consist systematically in a concentration of the harvesting devices at one of the cable’s ends, relying on deformation waves along the cable to carry the energy towards this harvesting site. Furthermore, we show that the performance of systems based on VIV of flexible cables is significantly more robust to flow velocity variations, in comparison with a rigid cylinder device. This results from two passive control mechanisms inherent to the cable geometry: (i) the adaptability to the flow velocity of the fundamental frequencies of cables through the flow-induced tension and (ii) the selection of successive vibration modes by the flow velocity for cables with gravity-induced tension. PMID:27956880

Dynamic analysis of the deployment for mesh reflector deployable antennas with the cable-net structure

NASA Astrophysics Data System (ADS)

Zhang, Yiqun; Li, Na; Yang, Guigeng; Ru, Wenrui

2017-02-01

This paper presents a dynamic analysis approach for the composite structure of a deployable truss and cable-net system. An Elastic Catenary Element is adopted to model the slack/tensioned cables. Then, from the energy standpoint, the kinetic energy, elasticity-potential energy and geopotential energy of the cable-net structure and deployable truss are derived. Thus, the flexible multi-body dynamic model of the deployable antenna is built based on the Lagrange equation. The effect of the cable-net tension on the antenna truss is discussed and compared with previous publications and a dynamic deployment analysis is performed. Both the simulation and experimental results verify the validity of the method presented.

Modelling in vivo action potential propagation along a giant axon.

PubMed

George, Stuart; Foster, Jamie M; Richardson, Giles

2015-01-01

A partial differential equation model for the three-dimensional current flow in an excitable, unmyelinated axon is considered. Where the axon radius is significantly below a critical value R(crit) (that depends upon intra- and extra-cellular conductivity and ion channel conductance) the resistance of the intracellular space is significantly higher than that of the extracellular space, such that the potential outside the axon is uniformly small whilst the intracellular potential is approximated by the transmembrane potential. In turn, since the current flow is predominantly axial, it can be shown that the transmembrane potential is approximated by a solution to the one-dimensional cable equation. It is noted that the radius of the squid giant axon, investigated by (Hodgkin and Huxley 1952e), lies close to R(crit). This motivates us to apply the three-dimensional model to the squid giant axon and compare the results thus found to those obtained using the cable equation. In the context of the in vitro experiments conducted in (Hodgkin and Huxley 1952e) we find only a small difference between the wave profiles determined using these two different approaches and little difference between the speeds of action potential propagation predicted. This suggests that the cable equation approximation is accurate in this scenario. However when applied to the it in vivo setting, in which the conductivity of the surrounding tissue is considerably lower than that of the axoplasm, there are marked differences in both wave profile and speed of action potential propagation calculated using the two approaches. In particular, the cable equation significantly over predicts the increase in the velocity of propagation as axon radius increases. The consequences of these results are discussed in terms of the evolutionary costs associated with increasing the speed of action potential propagation by increasing axon radius.

Distance and Cable Length Measurement System

PubMed Central

Hernández, Sergio Elias; Acosta, Leopoldo; Toledo, Jonay

2009-01-01

A simple, economic and successful design for distance and cable length detection is presented. The measurement system is based on the continuous repetition of a pulse that endlessly travels along the distance to be detected. There is a pulse repeater at both ends of the distance or cable to be measured. The endless repetition of the pulse generates a frequency that varies almost inversely with the distance to be measured. The resolution and distance or cable length range could be adjusted by varying the repetition time delay introduced at both ends and the measurement time. With this design a distance can be measured with centimeter resolution using electronic system with microsecond resolution, simplifying classical time of flight designs which require electronics with picosecond resolution. This design was also applied to position measurement. PMID:22303169

Experimental validation of ultrasonic guided modes in electrical cables by optical interferometry.

PubMed

Mateo, Carlos; de Espinosa, Francisco Montero; Gómez-Ullate, Yago; Talavera, Juan A

2008-03-01

In this work, the dispersion curves of elastic waves propagating in electrical cables and in bare copper wires are obtained theoretically and validated experimentally. The theoretical model, based on Gazis equations formulated according to the global matrix methodology, is resolved numerically. Viscoelasticity and attenuation are modeled theoretically using the Kelvin-Voigt model. Experimental tests are carried out using interferometry. There is good agreement between the simulations and the experiments despite the peculiarities of electrical cables.

Elastic guided wave propagation in electrical cables.

PubMed

Mateo, Carlos; Talavera, Juan A; Muñoz, Antonio

2007-07-01

This article analyzes the propagation modes of ultrasound waves inside an electrical cable in order to assess its behavior as an acoustic transmission channel. A theoretical model for propagation of elastic waves in electric power cables is presented. The power cables are represented as viscoelastic-layered cylindrical structures with a copper core and a dielectric cover. The model equations then have been applied and numerically resolved for this and other known structures such as solid and hollow cylinders. The results are compared with available data from other models. Several experimental measures were carried out and were compared with results from the numerical simulations. Experimental and simulated results showed a significant difference between elastic wave attenuation inside standard versus bare, low-voltage power cables.

Equations of motion of slung-load systems, including multilift systems

NASA Technical Reports Server (NTRS)

Cicolani, Luigi S.; Kanning, Gerd

1992-01-01

General simulation equations are derived for the rigid body motion of slung-load systems. This work is motivated by an interest in trajectory control for slung loads carried by two or more helicopters. An approximation of these systems consists of several rigid bodies connected by straight-line cables or links. The suspension can be assumed elastic or inelastic. Equations for the general system are obtained from the Newton-Euler rigid-body equations with the introduction of generalized velocity coordinates. Three forms are obtained: two generalize previous case-specific results for single-helicopter systems with elastic and inelastic suspensions, respectively; and the third is a new formulation for inelastic suspensions. The latter is derived from the elastic suspension equations by choosing the generalized coordinates so that motion induced by cable stretching is separated from motion with invariant cable lengths, and by then nulling the stretching coordinates to get a relation for the suspension forces. The result is computationally more efficient than the conventional formulation, is readily integrated with the elastic suspension formulation, and is easily applied to the complex dual-lift and multilift systems. Results are given for two-helicopter systems; three configurations are included and these can be integrated in a single simulation. Equations are also given for some single-helicopter systems, for comparison with the previous literature, and for a multilift system. Equations for degenerate-body approximations (point masses, rigid rods) are also formulated and results are given for dual-lift and multilift systems. Finally, linearlized equations of motion are given for general slung-load systems are presented along with results for the two-helicopter system with a spreader bar.

Hybrid modeling for dynamic analysis of cable-pulley systems with time-varying length cable and its application

NASA Astrophysics Data System (ADS)

Wang, Jing; Qi, Zhaohui; Wang, Gang

2017-10-01

The dynamic analysis of cable-pulley systems is investigated in this paper, where the time-varying length characteristic of the cable as well as the coupling motion between the cable and the pulleys are considered. The dynamic model for cable-pulley systems are presented based on the principle of virtual power. Firstly, the cubic spline interpolation is adopted for modeling the flexible cable elements and the virtual 1powers of tensile strain, inertia and gravity forces on the cable are formulated. Then, the coupled motions between the cable and the movable or fixed pulley are described by the input and output contact points, based on the no-slip assumption and the spatial description. The virtual powers of inertia, gravity and applied forces on the contact segment of the cable, the movable and fixed pulleys are formulated. In particular, the internal node degrees of freedom of spline cable elements are reduced, which results in that only the independent description parameters of the nodes connected to the pulleys are included in the final governing dynamic equations. At last, two cable-pulley lifting mechanisms are considered as demonstrative application examples where the vibration of the lifting process is investigated. The comparison with ADAMS models is given to prove the validity of the proposed method.

A highly precise frequency-based method for estimating the tension of an inclined cable with unknown boundary conditions

NASA Astrophysics Data System (ADS)

Ma, Lin

2017-11-01

This paper develops a method for precisely determining the tension of an inclined cable with unknown boundary conditions. First, the nonlinear motion equation of an inclined cable is derived, and a numerical model of the motion of the cable is proposed using the finite difference method. The proposed numerical model includes the sag-extensibility, flexural stiffness, inclination angle and rotational stiffness at two ends of the cable. Second, the influence of the dynamic parameters of the cable on its frequencies is discussed in detail, and a method for precisely determining the tension of an inclined cable is proposed based on the derivatives of the eigenvalues of the matrices. Finally, a multiparameter identification method is developed that can simultaneously identify multiple parameters, including the rotational stiffness at two ends. This scheme is applicable to inclined cables with varying sag, varying flexural stiffness and unknown boundary conditions. Numerical examples indicate that the method provides good precision. Because the parameters of cables other than tension (e.g., the flexural stiffness and rotational stiffness at the ends) are not accurately known in practical engineering, the multiparameter identification method could further improve the accuracy of cable tension measurements.

Vibration Testing of Electrical Cables to Quantify Loads at Tie-Down Locations

NASA Technical Reports Server (NTRS)

Dutson, Joseph D.

2013-01-01

The standard method for defining static equivalent structural load factors for components is based on Mile s equation. Unless test data is available, 5% critical damping is assumed for all components when calculating loads. Application of this method to electrical cable tie-down hardware often results in high loads, which often exceed the capability of typical tie-down options such as cable ties and P-clamps. Random vibration testing of electrical cables was used to better understand the factors that influence component loads: natural frequency, damping, and mass participation. An initial round of vibration testing successfully identified variables of interest, checked out the test fixture and instrumentation, and provided justification for removing some conservatism in the standard method. Additional testing is planned that will include a larger range of cable sizes for the most significant contributors to load as variables to further refine loads at cable tie-down points. Completed testing has provided justification to reduce loads at cable tie-downs by 45% with additional refinement based on measured cable natural frequencies.

On the relationship between the classical Dicke-Jaynes-Cummings-Gaudin model and the nonlinear Schroedinger equation

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

Du, Dianlou; Geng, Xue

2013-05-15

In this paper, the relationship between the classical Dicke-Jaynes-Cummings-Gaudin (DJCG) model and the nonlinear Schroedinger (NLS) equation is studied. It is shown that the classical DJCG model is equivalent to a stationary NLS equation. Moreover, the standard NLS equation can be solved by the classical DJCG model and a suitably chosen higher order flow. Further, it is also shown that classical DJCG model can be transformed into the classical Gaudin spin model in an external magnetic field through a deformation of Lax matrix. Finally, the separated variables are constructed on the common level sets of Casimir functions and the generalizedmore » action-angle coordinates are introduced via the Hamilton-Jacobi equation.« less

Stump-to-truck cable logging cost equations for young-growth douglas-fir

Treesearch

Chris B. LeDoux; Roger D. Fight; Tom L. Ortman

1986-01-01

Logging cost simulators and data from logging cost studies have been assembled and converted into a series of equations that can be used to estimate the cost of logging young-growth coastal Douglas-fir (Pseudotsuga menziesii [Mirb.] Franco var. menziesii) in mountainous terrain of the Pacific Northwest. These equations were...

The critical velocity of a body towed by a cable from an airplane

NASA Technical Reports Server (NTRS)

Koning, C; De Haas, T P

1937-01-01

It is sufficient to consider only the equations of motion of the towed body whereas those of the cable may be left out of consideration. The result obtained makes it possible to determine which factors affect the critical velocity and what modifications of the instrument are necessary for extending the upper limit of that velocity.

Segmented and "equivalent" representation of the cable equation.

PubMed

Andrietti, F; Bernardini, G

1984-11-01

The linear cable theory has been applied to a modular structure consisting of n repeating units each composed of two subunits with different values of resistance and capacitance. For n going to infinity, i.e., for infinite cables, we have derived analytically the Laplace transform of the solution by making use of a difference method and we have inverted it by means of a numerical procedure. The results have been compared with those obtained by the direct application of the cable equation to a simplified nonmodular model with "equivalent" electrical parameters. The implication of our work in the analysis of the time and space course of the potential of real fibers has been discussed. In particular, we have shown that the simplified ("equivalent") model is a very good representation of the segmented model for the nodal regions of myelinated fibers in a steady situation and in every condition for muscle fibers. An approximate solution for the steady potential of myelinated fibers has been derived for both nodal and internodal regions. The applications of our work to other cases dealing with repeating structures, such as earthworm giant fibers, have been discussed and our results have been compared with other attempts to solve similar problems.

Modeling extracellular electrical stimulation: I. Derivation and interpretation of neurite equations.

PubMed

Meffin, Hamish; Tahayori, Bahman; Grayden, David B; Burkitt, Anthony N

2012-12-01

Neuroprosthetic devices, such as cochlear and retinal implants, work by directly stimulating neurons with extracellular electrodes. This is commonly modeled using the cable equation with an applied extracellular voltage. In this paper a framework for modeling extracellular electrical stimulation is presented. To this end, a cylindrical neurite with confined extracellular space in the subthreshold regime is modeled in three-dimensional space. Through cylindrical harmonic expansion of Laplace's equation, we derive the spatio-temporal equations governing different modes of stimulation, referred to as longitudinal and transverse modes, under types of boundary conditions. The longitudinal mode is described by the well-known cable equation, however, the transverse modes are described by a novel ordinary differential equation. For the longitudinal mode, we find that different electrotonic length constants apply under the two different boundary conditions. Equations connecting current density to voltage boundary conditions are derived that are used to calculate the trans-impedance of the neurite-plus-thin-extracellular-sheath. A detailed explanation on depolarization mechanisms and the dominant current pathway under different modes of stimulation is provided. The analytic results derived here enable the estimation of a neurite's membrane potential under extracellular stimulation, hence bypassing the heavy computational cost of using numerical methods.

Quantum-enabled temporal and spectral mode conversion of microwave signals

PubMed Central

Andrews, R. W.; Reed, A. P.; Cicak, K.; Teufel, J. D.; Lehnert, K. W.

2015-01-01

Electromagnetic waves are ideal candidates for transmitting information in a quantum network as they can be routed rapidly and efficiently between locations using optical fibres or microwave cables. Yet linking quantum-enabled devices with cables has proved difficult because most cavity or circuit quantum electrodynamics systems used in quantum information processing can only absorb and emit signals with a specific frequency and temporal envelope. Here we show that the temporal and spectral content of microwave-frequency electromagnetic signals can be arbitrarily manipulated with a flexible aluminium drumhead embedded in a microwave circuit. The aluminium drumhead simultaneously forms a mechanical oscillator and a tunable capacitor. This device offers a way to build quantum microwave networks using separate and otherwise mismatched components. Furthermore, it will enable the preparation of non-classical states of motion by capturing non-classical microwave signals prepared by the most coherent circuit quantum electrodynamics systems. PMID:26617386

Cycle-time equation for the Koller K300 cable yarder operating on steep slopes in the Northeast

Treesearch

Neil K. Huyler; Chris B. LeDoux

1997-01-01

Describes a delay-free-cycle time equation for the Koller K300 skyline yarder operating on steep slopes in the Northeast. Using the equation, the average delay-free-cycle time was 5.72 minutes. This means that about 420 cubic feet of material per hour can be produced. The important variables used in the equation were slope yarding distance, lateral yarding distance,...

A Mixed Model for Real-Time, Interactive Simulation of a Cable Passing Through Several Pulleys

NASA Astrophysics Data System (ADS)

García-Fernández, Ignacio; Pla-Castells, Marta; Martínez-Durá, Rafael J.

2007-09-01

A model of a cable and pulleys is presented that can be used in Real Time Computer Graphics applications. The model is formulated by the coupling of a damped spring and a variable coefficient wave equation, and can be integrated in more complex mechanical models of lift systems, such as cranes, elevators, etc. with a high degree of interactivity.

Transient analysis for alternating over-current characteristics of HTSC power transmission cable

NASA Astrophysics Data System (ADS)

Lim, S. H.; Hwang, S. D.

2006-10-01

In this paper, the transient analysis for the alternating over-current distribution in case that the over-current was applied for a high-TC superconducting (HTSC) power transmission cable was performed. The transient analysis for the alternating over-current characteristics of HTSC power transmission cable with multi-layer is required to estimate the redistribution of the over-current between its conducting layers and to protect the cable system from the over-current in case that the quench in one or two layers of the HTSC power cable happens. For its transient analysis, the resistance generation of the conducting layers for the alternating over-current was reflected on its equivalent circuit, based on the resistance equation obtained by applying discrete Fourier transform (DFT) for the voltage and the current waveforms of the HTSC tape, which comprises each layer of the HTSC power transmission cable. It was confirmed through the numerical analysis on its equivalent circuit that after the current redistribution from the outermost layer into the inner layers first happened, the fast current redistribution between the inner layers developed as the amplitude of the alternating over-current increased.

Electromagnetic disturbances rejection with single skin contact in the context of ECG measurements with cooperative sensors.

PubMed

Rapin, M; Ferrario, D; Haenni, E; Wacker, J; Falhi, A; Meier, C; Porchet, J-A; Chetelat, O

2017-07-01

Classical approaches to make high-quality measurements of biopotential signals require the use of shielded or multi-wire cables connecting the electrodes to a central unit in a star arrangement. Consequently, increasing the number of leads increases cabling and connector complexity which is not only limiting patient comfort but also anticipated as the main limiting factor for future miniaturization and cost reduction of tomorrow's wearables. We have recently introduced a novel sensing architecture that significantly reduces cabling complexity by eliminating shielded or multi-wire cables as well as by allowing simple connectors thanks to a bus arrangement. In this architecture, electrodes are replaced by so-called cooperative sensors. However, in this design, one of the cooperative sensors needs to be equipped with two contacts with the skin for proper common mode rejection, thus making its miniaturization problematic. This paper presents a novel common mode rejection principle which overcomes this limitation. When compared to others, the suggested approach is advantageous as it keeps the cabling complexity to its minimum. First measurements demonstrated in a real-life scenario the feasibility of this common mode rejection principle for a wearable 12-lead electrocardiogram monitoring system.

Mechanism synthesis and 2-D control designs of an active three cable crane

NASA Technical Reports Server (NTRS)

Yang, Li-Farn; Mikulas, Martin M., Jr.

1992-01-01

A Lunar Crane with a suspension system based on a three cable mechanism is investigated to provide a stable end-effector for hoisting, positioning, and assembling large components during construction and servicing of a Lunar Base. The three cable suspension mechanism consists of a structural framework of three cables pointing to a common point that closely coincides with the suspended payload's center of gravity. The vibrational characteristics of this three cable suspension system are investigated by comparing a simple 2-D symmetric suspension model and a swinging pendulum in terms of their analytical natural frequency equations. A study is also made of actively controlling the dynamics of the crane using two different actuator concepts. Also, Lyapunov-based control algorithms are developed to determine two regulator-type control laws performing the system vibrational suppression for both system dynamics. Simulations including initial-valued dynamic responses as well as control performances for two different system dynamics are also presented.

Long-term monitoring FBG-based cable load sensor

NASA Astrophysics Data System (ADS)

Zhang, Zhichun; Zhou, Zhi; Wang, Chuan; Ou, Jinping

2006-03-01

Stay cables are the main load-bearing components of stayed-cable bridges. The cables stress status is an important factor to the stayed-cable bridge structure safety evaluation. So it's very important not only to the bridge construction, but also to the long-term safety evaluation for the bridge structure in-service. The accurate measurement for cable load depends on an effective sensor, especially to meet the long time durability and measurement demand. FBG, for its great advantage of corrosion resistance, absolute measurement, high accuracy, electro-magnetic resistance, quasi-distribution sensing, absolute measurement and so on, is the most promising sensor, which can cater for the cable force monitoring. In this paper, a load sensor has been developed, which is made up of a bushing elastic supporting body, 4 FBGs uniformly-spaced attached outside of the bushing supporting body, and a temperature compensation FBG for other four FBGs, moreover a cover for protection of FBGs. Firstly, the sensor measuring principle is analyzed, and relationship equation of FBG wavelength shifts and extrinsic load has also been gotten. And then the sensor calibration experiments of a steel cable stretching test with the FBG load sensor and a reference electric pressure sensor is finished, and the results shows excellent linearity of extrinsic load and FBG wavelength shifts, and good repeatability, which indicates that such kind of FBG-based load sensor is suitable for load measurement, especially for long-term, real time monitoring of stay-cables.

Cable vibration control with both lateral and rotational dampers attached at an intermediate location

NASA Astrophysics Data System (ADS)

Chen, Lin; Sun, Limin; Nagarajaiah, Satish

2016-09-01

Lateral dampers have been extensively studied and implemented for supplementing modal damping in cable vibration mitigation. When considering the cable flexural stiffness that is actually present, albeit small, there is another degree of freedom of the cable at the lateral damper, namely the rotation, that can be constrained by a rotational damper to achieve larger additional damping. This is of particular significance for long cables where the near-anchorage lateral damper alone is usually insufficient. The problem of a cable with bending stiffness, attached with both lateral and rotational dampers at an intermediate point, is therefore considered in this study. The characteristic equation of the resulting system is formulated by assembling the dynamic stiffness from the two segments divided by the damper, which is subsequently solved using argument principle method. Dynamics of the controlled system is thus discussed in general through parametric analysis. For the case where the damper location is close to the anchorage, asymptotic solutions for complex frequency and damping ratio are provided; explicit formulas for determining the optimal damper coefficients are also derived. It is found that when the lateral and rotational damper coefficients are properly balanced, the proposed strategy can achieve up to 30 percent damping enhancement compared to the case with only the lateral damper, in practical cable bending stiffness range.

Properties of the Boltzmann equation in the classical approximation

DOE PAGES

Epelbaum, Thomas; Gelis, François; Tanji, Naoto; ...

2014-12-30

We examine the Boltzmann equation with elastic point-like scalar interactions in two different versions of the the classical approximation. Although solving numerically the Boltzmann equation with the unapproximated collision term poses no problem, this allows one to study the effect of the ultraviolet cutoff in these approximations. This cutoff dependence in the classical approximations of the Boltzmann equation is closely related to the non-renormalizability of the classical statistical approximation of the underlying quantum field theory. The kinetic theory setup that we consider here allows one to study in a much simpler way the dependence on the ultraviolet cutoff, since onemore » has also access to the non-approximated result for comparison.« less

Rota-Baxter operators on sl (2,C) and solutions of the classical Yang-Baxter equation

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

Pei, Jun, E-mail: peitsun@163.com; Bai, Chengming, E-mail: baicm@nankai.edu.cn; Guo, Li, E-mail: liguo@rutgers.edu

2014-02-15

We explicitly determine all Rota-Baxter operators (of weight zero) on sl (2,C) under the Cartan-Weyl basis. For the skew-symmetric operators, we give the corresponding skew-symmetric solutions of the classical Yang-Baxter equation in sl (2,C), confirming the related study by Semenov-Tian-Shansky. In general, these Rota-Baxter operators give a family of solutions of the classical Yang-Baxter equation in the six-dimensional Lie algebra sl (2,C)⋉{sub ad{sup *}} sl (2,C){sup *}. They also give rise to three-dimensional pre-Lie algebras which in turn yield solutions of the classical Yang-Baxter equation in other six-dimensional Lie algebras.

Planar dynamics of large-deformation rods under moving loads

NASA Astrophysics Data System (ADS)

Zhao, X. W.; van der Heijden, G. H. M.

2018-01-01

We formulate the problem of a slender structure (a rod) undergoing large deformation under the action of a moving mass or load motivated by inspection robots crawling along bridge cables or high-voltage power lines. The rod is described by means of geometrically exact Cosserat theory which allows for arbitrary planar flexural, extensional and shear deformations. The equations of motion are discretised using the generalised-α method. The formulation is shown to handle the discontinuities of the problem well. Application of the method to a cable and an arch problem reveals interesting nonlinear phenomena. For the cable problem we find that large deformations have a resonance detuning effect on cable dynamics. The problem also offers a compelling illustration of the Timoshenko paradox. For the arch problem we find a stabilising (delay) effect on the in-plane collapse of the arch, with failure suppressed entirely at sufficiently high speed.

Calculating Dynamics Of Helicopters And Slung Loads

NASA Technical Reports Server (NTRS)

Cicolani, Luigi; Kanning, Gerd

1991-01-01

General equations derived for numerical simulations of motions of multiple-lift, slung-load systems consisting of two or more lifting helicopters and loads slung from them by various combinations of spreader bars, cables, nets, and attaching hardware. Equations readily programmable for efficient computation of motions and lend themselves well to analysis and design of control strategies for stabilization and coordination.

Vibrations of beams and rods carrying a moving mass

NASA Astrophysics Data System (ADS)

Zhao, X. W.; van der Heijden, G. H. M.; Hu, Z. D.

2016-05-01

We study the vibration of slender one-dimensional elastic structures (beams, cables, wires, rods) under the effect of a moving mass or load. We first consider the classical small- deflection (Euler-Bernoulli) beam case, where we look at tip vibrations of a cantilever as a model for a barreled launch system. Then we develop a theory for large deformations based on Cosserat rod theory. We illustrate the effect of moving loads on large-deformation structures with a few cable and arch problems. Large deformations are found to have a resonance detuning effect on the cable. For the arch we find different failure modes depending on its depth: a shallow arch fails by in-plane collapse, while a deep arch fails by sideways flopping. In both cases the speed of the traversing load is found to have a stabilising effect on the structure, with failure suppressed entirely at sufficiently high speed.

Fractional cable model for signal conduction in spiny neuronal dendrites

NASA Astrophysics Data System (ADS)

Vitali, Silvia; Mainardi, Francesco

2017-06-01

The cable model is widely used in several fields of science to describe the propagation of signals. A relevant medical and biological example is the anomalous subdiffusion in spiny neuronal dendrites observed in several studies of the last decade. Anomalous subdiffusion can be modelled in several ways introducing some fractional component into the classical cable model. The Chauchy problem associated to these kind of models has been investigated by many authors, but up to our knowledge an explicit solution for the signalling problem has not yet been published. Here we propose how this solution can be derived applying the generalized convolution theorem (known as Efros theorem) for Laplace transforms. The fractional cable model considered in this paper is defined by replacing the first order time derivative with a fractional derivative of order α ∈ (0, 1) of Caputo type. The signalling problem is solved for any input function applied to the accessible end of a semi-infinite cable, which satisfies the requirements of the Efros theorem. The solutions corresponding to the simple cases of impulsive and step inputs are explicitly calculated in integral form containing Wright functions. Thanks to the variability of the parameter α, the corresponding solutions are expected to adapt to the qualitative behaviour of the membrane potential observed in experiments better than in the standard case α = 1.

The Construction of Infrastructure for Library's Digital Document Telecommunications.

ERIC Educational Resources Information Center

Changxing, Ying; Zuzao, Lin

This paper discusses the construction of the infrastructure for libraries' digital document telecommunications. The first section describes the topologies of the library LAN (Local Area Network) cabling system, including the main characteristics of the LAN and three classical topologies typically used with LANs, i.e., the bus, star, and ring…

A geometrically exact formulation for three-dimensional numerical simulation of the umbilical cable in a deep-sea ROV system

NASA Astrophysics Data System (ADS)

Quan, Wei-cai; Zhang, Zhu-ying; Zhang, Ai-qun; Zhang, Qi-feng; Tian, Yu

2015-04-01

This paper proposes a geometrically exact formulation for three-dimensional static and dynamic analyses of the umbilical cable in a deep-sea remotely operated vehicle (ROV) system. The presented formulation takes account of the geometric nonlinearities of large displacement, effects of axial load and bending stiffness for modeling of slack cables. The resulting nonlinear second-order governing equations are discretized spatially by the finite element method and solved temporally by the generalized- α implicit time integration algorithm, which is adapted to the case of varying coefficient matrices. The ability to consider three-dimensional union action of ocean current and ship heave motion upon the umbilical cable is the key feature of this analysis. The presented formulation is firstly validated, and then three numerical examples for the umbilical cable in a deep-sea ROV system are demonstrated and discussed, including the steady configurations only under the action of depth-dependent ocean current, the dynamic responses in the case of the only ship heave motion, and in the case of the combined action of the ship heave motion and ocean current.

Bukhvostov-Lipatov model and quantum-classical duality

NASA Astrophysics Data System (ADS)

Bazhanov, Vladimir V.; Lukyanov, Sergei L.; Runov, Boris A.

2018-02-01

The Bukhvostov-Lipatov model is an exactly soluble model of two interacting Dirac fermions in 1 + 1 dimensions. The model describes weakly interacting instantons and anti-instantons in the O (3) non-linear sigma model. In our previous work [arxiv:arXiv:1607.04839] we have proposed an exact formula for the vacuum energy of the Bukhvostov-Lipatov model in terms of special solutions of the classical sinh-Gordon equation, which can be viewed as an example of a remarkable duality between integrable quantum field theories and integrable classical field theories in two dimensions. Here we present a complete derivation of this duality based on the classical inverse scattering transform method, traditional Bethe ansatz techniques and analytic theory of ordinary differential equations. In particular, we show that the Bethe ansatz equations defining the vacuum state of the quantum theory also define connection coefficients of an auxiliary linear problem for the classical sinh-Gordon equation. Moreover, we also present details of the derivation of the non-linear integral equations determining the vacuum energy and other spectral characteristics of the model in the case when the vacuum state is filled by 2-string solutions of the Bethe ansatz equations.

Effect of Morphologic Features of Neurons on the Extracellular Electric Potential: A Simulation Study Using Cable Theory and Electro-Quasi-Static Equations.

PubMed

Bestel, R; Appali, R; van Rienen, U; Thielemann, C

2017-11-01

Microelectrode arrays serve as an indispensable tool in electro-physiological research to study the electrical activity of neural cells, enabling measurements of single cell as well as network communication analysis. Recent experimental studies have reported that the neuronal geometry has an influence on electrical signaling and extracellular recordings. However, the corresponding mechanisms are not yet fully understood and require further investigation. Allowing systematic parameter studies, computational modeling provides the opportunity to examine the underlying effects that influence extracellular potentials. In this letter, we present an in silico single cell model to analyze the effect of geometrical variability on the extracellular electric potentials. We describe finite element models of a single neuron with varying geometric complexity in three-dimensional space. The electric potential generation of the neuron is modeled using Hodgkin-Huxley equations. The signal propagation is described with electro-quasi-static equations, and results are compared with corresponding cable equation descriptions. Our results show that both the geometric dimensions and the distribution of ion channels of a neuron are critical factors that significantly influence both the amplitude and shape of extracellular potentials.

Short distance modification of the quantum virial theorem

NASA Astrophysics Data System (ADS)

Zhao, Qin; Faizal, Mir; Zaz, Zaid

2017-07-01

In this letter, we will analyse the deformation of a semi-classical gravitational system from minimal measurable length scale. In the semi-classical approximation, the gravitational field will be analysed as a classical field, and the matter fields will be treated quantum mechanically. Thus, using this approximation, this system will be represented by a deformation of Schrödinger-Newton equation by the generalised uncertainty principle (GUP). We will analyse the effects of this GUP deformed Schrödinger-Newton equation on the behaviour of such a semi-classical gravitational system. As the quantum mechanical virial theorem can be obtained using the Schrödinger-Newton equation, a short distance modification of the Schrödinger-Newton equation will also result in a short distance modification of the quantum mechanical virial theorem.

Laguerre-Freud Equations for the Recurrence Coefficients of Some Discrete Semi-Classical Orthogonal Polynomials of Class Two

NASA Astrophysics Data System (ADS)

Hounga, C.; Hounkonnou, M. N.; Ronveaux, A.

2006-10-01

In this paper, we give Laguerre-Freud equations for the recurrence coefficients of discrete semi-classical orthogonal polynomials of class two, when the polynomials in the Pearson equation are of the same degree. The case of generalized Charlier polynomials is also presented.

A comparison of lightning and nuclear electromagnetic pulse response of a helicopter

NASA Technical Reports Server (NTRS)

Easterbrook, C. C.; Perala, R. A.

1984-01-01

A numerical modeling technique is utilized to investigate the response of a UH-60A helicopter to both lightning and nuclear electromagnetic pulses (NEMP). The analytical approach involves the three-dimensional time domain finite-difference solutions of Maxwell's equations. Both the external currents and charges as well as the internal electromagnetic fields and cable responses are computed. Results of the analysis indicate that, in general, the short circuit current on internal cables is larger for lightning, whereas the open-circuit voltages are slightly higher for NEMP. The lightning response is highly dependent upon the rise time of the injected current as was expected. The analysis shows that a coupling levels to cables in a helicopter are 20 to 30 dB larger than those observed in fixed-wing aircraft.

Generalizations of the classical Yang-Baxter equation and O-operators

NASA Astrophysics Data System (ADS)

Bai, Chengming; Guo, Li; Ni, Xiang

2011-06-01

Tensor solutions (r-matrices) of the classical Yang-Baxter equation (CYBE) in a Lie algebra, obtained as the classical limit of the R-matrix solution of the quantum Yang-Baxter equation, is an important structure appearing in different areas such as integrable systems, symplectic geometry, quantum groups, and quantum field theory. Further study of CYBE led to its interpretation as certain operators, giving rise to the concept of {O}-operators. The O-operators were in turn interpreted as tensor solutions of CYBE by enlarging the Lie algebra [Bai, C., "A unified algebraic approach to the classical Yang-Baxter equation," J. Phys. A: Math. Theor. 40, 11073 (2007)], 10.1088/1751-8113/40/36/007. The purpose of this paper is to extend this study to a more general class of operators that were recently introduced [Bai, C., Guo, L., and Ni, X., "Nonabelian generalized Lax pairs, the classical Yang-Baxter equation and PostLie algebras," Commun. Math. Phys. 297, 553 (2010)], 10.1007/s00220-010-0998-7 in the study of Lax pairs in integrable systems. Relations between O-operators, relative differential operators, and Rota-Baxter operators are also discussed.

Dynamic optimization and its relation to classical and quantum constrained systems

NASA Astrophysics Data System (ADS)

Contreras, Mauricio; Pellicer, Rely; Villena, Marcelo

2017-08-01

We study the structure of a simple dynamic optimization problem consisting of one state and one control variable, from a physicist's point of view. By using an analogy to a physical model, we study this system in the classical and quantum frameworks. Classically, the dynamic optimization problem is equivalent to a classical mechanics constrained system, so we must use the Dirac method to analyze it in a correct way. We find that there are two second-class constraints in the model: one fix the momenta associated with the control variables, and the other is a reminder of the optimal control law. The dynamic evolution of this constrained system is given by the Dirac's bracket of the canonical variables with the Hamiltonian. This dynamic results to be identical to the unconstrained one given by the Pontryagin equations, which are the correct classical equations of motion for our physical optimization problem. In the same Pontryagin scheme, by imposing a closed-loop λ-strategy, the optimality condition for the action gives a consistency relation, which is associated to the Hamilton-Jacobi-Bellman equation of the dynamic programming method. A similar result is achieved by quantizing the classical model. By setting the wave function Ψ(x , t) =e iS(x , t) in the quantum Schrödinger equation, a non-linear partial equation is obtained for the S function. For the right-hand side quantization, this is the Hamilton-Jacobi-Bellman equation, when S(x , t) is identified with the optimal value function. Thus, the Hamilton-Jacobi-Bellman equation in Bellman's maximum principle, can be interpreted as the quantum approach of the optimization problem.

Integrability in AdS/CFT correspondence: quasi-classical analysis

NASA Astrophysics Data System (ADS)

Gromov, Nikolay

2009-06-01

In this review, we consider a quasi-classical method applicable to integrable field theories which is based on a classical integrable structure—the algebraic curve. We apply it to the Green-Schwarz superstring on the AdS5 × S5 space. We show that the proposed method reproduces perfectly the earlier results obtained by expanding the string action for some simple classical solutions. The construction is explicitly covariant and is not based on a particular parameterization of the fields and as a result is free from ambiguities. On the other hand, the finite size corrections in some particularly important scaling limit are studied in this paper for a system of Bethe equations. For the general superalgebra \\su(N|K) , the result for the 1/L corrections is obtained. We find an integral equation which describes these corrections in a closed form. As an application, we consider the conjectured Beisert-Staudacher (BS) equations with the Hernandez-Lopez dressing factor where the finite size corrections should reproduce quasi-classical results around a general classical solution. Indeed, we show that our integral equation can be interpreted as a sum of all physical fluctuations and thus prove the complete one-loop consistency of the BS equations. We demonstrate that any local conserved charge (including the AdS energy) computed from the BS equations is indeed given at one loop by the sum of the charges of fluctuations with an exponential precision for large S5 angular momentum of the string. As an independent result, the BS equations in an \\su(2) sub-sector were derived from Zamolodchikovs's S-matrix. The paper is based on the author's PhD thesis.

Trajectory-based understanding of the quantum-classical transition for barrier scattering

NASA Astrophysics Data System (ADS)

Chou, Chia-Chun

2018-06-01

The quantum-classical transition of wave packet barrier scattering is investigated using a hydrodynamic description in the framework of a nonlinear Schrödinger equation. The nonlinear equation provides a continuous description for the quantum-classical transition of physical systems by introducing a degree of quantumness. Based on the transition equation, the transition trajectory formalism is developed to establish the connection between classical and quantum trajectories. The quantum-classical transition is then analyzed for the scattering of a Gaussian wave packet from an Eckart barrier and the decay of a metastable state. Computational results for the evolution of the wave packet and the transmission probabilities indicate that classical results are recovered when the degree of quantumness tends to zero. Classical trajectories are in excellent agreement with the transition trajectories in the classical limit, except in some regions where transition trajectories cannot cross because of the single-valuedness of the transition wave function. As the computational results demonstrate, the process that the Planck constant tends to zero is equivalent to the gradual removal of quantum effects originating from the quantum potential. This study provides an insightful trajectory interpretation for the quantum-classical transition of wave packet barrier scattering.

On Generalized Continuous D Semi-Classical Hermite and Chebychev Orthogonal Polynomials of Class One

NASA Astrophysics Data System (ADS)

Azatassou, E.; Hounkonnou, M. N.

2002-10-01

In this contribution, starting from the system of equations for recurrence coefficients generated by continuous D semi-classical Laguerre-Freud equations of class 1, we deduce the β constant recurrence relation coefficient γn leading to the generalized D semi-classical Hermite and Chebychev orthogonal polynomials of class 1. Various interesting cases are pointed out.

The recurrence coefficients of semi-classical Laguerre polynomials and the fourth Painlevé equation

NASA Astrophysics Data System (ADS)

Filipuk, Galina; Van Assche, Walter; Zhang, Lun

2012-05-01

We show that the coefficients of the three-term recurrence relation for orthogonal polynomials with respect to a semi-classical extension of the Laguerre weight satisfy the fourth Painlevé equation when viewed as functions of one of the parameters in the weight. We compare different approaches to derive this result, namely, the ladder operators approach, the isomonodromy deformations approach and combining the Toda system for the recurrence coefficients with a discrete equation. We also discuss a relation between the recurrence coefficients for the Freud weight and the semi-classical Laguerre weight and show how it arises from the Bäcklund transformation of the fourth Painlevé equation.

Finite element solution of torsion and other 2-D Poisson equations

NASA Technical Reports Server (NTRS)

Everstine, G. C.

1982-01-01

The NASTRAN structural analysis computer program may be used, without modification, to solve two dimensional Poisson equations such as arise in the classical Saint Venant torsion problem. The nonhomogeneous term (the right-hand side) in the Poisson equation can be handled conveniently by specifying a gravitational load in a "structural" analysis. The use of an analogy between the equations of elasticity and those of classical mathematical physics is summarized in detail.

Brownian motion of classical spins: Anomalous dissipation and generalized Langevin equation

NASA Astrophysics Data System (ADS)

Bandyopadhyay, Malay; Jayannavar, A. M.

2017-10-01

In this work, we derive the Langevin equation (LE) of a classical spin interacting with a heat bath through momentum variables, starting from the fully dynamical Hamiltonian description. The derived LE with anomalous dissipation is analyzed in detail. The obtained LE is non-Markovian with multiplicative noise terms. The concomitant dissipative terms obey the fluctuation-dissipation theorem. The Markovian limit correctly produces the Kubo and Hashitsume equation. The perturbative treatment of our equations produces the Landau-Lifshitz equation and the Seshadri-Lindenberg equation. Then we derive the Fokker-Planck equation corresponding to LE and the concept of equilibrium probability distribution is analyzed.

Linear Quantum Systems: Non-Classical States and Robust Stability

DTIC Science & Technology

2016-06-29

quantum linear systems subject to non-classical quantum fields. The major outcomes of this project are (i) derivation of quantum filtering equations for...derivation of quantum filtering equations for systems non-classical input states including single photon states, (ii) determination of how linear...history going back some 50 years, to the birth of modern control theory with Kalman’s foundational work on filtering and LQG optimal control

Classical and quantum cosmology of minimal massive bigravity

NASA Astrophysics Data System (ADS)

Darabi, F.; Mousavi, M.

2016-10-01

In a Friedmann-Robertson-Walker (FRW) space-time background we study the classical cosmological models in the context of recently proposed theory of nonlinear minimal massive bigravity. We show that in the presence of perfect fluid the classical field equations acquire contribution from the massive graviton as a cosmological term which is positive or negative depending on the dynamical competition between two scale factors of bigravity metrics. We obtain the classical field equations for flat and open universes in the ordinary and Schutz representation of perfect fluid. Focusing on the Schutz representation for flat universe, we find classical solutions exhibiting singularities at early universe with vacuum equation of state. Then, in the Schutz representation, we study the quantum cosmology for flat universe and derive the Schrodinger-Wheeler-DeWitt equation. We find its exact and wave packet solutions and discuss on their properties to show that the initial singularity in the classical solutions can be avoided by quantum cosmology. Similar to the study of Hartle-Hawking no-boundary proposal in the quantum cosmology of de Rham, Gabadadze and Tolley (dRGT) massive gravity, it turns out that the mass of graviton predicted by quantum cosmology of the minimal massive bigravity is large at early universe. This is in agreement with the fact that at early universe the cosmological constant should be large.

SDRE controller for motion design of cable-suspended robot with uncertainties and moving obstacles

NASA Astrophysics Data System (ADS)

Behboodi, Ahad; Salehi, Seyedmohammad

2017-10-01

In this paper an optimal control approach for nonlinear dynamical systems was proposed based on State Dependent Riccati Equation (SDRE) and its robustness against uncertainties is shown by simulation results. The proposed method was applied on a spatial six-cable suspended robot, which was designed to carry loads or perform different tasks in huge workspaces. Motion planning for cable-suspended robots in such a big workspace is subjected to uncertainties and obstacles. First, we emphasized the ability of SDRE to construct a systematic basis and efficient design of controller for wide variety of nonlinear dynamical systems. Then we showed how this systematic design improved the robustness of the system and facilitated the integration of motion planning techniques with the controller. In particular, obstacle avoidance technique based on artificial potential field (APF) can be easily combined with SDRE controller with efficient performance. Due to difficulties of exact solution for SDRE, an approximation method was used based on power series expansion. The efficiency and robustness of the SDRE controller was illustrated on a six-cable suspended robot with proper simulations.

Schrödinger-Poisson-Vlasov-Poisson correspondence

NASA Astrophysics Data System (ADS)

Mocz, Philip; Lancaster, Lachlan; Fialkov, Anastasia; Becerra, Fernando; Chavanis, Pierre-Henri

2018-04-01

The Schrödinger-Poisson equations describe the behavior of a superfluid Bose-Einstein condensate under self-gravity with a 3D wave function. As ℏ/m →0 , m being the boson mass, the equations have been postulated to approximate the collisionless Vlasov-Poisson equations also known as the collisionless Boltzmann-Poisson equations. The latter describe collisionless matter with a 6D classical distribution function. We investigate the nature of this correspondence with a suite of numerical test problems in 1D, 2D, and 3D along with analytic treatments when possible. We demonstrate that, while the density field of the superfluid always shows order unity oscillations as ℏ/m →0 due to interference and the uncertainty principle, the potential field converges to the classical answer as (ℏ/m )2. Thus, any dynamics coupled to the superfluid potential is expected to recover the classical collisionless limit as ℏ/m →0 . The quantum superfluid is able to capture rich phenomena such as multiple phase-sheets, shell-crossings, and warm distributions. Additionally, the quantum pressure tensor acts as a regularizer of caustics and singularities in classical solutions. This suggests the exciting prospect of using the Schrödinger-Poisson equations as a low-memory method for approximating the high-dimensional evolution of the Vlasov-Poisson equations. As a particular example we consider dark matter composed of ultralight axions, which in the classical limit (ℏ/m →0 ) is expected to manifest itself as collisionless cold dark matter.

Principles of Discrete Time Mechanics

NASA Astrophysics Data System (ADS)

Jaroszkiewicz, George

2014-04-01

1. Introduction; 2. The physics of discreteness; 3. The road to calculus; 4. Temporal discretization; 5. Discrete time dynamics architecture; 6. Some models; 7. Classical cellular automata; 8. The action sum; 9. Worked examples; 10. Lee's approach to discrete time mechanics; 11. Elliptic billiards; 12. The construction of system functions; 13. The classical discrete time oscillator; 14. Type 2 temporal discretization; 15. Intermission; 16. Discrete time quantum mechanics; 17. The quantized discrete time oscillator; 18. Path integrals; 19. Quantum encoding; 20. Discrete time classical field equations; 21. The discrete time Schrodinger equation; 22. The discrete time Klein-Gordon equation; 23. The discrete time Dirac equation; 24. Discrete time Maxwell's equations; 25. The discrete time Skyrme model; 26. Discrete time quantum field theory; 27. Interacting discrete time scalar fields; 28. Space, time and gravitation; 29. Causality and observation; 30. Concluding remarks; Appendix A. Coherent states; Appendix B. The time-dependent oscillator; Appendix C. Quaternions; Appendix D. Quantum registers; References; Index.

Stoichiometric network analysis and associated dimensionless kinetic equations. Application to a model of the Bray-Liebhafsky reaction.

PubMed

Schmitz, Guy; Kolar-Anić, Ljiljana Z; Anić, Slobodan R; Cupić, Zeljko D

2008-12-25

The stoichiometric network analysis (SNA) introduced by B. L. Clarke is applied to a simplified model of the complex oscillating Bray-Liebhafsky reaction under batch conditions, which was not examined by this method earlier. This powerful method for the analysis of steady-states stability is also used to transform the classical differential equations into dimensionless equations. This transformation is easy and leads to a form of the equations combining the advantages of classical dimensionless equations with the advantages of the SNA. The used dimensionless parameters have orders of magnitude given by the experimental information about concentrations and currents. This simplifies greatly the study of the slow manifold and shows which parameters are essential for controlling its shape and consequently have an important influence on the trajectories. The effectiveness of these equations is illustrated on two examples: the study of the bifurcations points and a simple sensitivity analysis, different from the classical one, more based on the chemistry of the studied system.

Dynamics of tethered satellites in the vicinity of the Lagrangian point L2 of the Earth-Moon system

NASA Astrophysics Data System (ADS)

Baião, M. F.; Stuchi, T. J.

2017-08-01

This paper analyzes the dynamical evolution of satellites formed by two masses connected by a cable— tethered satellites. We derive the Lagrangian equations of motion in the neighborhood of the collinear equilibrium points, especially for the L2 , of the restricted problem of three bodies. The rigid body configuration is expanded in Legendre polynomials up to fourth degree. We present some numerical simulations of the influence of the parameters such as cable length, mass ratio and initial conditions in the behavior of the tethered satellites. The equation for the collinear equilibrium point is derived and numerically solved. The evolution of the equilibria with the variation of the cable length as a parameter is studied. We also present a discussion of the linear stability around these equilibria. Based on this analysis calculate some unstable Lyapunov orbits associated to these equilibrium points. We found periodic orbits in which the tether travels parallel to itself without involving the angular motion. The numerical applications are focused on the Earth-Moon system. However, the general character of the equations allows applications to the L1 equilibrium and obviously to systems other than the Earth-Moon.

Compressible Flow Toolbox

NASA Technical Reports Server (NTRS)

Melcher, Kevin J.

2006-01-01

The Compressible Flow Toolbox is primarily a MATLAB-language implementation of a set of algorithms that solve approximately 280 linear and nonlinear classical equations for compressible flow. The toolbox is useful for analysis of one-dimensional steady flow with either constant entropy, friction, heat transfer, or Mach number greater than 1. The toolbox also contains algorithms for comparing and validating the equation-solving algorithms against solutions previously published in open literature. The classical equations solved by the Compressible Flow Toolbox are as follows: The isentropic-flow equations, The Fanno flow equations (pertaining to flow of an ideal gas in a pipe with friction), The Rayleigh flow equations (pertaining to frictionless flow of an ideal gas, with heat transfer, in a pipe of constant cross section), The normal-shock equations, The oblique-shock equations, and The expansion equations.

Development and application of a local linearization algorithm for the integration of quaternion rate equations in real-time flight simulation problems

NASA Technical Reports Server (NTRS)

Barker, L. E., Jr.; Bowles, R. L.; Williams, L. H.

1973-01-01

High angular rates encountered in real-time flight simulation problems may require a more stable and accurate integration method than the classical methods normally used. A study was made to develop a general local linearization procedure of integrating dynamic system equations when using a digital computer in real-time. The procedure is specifically applied to the integration of the quaternion rate equations. For this application, results are compared to a classical second-order method. The local linearization approach is shown to have desirable stability characteristics and gives significant improvement in accuracy over the classical second-order integration methods.

Simple vector bundles on a nodal Weierstrass cubic and quasi-trigonometric solutions of the classical Yang-Baxter equation

NASA Astrophysics Data System (ADS)

Burban, Igor; Galinat, Lennart; Stolin, Alexander

2017-11-01

In this paper we study the combinatorics of quasi-trigonometric solutions of the classical Yang-Baxter equation, arising from simple vector bundles on a nodal Weierstraß cubic. Dedicated to the memory of Petr Petrovich Kulish.

Integral approximations to classical diffusion and smoothed particle hydrodynamics

DOE PAGES

Du, Qiang; Lehoucq, R. B.; Tartakovsky, A. M.

2014-12-31

The contribution of the paper is the approximation of a classical diffusion operator by an integral equation with a volume constraint. A particular focus is on classical diffusion problems associated with Neumann boundary conditions. By exploiting this approximation, we can also approximate other quantities such as the flux out of a domain. Our analysis of the model equation on the continuum level is closely related to the recent work on nonlocal diffusion and peridynamic mechanics. In particular, we elucidate the role of a volumetric constraint as an approximation to a classical Neumann boundary condition in the presence of physical boundary.more » The volume-constrained integral equation then provides the basis for accurate and robust discretization methods. As a result, an immediate application is to the understanding and improvement of the Smoothed Particle Hydrodynamics (SPH) method.« less

Entanglement in Quantum-Classical Hybrid

NASA Technical Reports Server (NTRS)

Zak, Michail

2011-01-01

It is noted that the phenomenon of entanglement is not a prerogative of quantum systems, but also occurs in other, non-classical systems such as quantum-classical hybrids, and covers the concept of entanglement as a special type of global constraint imposed upon a broad class of dynamical systems. Application of hybrid systems for physics of life, as well as for quantum-inspired computing, has been outlined. In representing the Schroedinger equation in the Madelung form, there is feedback from the Liouville equation to the Hamilton-Jacobi equation in the form of the quantum potential. Preserving the same topology, the innovators replaced the quantum potential with other types of feedback, and investigated the property of these hybrid systems. A function of probability density has been introduced. Non-locality associated with a global geometrical constraint that leads to an entanglement effect was demonstrated. Despite such a quantum like characteristic, the hybrid can be of classical scale and all the measurements can be performed classically. This new emergence of entanglement sheds light on the concept of non-locality in physics.

On the motion of classical three-body system with consideration of quantum fluctuations

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

Gevorkyan, A. S., E-mail: g-ashot@sci.am

2017-03-15

We obtained the systemof stochastic differential equations which describes the classicalmotion of the three-body system under influence of quantum fluctuations. Using SDEs, for the joint probability distribution of the total momentum of bodies system were obtained the partial differential equation of the second order. It is shown, that the equation for the probability distribution is solved jointly by classical equations, which in turn are responsible for the topological peculiarities of tubes of quantum currents, transitions between asymptotic channels and, respectively for arising of quantum chaos.

A quantum analogy to the classical gravitomagnetic clock effect

NASA Astrophysics Data System (ADS)

Faruque, S. B.

2018-06-01

We present an approximation to the solution of Dirac equation in Schwarzschild field found through the use of Foldy-Wouthuysen Hamiltonian. We solve the equation for the positive energy states and found the frequencies by which the states oscillate. Difference of the periods of oscillation of the two states with two different total angular momentum quantum number j has an analogical form of the classical clock effect found in general relativity. But unlike the term that appears as clock effect in classical physics, here the term is quantized. Thus, we find a quantum analogue of the classical gravitomagnetic clock effect.

APPROACH TO EQUILIBRIUM OF A QUANTUM PLASMA

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

Balescu, R.

1961-01-01

The treatment of irreversible processes in a classical plasma (R. Balescu, Phys. Fluids 3, 62(1960)) was extended to a gas of charged particles obeying quantum statistics. The various contributions to the equation of evolution for the reduced one-particle Wigner function were written in a form analogous to the classical formalism. The summation was then performed in a straightforward manner. The resulting equation describes collisions between particles "dressed" by their polarization clouds, exactly as in the classical situation. (auth)

Two-Dimensional Analysis of Cable Stayed Bridge under Wave Loading

NASA Astrophysics Data System (ADS)

Seeram, Madhuri; Manohar, Y.

2018-06-01

In the present study finite element analysis is performed for a modified fan type cable-stayed bridge using ANSYS Mechanical. A cable stayed bridge with two towers and main deck is considered for the present study. Dynamic analysis is performed to evaluate natural frequencies. The obtained natural frequencies and mode shapes of cable stayed bridge are compared to the existing results. Further studies have been conducted for offshore area application by increasing the pylon/tower height depending upon the water depth. Natural frequencies and mode shapes are evaluated for the cable stayed bridge for offshore area application. The results indicate that the natural periods are higher than the existing results due to the effect of increase in mass of the structure and decrease in stiffness of the pylon/tower. The cable stayed bridge is analyzed under various environmental loads such as dead, live, vehicle, seismic and wave loading. Morison equation is considered to evaluate the wave force. The sum of inertia and drag force is taken as the wave force distribution along the fluid interacting height of the pylon. Airy's wave theory is used to assess water particle kinematics, for the wave periods ranging from 5 to 20 s and unit wave height. The maximum wave force among the different regular waves is considered in the wave load case. The support reactions, moments and deflections for offshore area application are highlighted. It is observed that the maximum support reactions and support moments are obtained due to wave and earthquake loading respectively. Hence, it is concluded that the wave and earthquake forces shall be given significance in the design of cable stayed bridge.

Two-Dimensional Analysis of Cable Stayed Bridge under Wave Loading

NASA Astrophysics Data System (ADS)

Seeram, Madhuri; Manohar, Y.

2018-02-01

In the present study finite element analysis is performed for a modified fan type cable-stayed bridge using ANSYS Mechanical. A cable stayed bridge with two towers and main deck is considered for the present study. Dynamic analysis is performed to evaluate natural frequencies. The obtained natural frequencies and mode shapes of cable stayed bridge are compared to the existing results. Further studies have been conducted for offshore area application by increasing the pylon/tower height depending upon the water depth. Natural frequencies and mode shapes are evaluated for the cable stayed bridge for offshore area application. The results indicate that the natural periods are higher than the existing results due to the effect of increase in mass of the structure and decrease in stiffness of the pylon/tower. The cable stayed bridge is analyzed under various environmental loads such as dead, live, vehicle, seismic and wave loading. Morison equation is considered to evaluate the wave force. The sum of inertia and drag force is taken as the wave force distribution along the fluid interacting height of the pylon. Airy's wave theory is used to assess water particle kinematics, for the wave periods ranging from 5 to 20 s and unit wave height. The maximum wave force among the different regular waves is considered in the wave load case. The support reactions, moments and deflections for offshore area application are highlighted. It is observed that the maximum support reactions and support moments are obtained due to wave and earthquake loading respectively. Hence, it is concluded that the wave and earthquake forces shall be given significance in the design of cable stayed bridge.

In-place recalibration technique applied to a capacitance-type system for measuring rotor blade tip clearance

NASA Technical Reports Server (NTRS)

Barranger, J. P.

1978-01-01

The rotor blade tip clearance measurement system consists of a capacitance sensing probe with self contained tuning elements, a connecting coaxial cable, and remotely located electronics. Tests show that the accuracy of the system suffers from a strong dependence on probe tip temperature and humidity. A novel inplace recalibration technique was presented which partly overcomes this problem through a simple modification of the electronics that permits a scale factor correction. This technique, when applied to a commercial system significantly reduced errors under varying conditions of humidity and temperature. Equations were also found that characterize the important cable and probe design quantities.

Experimental quantum computing to solve systems of linear equations.

PubMed

Cai, X-D; Weedbrook, C; Su, Z-E; Chen, M-C; Gu, Mile; Zhu, M-J; Li, Li; Liu, Nai-Le; Lu, Chao-Yang; Pan, Jian-Wei

2013-06-07

Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time proportional to the number of variables N. A recently proposed quantum algorithm shows that quantum computers could solve linear systems in a time scale of order log(N), giving an exponential speedup over classical computers. Here we realize the simplest instance of this algorithm, solving 2×2 linear equations for various input vectors on a quantum computer. We use four quantum bits and four controlled logic gates to implement every subroutine required, demonstrating the working principle of this algorithm.

Classical Yang-Baxter equations and quantum integrable systems

NASA Astrophysics Data System (ADS)

Jurčo, Branislav

1989-06-01

Quantum integrable models associated with nondegenerate solutions of classical Yang-Baxter equations related to the simple Lie algebras are investigated. These models are diagonalized for rational and trigonometric solutions in the cases of sl(N)/gl(N)/, o(N) and sp(N) algebras. The analogy with the quantum inverse scattering method is demonstrated.

Generalized quantum Fokker-Planck, diffusion, and Smoluchowski equations with true probability distribution functions.

PubMed

Banik, Suman Kumar; Bag, Bidhan Chandra; Ray, Deb Shankar

2002-05-01

Traditionally, quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasiprobability distribution functions, e.g., Wigner functions. These often become singular or negative in the full quantum regime. In this paper a simple approach to non-Markovian theory of quantum Brownian motion using true probability distribution functions is presented. Based on an initial coherent state representation of the bath oscillators and an equilibrium canonical distribution of the quantum mechanical mean values of their coordinates and momenta, we derive a generalized quantum Langevin equation in c numbers and show that the latter is amenable to a theoretical analysis in terms of the classical theory of non-Markovian dynamics. The corresponding Fokker-Planck, diffusion, and Smoluchowski equations are the exact quantum analogs of their classical counterparts. The present work is independent of path integral techniques. The theory as developed here is a natural extension of its classical version and is valid for arbitrary temperature and friction (the Smoluchowski equation being considered in the overdamped limit).

Trajectory description of the quantum–classical transition for wave packet interference

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

Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw

2016-08-15

The quantum–classical transition for wave packet interference is investigated using a hydrodynamic description. A nonlinear quantum–classical transition equation is obtained by introducing a degree of quantumness ranging from zero to one into the classical time-dependent Schrödinger equation. This equation provides a continuous description for the transition process of physical systems from purely quantum to purely classical regimes. In this study, the transition trajectory formalism is developed to provide a hydrodynamic description for the quantum–classical transition. The flow momentum of transition trajectories is defined by the gradient of the action function in the transition wave function and these trajectories follow themore » main features of the evolving probability density. Then, the transition trajectory formalism is employed to analyze the quantum–classical transition of wave packet interference. For the collision-like wave packet interference where the propagation velocity is faster than the spreading speed of the wave packet, the interference process remains collision-like for all the degree of quantumness. However, the interference features demonstrated by transition trajectories gradually disappear when the degree of quantumness approaches zero. For the diffraction-like wave packet interference, the interference process changes continuously from a diffraction-like to collision-like case when the degree of quantumness gradually decreases. This study provides an insightful trajectory interpretation for the quantum–classical transition of wave packet interference.« less

A single-sided representation for the homogeneous Green's function of a unified scalar wave equation.

PubMed

Wapenaar, Kees

2017-06-01

A unified scalar wave equation is formulated, which covers three-dimensional (3D) acoustic waves, 2D horizontally-polarised shear waves, 2D transverse-electric EM waves, 2D transverse-magnetic EM waves, 3D quantum-mechanical waves and 2D flexural waves. The homogeneous Green's function of this wave equation is a combination of the causal Green's function and its time-reversal, such that their singularities at the source position cancel each other. A classical representation expresses this homogeneous Green's function as a closed boundary integral. This representation finds applications in holographic imaging, time-reversed wave propagation and Green's function retrieval by cross correlation. The main drawback of the classical representation in those applications is that it requires access to a closed boundary around the medium of interest, whereas in many practical situations the medium can be accessed from one side only. Therefore, a single-sided representation is derived for the homogeneous Green's function of the unified scalar wave equation. Like the classical representation, this single-sided representation fully accounts for multiple scattering. The single-sided representation has the same applications as the classical representation, but unlike the classical representation it is applicable in situations where the medium of interest is accessible from one side only.

Fate of classical solitons in one-dimensional quantum systems.

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

Pustilnik, M.; Matveev, K. A.

We study one-dimensional quantum systems near the classical limit described by the Korteweg-de Vries (KdV) equation. The excitations near this limit are the well-known solitons and phonons. The classical description breaks down at long wavelengths, where quantum effects become dominant. Focusing on the spectra of the elementary excitations, we describe analytically the entire classical-to-quantum crossover. We show that the ultimate quantum fate of the classical KdV excitations is to become fermionic quasiparticles and quasiholes. We discuss in detail two exactly solvable models exhibiting such crossover, the Lieb-Liniger model of bosons with weak contact repulsion and the quantum Toda model, andmore » argue that the results obtained for these models are universally applicable to all quantum one-dimensional systems with a well-defined classical limit described by the KdV equation.« less

On the anisotropic advection-diffusion equation with time dependent coefficients

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

Hernandez-Coronado, Hector; Coronado, Manuel; Del-Castillo-Negrete, Diego B.

The advection-diffusion equation with time dependent velocity and anisotropic time dependent diffusion tensor is examined in regard to its non-classical transport features and to the use of a non-orthogonal coordinate system. Although this equation appears in diverse physical problems, particularly in particle transport in stochastic velocity fields and in underground porous media, a detailed analysis of its solutions is lacking. In order to study the effects of the time-dependent coefficients and the anisotropic diffusion on transport, we solve analytically the equation for an initial Dirac delta pulse. Here, we discuss the solutions to three cases: one based on power-law correlationmore » functions where the pulse diffuses faster than the classical rate ~t, a second case specically designed to display slower rate of diffusion than the classical one, and a third case to describe hydrodynamic dispersion in porous media« less

On the anisotropic advection-diffusion equation with time dependent coefficients

DOE PAGES

Hernandez-Coronado, Hector; Coronado, Manuel; Del-Castillo-Negrete, Diego B.

2017-02-01

The advection-diffusion equation with time dependent velocity and anisotropic time dependent diffusion tensor is examined in regard to its non-classical transport features and to the use of a non-orthogonal coordinate system. Although this equation appears in diverse physical problems, particularly in particle transport in stochastic velocity fields and in underground porous media, a detailed analysis of its solutions is lacking. In order to study the effects of the time-dependent coefficients and the anisotropic diffusion on transport, we solve analytically the equation for an initial Dirac delta pulse. Here, we discuss the solutions to three cases: one based on power-law correlationmore » functions where the pulse diffuses faster than the classical rate ~t, a second case specically designed to display slower rate of diffusion than the classical one, and a third case to describe hydrodynamic dispersion in porous media« less

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

Garcia-Fernandez, Ignacio; Pla-Castells, Marta; Martinez-Dura, Rafael J.

A model of a cable and pulleys is presented that can be used in Real Time Computer Graphics applications. The model is formulated by the coupling of a damped spring and a variable coefficient wave equation, and can be integrated in more complex mechanical models of lift systems, such as cranes, elevators, etc. with a high degree of interactivity.

The Effect of Mass, Wind Angle, and Erection Technique on the Aeroelastic Behaviour of a Cable-Stayed Bridge Model (Effet de la Masse, de L’Angle du Vent et de la Technique D’Erection sur le Comportement Aeroelastique d’une Marquette de Pont a Haubans).

DTIC Science & Technology

1987-09-01

response. An estimate of the buffeting response for the two cases is presented in Figure 4, using the theory of Irwin (Reference 7). Data acquisition was...values were obtained using the log decrement method by exciting the bridge in one mode and observing the decay of the response. Classical theory would...added mass or structural damping level. The addition of inertia to the deck would tend to lower the response according to classical vibration theory

Experimental Results of Schlicher's Thrusting Antenna

NASA Technical Reports Server (NTRS)

Fralick, Gustave C.; Niedra, Janis M.

2001-01-01

Experiments were conducted to test the claims by Rex L. Schlicher, et al., (Patent 5,142,86 1) that a certain antenna geometry produces thrust greatly exceeding radiation reaction, when driven by repetitive, fast rise, and relatively slower decay current pulses. In order to test this hypothesis, the antenna was suspended by strings as a 3 in pendulum. Current pulses were fed to the antenna along the suspension path by a very flexible coaxial line constructed from loudspeaker cable and copper braid sheath. When driving the antenna via this cabling, our pulser was capable of sustaining 1200 A pulses at a rate of 30 per second up to a minute. In this way, bursts of pulses could be delivered in synch with the pendulum period in order to build up any motion. However, when using a laser beam passing through a lens attached to the antenna to amplify linear displacement by a factor of at least 25, no correlated motion of the beam spot could be detected on a distant wall. We conclude, in agreement with the momentum theorem of classical electromagnetic theory, that any thrust produced is far below practically useful levels. Hence, within classical electrodynamics, there is little hope of detecting any low level motion that cannot be explained by interactions with surrounding structural steel and the Earth's magnetic field.

Nucleation theory - Is replacement free energy needed?. [error analysis of capillary approximation

NASA Technical Reports Server (NTRS)

Doremus, R. H.

1982-01-01

It has been suggested that the classical theory of nucleation of liquid from its vapor as developed by Volmer and Weber (1926) needs modification with a factor referred to as the replacement free energy and that the capillary approximation underlying the classical theory is in error. Here, the classical nucleation equation is derived from fluctuation theory, Gibb's result for the reversible work to form a critical nucleus, and the rate of collision of gas molecules with a surface. The capillary approximation is not used in the derivation. The chemical potential of small drops is then considered, and it is shown that the capillary approximation can be derived from thermodynamic equations. The results show that no corrections to Volmer's equation are needed.

Interacting charges and the classical electron radius

NASA Astrophysics Data System (ADS)

De Luca, Roberto; Di Mauro, Marco; Faella, Orazio; Naddeo, Adele

2018-03-01

The equation of the motion of a point charge q repelled by a fixed point-like charge Q is derived and studied. In solving this problem useful concepts in classical and relativistic kinematics, in Newtonian mechanics and in non-linear ordinary differential equations are revised. The validity of the approximations is discussed from the physical point of view. In particular the classical electron radius emerges naturally from the requirement that the initial distance is large enough for the non-relativistic approximation to be valid. The relevance of this topic for undergraduate physics teaching is pointed out.

Resonances and vibrations in an elevator cable system due to boundary sway

NASA Astrophysics Data System (ADS)

Gaiko, Nick V.; van Horssen, Wim T.

2018-06-01

In this paper, an analytical method is presented to study an initial-boundary value problem describing the transverse displacements of a vertically moving beam under boundary excitation. The length of the beam is linearly varying in time, i.e., the axial, vertical velocity of the beam is assumed to be constant. The bending stiffness of the beam is assumed to be small. This problem may be regarded as a model describing the lateral vibrations of an elevator cable excited at its boundaries by the wind-induced building sway. Slow variation of the cable length leads to a singular perturbation problem which is expressed in slowly changing, time-dependent coefficients in the governing differential equation. By providing an interior layer analysis, infinitely many resonance manifolds are detected. Further, the initial-boundary value problem is studied in detail using a three-timescales perturbation method. The constructed formal approximations of the solutions are in agreement with the numerical results.

On the classic and modern theories of matching.

PubMed

McDowell, J J

2005-07-01

Classic matching theory, which is based on Herrnstein's (1961) original matching equation and includes the well-known quantitative law of effect, is almost certainly false. The theory is logically inconsistent with known experimental findings, and experiments have shown that its central constant-k assumption is not tenable. Modern matching theory, which is based on the power function version of the original matching equation, remains tenable, although it has not been discussed or studied extensively. The modern theory is logically consistent with known experimental findings, it predicts the fact and details of the violation of the classic theory's constant-k assumption, and it accurately describes at least some data that are inconsistent with the classic theory.

On the effective field theory of intersecting D3-branes

NASA Astrophysics Data System (ADS)

Abbaspur, Reza

2018-05-01

We study the effective field theory of two intersecting D3-branes with one common dimension along the lines recently proposed in ref. [1]. We introduce a systematic way of deriving the classical effective action to arbitrary orders in perturbation theory. Using a proper renormalization prescription to handle logarithmic divergencies arising at all orders in the perturbation series, we recover the first order renormalization group equation of ref. [1] plus an infinite set of higher order equations. We show the consistency of the higher order equations with the first order one and hence interpret the first order result as an exact RG flow equation in the classical theory.

Classical integrable defects as quasi Bäcklund transformations

NASA Astrophysics Data System (ADS)

Doikou, Anastasia

2016-10-01

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

Nonlinear Schrödinger equation and classical-field description of thermal radiation

NASA Astrophysics Data System (ADS)

Rashkovskiy, Sergey A.

2018-03-01

It is shown that the thermal radiation can be described without quantization of energy in the framework of classical field theory using the nonlinear Schrödinger equation which is considered as a classical field equation. Planck's law for the spectral energy density of thermal radiation and the Einstein A-coefficient for spontaneous emission are derived without using the concept of the energy quanta. It is shown that the spectral energy density of thermal radiation is apparently not a universal function of frequency, as follows from the Planck's law, but depends weakly on the nature of atoms, while Planck's law is valid only as an approximation in the limit of weak excitation of atoms. Spin and relativistic effects are not considered in this paper.

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

ERIC Educational Resources Information Center

Savoye, Philippe

2009-01-01

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

Solution of the classical Yang-Baxter equation with an exotic symmetry, and integrability of a multi-species boson tunnelling model

NASA Astrophysics Data System (ADS)

Links, Jon

2017-03-01

Solutions of the classical Yang-Baxter equation provide a systematic method to construct integrable quantum systems in an algebraic manner. A Lie algebra can be associated with any solution of the classical Yang-Baxter equation, from which commuting transfer matrices may be constructed. This procedure is reviewed, specifically for solutions without skew-symmetry. A particular solution with an exotic symmetry is identified, which is not obtained as a limiting expansion of the usual Yang-Baxter equation. This solution facilitates the construction of commuting transfer matrices which will be used to establish the integrability of a multi-species boson tunnelling model. The model generalises the well-known two-site Bose-Hubbard model, to which it reduces in the one-species limit. Due to the lack of an apparent reference state, application of the algebraic Bethe Ansatz to solve the model is prohibitive. Instead, the Bethe Ansatz solution is obtained by the use of operator identities and tensor product decompositions.

Classical r-matrices for the generalised Chern–Simons formulation of 3d gravity

NASA Astrophysics Data System (ADS)

Osei, Prince K.; Schroers, Bernd J.

2018-04-01

We study the conditions for classical r-matrices to be compatible with the generalised Chern–Simons action for 3d gravity. Compatibility means solving the classical Yang–Baxter equations with a prescribed symmetric part for each of the real Lie algebras and bilinear pairings arising in the generalised Chern–Simons action. We give a new construction of r-matrices via a generalised complexification and derive a non-linear set of matrix equations determining the most general compatible r-matrix. We exhibit new families of solutions and show that they contain some known r-matrices for special parameter values.

User Guide for Compressible Flow Toolbox Version 2.1 for Use With MATLAB(Registered Trademark); Version 7

NASA Technical Reports Server (NTRS)

Melcher, Kevin J.

2006-01-01

This report provides a user guide for the Compressible Flow Toolbox, a collection of algorithms that solve almost 300 linear and nonlinear classical compressible flow relations. The algorithms, implemented in the popular MATLAB programming language, are useful for analysis of one-dimensional steady flow with constant entropy, friction, heat transfer, or shock discontinuities. The solutions do not include any gas dissociative effects. The toolbox also contains functions for comparing and validating the equation-solving algorithms against solutions previously published in the open literature. The classical equations solved by the Compressible Flow Toolbox are: isentropic-flow equations, Fanno flow equations (pertaining to flow of an ideal gas in a pipe with friction), Rayleigh flow equations (pertaining to frictionless flow of an ideal gas, with heat transfer, in a pipe of constant cross section.), normal-shock equations, oblique-shock equations, and Prandtl-Meyer expansion equations. At the time this report was published, the Compressible Flow Toolbox was available without cost from the NASA Software Repository.

Axion as a cold dark matter candidate: analysis to third order perturbation for classical axion

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

Noh, Hyerim; Hwang, Jai-chan; Park, Chan-Gyung, E-mail: hr@kasi.re.kr, E-mail: jchan@knu.ac.kr, E-mail: park.chan.gyung@gmail.com

2015-12-01

We investigate aspects of axion as a coherently oscillating massive classical scalar field by analyzing third order perturbations in Einstein's gravity in the axion-comoving gauge. The axion fluid has its characteristic pressure term leading to an axion Jeans scale which is cosmologically negligible for a canonical axion mass. Our classically derived axion pressure term in Einstein's gravity is identical to the one derived in the non-relativistic quantum mechanical context in the literature. We present the general relativistic continuity and Euler equations for an axion fluid valid up to third order perturbation. Equations for axion are exactly the same as thatmore » of a zero-pressure fluid in Einstein's gravity except for an axion pressure term in the Euler equation. Our analysis includes the cosmological constant.« less

Parametric Stiffness Control of Flexible Structures

NASA Technical Reports Server (NTRS)

Moon, F. C.; Rand, R. H.

1985-01-01

An unconventional method for control of flexible space structures using feedback control of certain elements of the stiffness matrix is discussed. The advantage of using this method of configuration control is that it can be accomplished in practical structures by changing the initial stress state in the structure. The initial stress state can be controlled hydraulically or by cables. The method leads, however, to nonlinear control equations. In particular, a long slender truss structure under cable induced initial compression is examined. both analytical and numerical analyses are presented. Nonlinear analysis using center manifold theory and normal form theory is used to determine criteria on the nonlinear control gains for stable or unstable operation. The analysis is made possible by the use of the exact computer algebra system MACSYMA.

Simulation of wave packet tunneling of interacting identical particles

NASA Astrophysics Data System (ADS)

Lozovik, Yu. E.; Filinov, A. V.; Arkhipov, A. S.

2003-02-01

We demonstrate a different method of simulation of nonstationary quantum processes, considering the tunneling of two interacting identical particles, represented by wave packets. The used method of quantum molecular dynamics (WMD) is based on the Wigner representation of quantum mechanics. In the context of this method ensembles of classical trajectories are used to solve quantum Wigner-Liouville equation. These classical trajectories obey Hamiltonian-like equations, where the effective potential consists of the usual classical term and the quantum term, which depends on the Wigner function and its derivatives. The quantum term is calculated using local distribution of trajectories in phase space, therefore, classical trajectories are not independent, contrary to classical molecular dynamics. The developed WMD method takes into account the influence of exchange and interaction between particles. The role of direct and exchange interactions in tunneling is analyzed. The tunneling times for interacting particles are calculated.

A classical but new kinetic equation for hydride transfer reactions.

PubMed

Zhu, Xiao-Qing; Deng, Fei-Huang; Yang, Jin-Dong; Li, Xiu-Tao; Chen, Qiang; Lei, Nan-Ping; Meng, Fan-Kun; Zhao, Xiao-Peng; Han, Su-Hui; Hao, Er-Jun; Mu, Yuan-Yuan

2013-09-28

A classical but new kinetic equation to estimate activation energies of various hydride transfer reactions was developed according to transition state theory using the Morse-type free energy curves of hydride donors to release a hydride anion and hydride acceptors to capture a hydride anion and by which the activation energies of 187 typical hydride self-exchange reactions and more than thirty thousand hydride cross transfer reactions in acetonitrile were safely estimated in this work. Since the development of the kinetic equation is only on the basis of the related chemical bond changes of the hydride transfer reactants, the kinetic equation should be also suitable for proton transfer reactions, hydrogen atom transfer reactions and all the other chemical reactions involved with breaking and formation of chemical bonds. One of the most important contributions of this work is to have achieved the perfect unity of the kinetic equation and thermodynamic equation for hydride transfer reactions.

New Equating Methods and Their Relationships with Levine Observed Score Linear Equating under the Kernel Equating Framework

ERIC Educational Resources Information Center

Chen, Haiwen; Holland, Paul

2010-01-01

In this paper, we develop a new curvilinear equating for the nonequivalent groups with anchor test (NEAT) design under the assumption of the classical test theory model, that we name curvilinear Levine observed score equating. In fact, by applying both the kernel equating framework and the mean preserving linear transformation of…

Modeling magnetic fields from a DC power cable buried beneath San Francisco Bay based on empirical measurements

DOE PAGES

Kavet, Robert; Wyman, Megan T.; Klimley, A. Peter; ...

2016-02-25

Here, the Trans Bay Cable (TBC) is a ±200-kilovolt (kV), 400 MW 85-km long High Voltage Direct Current (DC) buried transmission line linking Pittsburg, CA with San Francisco, CA (SF) beneath the San Francisco Estuary. The TBC runs parallel to the migratory route of various marine species, including green sturgeon, Chinook salmon, and steelhead trout. In July and August 2014, an extensive series of magnetic field measurements were taken using a pair of submerged Geometrics magnetometers towed behind a survey vessel in four locations in the San Francisco estuary along profiles that cross the cable’s path; these included the Sanmore » Francisco-Oakland Bay Bridge (BB), the Richmond-San Rafael Bridge (RSR), the Benicia- Martinez Bridge (Ben) and an area in San Pablo Bay (SP) in which a bridge is not present. In this paper, we apply basic formulas that ideally describe the magnetic field from a DC cable summed vectorially with the background geomagnetic field (in the absence of other sources that would perturb the ambient field) to derive characteristics of the cable that are otherwise not immediately observable. Magnetic field profiles from measurements taken along 170 survey lines were inspected visually for evidence of a distinct pattern representing the presence of the cable. Many profiles were dominated by field distortions unrelated to the cable caused by bridge structures or other submerged objects, and the cable’s contribution to the field was not detectable. BB, with 40 of the survey lines, did not yield usable data for these reasons. The unrelated anomalies could be up to 100 times greater than those from the cable. In total, discernible magnetic field profiles measured from 76 survey lines were regressed against the equations, representing eight days of measurement. The modeled field anomalies due to the cable (the difference between the maximum and minimum field along the survey line at the cable crossing) were virtually identical to the measured values. The modeling yielded a pooled cable depth below the bay floor of 2.06 m (±1.46 std dev), and estimated the angle to the horizontal of the imaginary line connecting the crosssectional center of the cable’s two conductors (0.1143 m apart) as 178.9° ±61.9° (std dev) for Ben, 78.6°±37.0° (std dev) for RSR, and 139.9°±27.4° (std dev) for SP. The mean of the eight daily average currents derived from the regressions was 986 ±185 amperes (A) (std dev), as compared to 722 ±95 A (std dev) provided by Trans Bay Cable LLC. Overall, the regressions based on fundamental principles (Biot Savart law) and the vectorial summation of cable and geomagnetic fields provide estimates of cable characteristics consistent with plausible expectations.« less

Modeling magnetic fields from a DC power cable buried beneath San Francisco Bay based on empirical measurements

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

Kavet, Robert; Wyman, Megan T.; Klimley, A. Peter

Here, the Trans Bay Cable (TBC) is a ±200-kilovolt (kV), 400 MW 85-km long High Voltage Direct Current (DC) buried transmission line linking Pittsburg, CA with San Francisco, CA (SF) beneath the San Francisco Estuary. The TBC runs parallel to the migratory route of various marine species, including green sturgeon, Chinook salmon, and steelhead trout. In July and August 2014, an extensive series of magnetic field measurements were taken using a pair of submerged Geometrics magnetometers towed behind a survey vessel in four locations in the San Francisco estuary along profiles that cross the cable’s path; these included the Sanmore » Francisco-Oakland Bay Bridge (BB), the Richmond-San Rafael Bridge (RSR), the Benicia- Martinez Bridge (Ben) and an area in San Pablo Bay (SP) in which a bridge is not present. In this paper, we apply basic formulas that ideally describe the magnetic field from a DC cable summed vectorially with the background geomagnetic field (in the absence of other sources that would perturb the ambient field) to derive characteristics of the cable that are otherwise not immediately observable. Magnetic field profiles from measurements taken along 170 survey lines were inspected visually for evidence of a distinct pattern representing the presence of the cable. Many profiles were dominated by field distortions unrelated to the cable caused by bridge structures or other submerged objects, and the cable’s contribution to the field was not detectable. BB, with 40 of the survey lines, did not yield usable data for these reasons. The unrelated anomalies could be up to 100 times greater than those from the cable. In total, discernible magnetic field profiles measured from 76 survey lines were regressed against the equations, representing eight days of measurement. The modeled field anomalies due to the cable (the difference between the maximum and minimum field along the survey line at the cable crossing) were virtually identical to the measured values. The modeling yielded a pooled cable depth below the bay floor of 2.06 m (±1.46 std dev), and estimated the angle to the horizontal of the imaginary line connecting the crosssectional center of the cable’s two conductors (0.1143 m apart) as 178.9° ±61.9° (std dev) for Ben, 78.6°±37.0° (std dev) for RSR, and 139.9°±27.4° (std dev) for SP. The mean of the eight daily average currents derived from the regressions was 986 ±185 amperes (A) (std dev), as compared to 722 ±95 A (std dev) provided by Trans Bay Cable LLC. Overall, the regressions based on fundamental principles (Biot Savart law) and the vectorial summation of cable and geomagnetic fields provide estimates of cable characteristics consistent with plausible expectations.« less

Yang-Baxter maps, discrete integrable equations and quantum groups

NASA Astrophysics Data System (ADS)

Bazhanov, Vladimir V.; Sergeev, Sergey M.

2018-01-01

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

Planck constant as spectral parameter in integrable systems and KZB equations

NASA Astrophysics Data System (ADS)

Levin, A.; Olshanetsky, M.; Zotov, A.

2014-10-01

We construct special rational gl N Knizhnik-Zamolodchikov-Bernard (KZB) equations with Ñ punctures by deformation of the corresponding quantum gl N rational R-matrix. They have two parameters. The limit of the first one brings the model to the ordinary rational KZ equation. Another one is τ. At the level of classical mechanics the deformation parameter τ allows to extend the previously obtained modified Gaudin models to the modified Schlesinger systems. Next, we notice that the identities underlying generic (elliptic) KZB equations follow from some additional relations for the properly normalized R-matrices. The relations are noncommutative analogues of identities for (scalar) elliptic functions. The simplest one is the unitarity condition. The quadratic (in R matrices) relations are generated by noncommutative Fay identities. In particular, one can derive the quantum Yang-Baxter equations from the Fay identities. The cubic relations provide identities for the KZB equations as well as quadratic relations for the classical r-matrices which can be treated as halves of the classical Yang-Baxter equation. At last we discuss the R-matrix valued linear problems which provide gl Ñ CM models and Painlevé equations via the above mentioned identities. The role of the spectral parameter plays the Planck constant of the quantum R-matrix. When the quantum gl N R-matrix is scalar ( N = 1) the linear problem reproduces the Krichever's ansatz for the Lax matrices with spectral parameter for the gl Ñ CM models. The linear problems for the quantum CM models generalize the KZ equations in the same way as the Lax pairs with spectral parameter generalize those without it.

Extension of lattice Boltzmann flux solver for simulation of compressible multi-component flows

NASA Astrophysics Data System (ADS)

Yang, Li-Ming; Shu, Chang; Yang, Wen-Ming; Wang, Yan

2018-05-01

The lattice Boltzmann flux solver (LBFS), which was presented by Shu and his coworkers for solving compressible fluid flow problems, is extended to simulate compressible multi-component flows in this work. To solve the two-phase gas-liquid problems, the model equations with stiffened gas equation of state are adopted. In this model, two additional non-conservative equations are introduced to represent the material interfaces, apart from the classical Euler equations. We first convert the interface equations into the full conservative form by applying the mass equation. After that, we calculate the numerical fluxes of the classical Euler equations by the existing LBFS and the numerical fluxes of the interface equations by the passive scalar approach. Once all the numerical fluxes at the cell interface are obtained, the conservative variables at cell centers can be updated by marching the equations in time and the material interfaces can be identified via the distributions of the additional variables. The numerical accuracy and stability of present scheme are validated by its application to several compressible multi-component fluid flow problems.

Algorithmic framework for group analysis of differential equations and its application to generalized Zakharov-Kuznetsov equations

NASA Astrophysics Data System (ADS)

Huang, Ding-jiang; Ivanova, Nataliya M.

2016-02-01

In this paper, we explain in more details the modern treatment of the problem of group classification of (systems of) partial differential equations (PDEs) from the algorithmic point of view. More precisely, we revise the classical Lie algorithm of construction of symmetries of differential equations, describe the group classification algorithm and discuss the process of reduction of (systems of) PDEs to (systems of) equations with smaller number of independent variables in order to construct invariant solutions. The group classification algorithm and reduction process are illustrated by the example of the generalized Zakharov-Kuznetsov (GZK) equations of form ut +(F (u)) xxx +(G (u)) xyy +(H (u)) x = 0. As a result, a complete group classification of the GZK equations is performed and a number of new interesting nonlinear invariant models which have non-trivial invariance algebras are obtained. Lie symmetry reductions and exact solutions for two important invariant models, i.e., the classical and modified Zakharov-Kuznetsov equations, are constructed. The algorithmic framework for group analysis of differential equations presented in this paper can also be applied to other nonlinear PDEs.

New analytical exact solutions of time fractional KdV-KZK equation by Kudryashov methods

NASA Astrophysics Data System (ADS)

S Saha, Ray

2016-04-01

In this paper, new exact solutions of the time fractional KdV-Khokhlov-Zabolotskaya-Kuznetsov (KdV-KZK) equation are obtained by the classical Kudryashov method and modified Kudryashov method respectively. For this purpose, the modified Riemann-Liouville derivative is used to convert the nonlinear time fractional KdV-KZK equation into the nonlinear ordinary differential equation. In the present analysis, the classical Kudryashov method and modified Kudryashov method are both used successively to compute the analytical solutions of the time fractional KdV-KZK equation. As a result, new exact solutions involving the symmetrical Fibonacci function, hyperbolic function and exponential function are obtained for the first time. The methods under consideration are reliable and efficient, and can be used as an alternative to establish new exact solutions of different types of fractional differential equations arising from mathematical physics. The obtained results are exhibited graphically in order to demonstrate the efficiencies and applicabilities of these proposed methods of solving the nonlinear time fractional KdV-KZK equation.

Arbitrarily Curved and Twisted Space Beams. Ph.D. Thesis - Va. Polytech. Inst. and State Univ.; [Elastic Deformation, Stress Analysis

NASA Technical Reports Server (NTRS)

Hunter, W. F.

1974-01-01

A derivation of the equations which govern the deformation of an arbitrarily curved and twisted space beam is presented. These equations differ from those of the classical theory in that (1) extensional effects are included; (2) the strain-displacement relations are derived; and (3) the expressions for the stress resultants are developed from the strain displacement relations. It is shown that the torsional stress resultant obtained by the classical approach is basically incorrect except when the cross-section is circular. The governing equations are given in the form of first-order differential equations. A numerical algorithm is given for obtaining the natural vibration characteristics and example problems are presented.

Construction of Chained True Score Equipercentile Equatings under the Kernel Equating (KE) Framework and Their Relationship to Levine True Score Equating. Research Report. ETS RR-09-24

ERIC Educational Resources Information Center

Chen, Haiwen; Holland, Paul

2009-01-01

In this paper, we develop a new chained equipercentile equating procedure for the nonequivalent groups with anchor test (NEAT) design under the assumptions of the classical test theory model. This new equating is named chained true score equipercentile equating. We also apply the kernel equating framework to this equating design, resulting in a…

A Classical Based Derivation of Time Dilation Providing First Order Accuracy to Schwarzschild's Solution of Einstein's Field Equations

NASA Astrophysics Data System (ADS)

Austin, Rickey W.

In Einstein's theory of Special Relativity (SR), one method to derive relativistic kinetic energy is via applying the classical work-energy theorem to relativistic momentum. This approach starts with a classical based work-energy theorem and applies SR's momentum to the derivation. One outcome of this derivation is relativistic kinetic energy. From this derivation, it is rather straight forward to form a kinetic energy based time dilation function. In the derivation of General Relativity a common approach is to bypass classical laws as a starting point. Instead a rigorous development of differential geometry and Riemannian space is constructed, from which classical based laws are derived. This is in contrast to SR's approach of starting with classical laws and applying the consequences of the universal speed of light by all observers. A possible method to derive time dilation due to Newtonian gravitational potential energy (NGPE) is to apply SR's approach to deriving relativistic kinetic energy. It will be shown this method gives a first order accuracy compared to Schwarzschild's metric. The SR's kinetic energy and the newly derived NGPE derivation are combined to form a Riemannian metric based on these two energies. A geodesic is derived and calculations compared to Schwarzschild's geodesic for an orbiting test mass about a central, non-rotating, non-charged massive body. The new metric results in high accuracy calculations when compared to Einsteins General Relativity's prediction. The new method provides a candidate approach for starting with classical laws and deriving General Relativity effects. This approach mimics SR's method of starting with classical mechanics when deriving relativistic equations. As a compliment to introducing General Relativity, it provides a plausible scaffolding method from classical physics when teaching introductory General Relativity. A straight forward path from classical laws to General Relativity will be derived. This derivation provides a minimum first order accuracy to Schwarzschild's solution to Einstein's field equations.

Quantum-classical analogies in waveguide arrays: From Fourier transforms to ion-laser interactions

NASA Astrophysics Data System (ADS)

Moya-Cessa, Héctor M.

2018-04-01

By using the fact that infinite and semi-infinite systems of differential equations may be casted as Schrödinger-like equations we show how quantum-classical analogies may be achieved. In particular we show how the analogies of ion-laser, functions of a phase operator and quantised-field-two-level-atom interactions may be emulated. We also show a realization of the fractional discrete Fourier transform.

On the dynamics of chain systems. [applications in manipulator and human body models

NASA Technical Reports Server (NTRS)

Huston, R. L.; Passerello, C. E.

1974-01-01

A computer-oriented method for obtaining dynamical equations of motion for chain systems is presented. A chain system is defined as an arbitrarily assembled set of rigid bodies such that adjoining bodies have at least one common point and such that closed loops are not formed. The equations of motion are developed through the use of Lagrange's form of d'Alembert's principle. The method and procedure is illustrated with an elementary study of a tripod space manipulator. The method is designed for application with systems such as human body models, chains and cables, and dynamic finite-segment models.

An Evaluation of Kernel Equating: Parallel Equating with Classical Methods in the SAT Subject Tests[TM] Program. Research Report. ETS RR-09-06

ERIC Educational Resources Information Center

Grant, Mary C.; Zhang, Lilly; Damiano, Michele

2009-01-01

This study investigated kernel equating methods by comparing these methods to operational equatings for two tests in the SAT Subject Tests[TM] program. GENASYS (ETS, 2007) was used for all equating methods and scaled score kernel equating results were compared to Tucker, Levine observed score, chained linear, and chained equipercentile equating…

Foundations of Quantum Mechanics: Derivation of a dissipative Schrödinger equation from first principles

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

Gonçalves, L.A.; Olavo, L.S.F., E-mail: olavolsf@gmail.com

Dissipation in Quantum Mechanics took some time to become a robust field of investigation after the birth of the field. The main issue hindering developments in the field is that the Quantization process was always tightly connected to the Hamiltonian formulation of Classical Mechanics. In this paper we present a quantization process that does not depend upon the Hamiltonian formulation of Classical Mechanics (although still departs from Classical Mechanics) and thus overcome the problem of finding, from first principles, a completely general Schrödinger equation encompassing dissipation. This generalized process of quantization is shown to be nothing but an extension ofmore » a more restricted version that is shown to produce the Schrödinger equation for Hamiltonian systems from first principles (even for Hamiltonian velocity dependent potential). - Highlights: • A Quantization process independent of the Hamiltonian formulation of quantum Mechanics is proposed. • This quantization method is applied to dissipative or absorptive systems. • A Dissipative Schrödinger equation is derived from first principles.« less

On the correspondence between quantum and classical variational principles

DOE PAGES

Ruiz, D. E.; Dodin, I. Y.

2015-06-10

Here, classical variational principles can be deduced from quantum variational principles via formal reparameterization of the latter. It is shown that such reparameterization is possible without invoking any assumptions other than classicality and without appealing to dynamical equations. As examples, first principle variational formulations of classical point-particle and cold-fluid motion are derived from their quantum counterparts for Schrodinger, Pauli, and Klein-Gordon particles.

Quantum to classical transition in quantum field theory

NASA Astrophysics Data System (ADS)

Lombardo, Fernando C.

1998-12-01

We study the quatum to classical transition process in the context of quantum field theory. Extending the influence functional formalism of Feynman and Vernon, we study the decoherence process for self-interacting quantum fields in flat space. We also use this formalism for arbitrary geometries to analyze the quantum to classical transition in quantum gravity. After summarizing the main results known for the quantum Brownian motion, we consider a self-interacting field theory in Minkowski spacetime. We compute a coarse grained effective action by integrating out the field modes with wavelength shorter than a critical value. From this effective action we obtain the evolution equation for the reduced density matrix (master equation). We compute the diffusion coefficients for this equation and analyze the decoherence induced on the long-wavelength modes. We generalize the results to the case of a conformally coupled scalar field in de Sitter spacetime. We show that the decoherence is effective as long as the critical wavelength is taken to be not shorter than the Hubble radius. On the other hand, we study the classical limit for scalar-tensorial models in two dimensions. We consider different couplings between the dilaton and the scalar field. We discuss the Hawking radiation process and, from an exact evaluation of the influence functional, we study the conditions by which decoherence ensures the validity of the semiclassical approximation in cosmological metrics. Finally we consider four dimensional models with massive scalar fields, arbitrary coupled to the geometry. We compute the Einstein-Langevin equations in order to study the effect of the fluctuations induced by the quantum fields on the classical geometry.

Derivation of the Schrodinger Equation from the Hamilton-Jacobi Equation in Feynman's Path Integral Formulation of Quantum Mechanics

ERIC Educational Resources Information Center

Field, J. H.

2011-01-01

It is shown how the time-dependent Schrodinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics. Schrodinger's own published derivations of quantum wave equations, the first of which was also based on the Hamilton-Jacobi…

An Introduction to the properties of Superconductors

NASA Astrophysics Data System (ADS)

Letarte, Alec

2001-03-01

A brief introductory presentation of the various properties of superconductors. The discussion will be focussed mainly on the newer ceramic superconductors, but the classic metal ones will also be touched upon. Some of the properties to be considered are: Optical properties, transport properties, persistent currents, coherence length, flux magnetisation, and the ``anti-gravity effect" produced be superconductors Another subject to be looked at will be the recent technological uses and developments of superconductors. For example, they have developed thin superconductors which they are making into a superconducting cable.

Predicting the payload capability of cable logging systems including the effect of partial suspension

Treesearch

Gary D. Falk

1981-01-01

A systematic procedure for predicting the payload capability of running, live, and standing skylines is presented. Three hand-held calculator programs are used to predict payload capability that includes the effect of partial suspension. The programs allow for predictions for downhill yarding and for yarding away from the yarder. The equations and basic principles...

Symbolic Solution of Linear Differential Equations

NASA Technical Reports Server (NTRS)

Feinberg, R. B.; Grooms, R. G.

1981-01-01

An algorithm for solving linear constant-coefficient ordinary differential equations is presented. The computational complexity of the algorithm is discussed and its implementation in the FORMAC system is described. A comparison is made between the algorithm and some classical algorithms for solving differential equations.

STABILITY OF A CABLE-MOORED AIRSHIP

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

Bennett, M.D.

1959-03-01

Equations of motion for the longitudinal and directional stability of a cable-moored airship were analyzed on an analog computer by subjecting the configuration to a horizontals ramp-type gust and observing the induced motion. The results indicate that the proposed configuration is dynamically stable (overdamped, essentially), and that it possesses a sufficiently high degree of stability to permit a 20-percent reduction in the fin planform area governing stability in the longitudinal direction. However, this reduction cannot be accomplished by decreasing the appropriate area of the proposed three-fintail because such a decrease causes the airship to become directionally unstable. Aerodynamically, the desiredmore » area reduction can best be effected by the use of a four-fin tail. Motions are calculated for various modifications to the proposed configuration. (auth)« less

An Exploration of Kernel Equating Using SAT® Data: Equating to a Similar Population and to a Distant Population. Research Report. ETS RR-07-17

ERIC Educational Resources Information Center

Liu, Jinghua; Low, Albert C.

2007-01-01

This study applied kernel equating (KE) in two scenarios: equating to a very similar population and equating to a very different population, referred to as a distant population, using SAT® data. The KE results were compared to the results obtained from analogous classical equating methods in both scenarios. The results indicate that KE results are…

Foldy-Wouthuysen transformation for a Dirac-Pauli dyon and the Thomas-Bargmann-Michel-Telegdi equation

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

Chen, Tsung-Wei; Chiou, Dah-Wei; Department of Physics and Center for Theoretical Sciences, National Taiwan University, Taipei 106, Taiwan

The classical dynamics for a charged point particle with intrinsic spin is governed by a relativistic Hamiltonian for the orbital motion and by the Thomas-Bargmann-Michel-Telegdi equation for the precession of the spin. It is natural to ask whether the classical Hamiltonian (with both the orbital and spin parts) is consistent with that in the relativistic quantum theory for a spin-1/2 charged particle, which is described by the Dirac equation. In the low-energy limit, up to terms of the seventh order in 1/E{sub g} (E{sub g}=2mc{sup 2} and m is the particle mass), we investigate the Foldy-Wouthuysen (FW) transformation of themore » Dirac Hamiltonian in the presence of homogeneous and static electromagnetic fields and show that it is indeed in agreement with the classical Hamiltonian with the gyromagnetic ratio being equal to 2. Through electromagnetic duality, this result can be generalized for a spin-1/2 dyon, which has both electric and magnetic charges and thus possesses both intrinsic electric and magnetic dipole moments. Furthermore, the relativistic quantum theory for a spin-1/2 dyon with arbitrary values of the gyromagnetic and gyroelectric ratios can be described by the Dirac-Pauli equation, which is the Dirac equation with augmentation for the anomalous electric and anomalous magnetic dipole moments. The FW transformation of the Dirac-Pauli Hamiltonian is shown, up to the seventh-order again, to be in accord with the classical Hamiltonian as well.« less

Does ℏ play a role in multidimensional spectroscopy? Reduced hierarchy equations of motion approach to molecular vibrations.

PubMed

Sakurai, Atsunori; Tanimura, Yoshitaka

2011-04-28

To investigate the role of quantum effects in vibrational spectroscopies, we have carried out numerically exact calculations of linear and nonlinear response functions for an anharmonic potential system nonlinearly coupled to a harmonic oscillator bath. Although one cannot carry out the quantum calculations of the response functions with full molecular dynamics (MD) simulations for a realistic system which consists of many molecules, it is possible to grasp the essence of the quantum effects on the vibrational spectra by employing a model Hamiltonian that describes an intra- or intermolecular vibrational motion in a condensed phase. The present model fully includes vibrational relaxation, while the stochastic model often used to simulate infrared spectra does not. We have employed the reduced quantum hierarchy equations of motion approach in the Wigner space representation to deal with nonperturbative, non-Markovian, and nonsecular system-bath interactions. Taking the classical limit of the hierarchy equations of motion, we have obtained the classical equations of motion that describe the classical dynamics under the same physical conditions as in the quantum case. By comparing the classical and quantum mechanically calculated linear and multidimensional spectra, we found that the profiles of spectra for a fast modulation case were similar, but different for a slow modulation case. In both the classical and quantum cases, we identified the resonant oscillation peak in the spectra, but the quantum peak shifted to the red compared with the classical one if the potential is anharmonic. The prominent quantum effect is the 1-2 transition peak, which appears only in the quantum mechanically calculated spectra as a result of anharmonicity in the potential or nonlinearity of the system-bath coupling. While the contribution of the 1-2 transition is negligible in the fast modulation case, it becomes important in the slow modulation case as long as the amplitude of the frequency fluctuation is small. Thus, we observed a distinct difference between the classical and quantum mechanically calculated multidimensional spectra in the slow modulation case where spectral diffusion plays a role. This fact indicates that one may not reproduce the experimentally obtained multidimensional spectrum for high-frequency vibrational modes based on classical molecular dynamics simulations if the modulation that arises from surrounding molecules is weak and slow. A practical way to overcome the difference between the classical and quantum simulations was discussed.

Electron dynamics in solid state via time varying wavevectors

NASA Astrophysics Data System (ADS)

Khaneja, Navin

2018-06-01

In this paper, we study electron wavepacket dynamics in electric and magnetic fields. We rigorously derive the semiclassical equations of electron dynamics in electric and magnetic fields. We do it both for free electron and electron in a periodic potential. We do this by introducing time varying wavevectors k(t). In the presence of magnetic field, our wavepacket reproduces the classical cyclotron orbits once the origin of the Schröedinger equation is correctly chosen to be center of cyclotron orbit. In the presence of both electric and magnetic fields, our equations for wavepacket dynamics differ from classical Lorentz force equations. We show that in a periodic potential, on application of electric field, the electron wave function adiabatically follows the wavefunction of a time varying Bloch wavevector k(t), with its energies suitably shifted with time. We derive the effective mass equation and discuss conduction in conductors and insulators.

Causal dissipation for the relativistic dynamics of ideal gases

NASA Astrophysics Data System (ADS)

Freistühler, Heinrich; Temple, Blake

2017-05-01

We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier-Stokes equations.

Zubarev's Nonequilibrium Statistical Operator Method in the Generalized Statistics of Multiparticle Systems

NASA Astrophysics Data System (ADS)

Glushak, P. A.; Markiv, B. B.; Tokarchuk, M. V.

2018-01-01

We present a generalization of Zubarev's nonequilibrium statistical operator method based on the principle of maximum Renyi entropy. In the framework of this approach, we obtain transport equations for the basic set of parameters of the reduced description of nonequilibrium processes in a classical system of interacting particles using Liouville equations with fractional derivatives. For a classical systems of particles in a medium with a fractal structure, we obtain a non-Markovian diffusion equation with fractional spatial derivatives. For a concrete model of the frequency dependence of a memory function, we obtain generalized Kettano-type diffusion equation with the spatial and temporal fractality taken into account. We present a generalization of nonequilibrium thermofield dynamics in Zubarev's nonequilibrium statistical operator method in the framework of Renyi statistics.

Causal dissipation for the relativistic dynamics of ideal gases

PubMed Central

2017-01-01

We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier–Stokes equations. PMID:28588397

Causal dissipation for the relativistic dynamics of ideal gases.

PubMed

Freistühler, Heinrich; Temple, Blake

2017-05-01

We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier-Stokes equations.

Spinomotive force induced by a transverse displacement current in a thin metal or doped-semiconductor sheet: Classical and quantum views.

NASA Astrophysics Data System (ADS)

Hu, Chia-Ren

2004-03-01

We present classical macroscopic, microscopic, and quantum mechanical arguments to show that in a metallic or electron/hole-doped semiconducting sheet thinner than the screening length, a displacement current applied normal to it can induce a spinomotive force along it. The magnitude is weak but clearly detectable. The classical arguments are purely electromagnetic. The quantum argument, based on the Dirac equation, shows that the predicted effect originates from the spin-orbit interaction, but not of the usual kind. That is, it relies on an external electric field, whereas the usual S-O interaction involves the electric field generated by the ions. Because the Dirac equation incorporatesThomas precession, which is due to relativistic kinematics, the quantum prediction is a factor of two smaller than the classical prediction. Replacing the displacement current by a charge current, and one obtains a new source for the spin-Hall effect. Classical macroscopic argument also predicts its existence, but the other two views are controversial.

Cumulants, free cumulants and half-shuffles

PubMed Central

Ebrahimi-Fard, Kurusch; Patras, Frédéric

2015-01-01

Free cumulants were introduced as the proper analogue of classical cumulants in the theory of free probability. There is a mix of similarities and differences, when one considers the two families of cumulants. Whereas the combinatorics of classical cumulants is well expressed in terms of set partitions, that of free cumulants is described and often introduced in terms of non-crossing set partitions. The formal series approach to classical and free cumulants also largely differs. The purpose of this study is to put forward a different approach to these phenomena. Namely, we show that cumulants, whether classical or free, can be understood in terms of the algebra and combinatorics underlying commutative as well as non-commutative (half-)shuffles and (half-) unshuffles. As a corollary, cumulants and free cumulants can be characterized through linear fixed point equations. We study the exponential solutions of these linear fixed point equations, which display well the commutative, respectively non-commutative, character of classical and free cumulants. PMID:27547078

Computational method for exact frequency-dependent rays on the basis of the solution of the Helmholtz equation

NASA Astrophysics Data System (ADS)

Protasov, M.; Gadylshin, K.

2017-07-01

A numerical method is proposed for the calculation of exact frequency-dependent rays when the solution of the Helmholtz equation is known. The properties of frequency-dependent rays are analysed and compared with classical ray theory and with the method of finite-difference modelling for the first time. In this paper, we study the dependence of these rays on the frequency of signals and show the convergence of the exact rays to the classical rays with increasing frequency. A number of numerical experiments demonstrate the distinctive features of exact frequency-dependent rays, in particular, their ability to penetrate into shadow zones that are impenetrable for classical rays.

Fokker-Planck equation of the reduced Wigner function associated to an Ohmic quantum Langevin dynamics

NASA Astrophysics Data System (ADS)

Colmenares, Pedro J.

2018-05-01

This article has to do with the derivation and solution of the Fokker-Planck equation associated to the momentum-integrated Wigner function of a particle subjected to a harmonic external field in contact with an ohmic thermal bath of quantum harmonic oscillators. The strategy employed is a simplified version of the phenomenological approach of Schramm, Jung, and Grabert of interpreting the operators as c numbers to derive the quantum master equation arising from a twofold transformation of the Wigner function of the entire phase space. The statistical properties of the random noise comes from the integral functional theory of Grabert, Schramm, and Ingold. By means of a single Wigner transformation, a simpler equation than that mentioned before is found. The Wigner function reproduces the known results of the classical limit. This allowed us to rewrite the underdamped classical Langevin equation as a first-order stochastic differential equation with time-dependent drift and diffusion terms.

Underwater spark discharge with long transmission line for cleaning horizontal wells

NASA Astrophysics Data System (ADS)

Lee, Kern; Chung, Kyoung-Jae; Hwang, Y. S.; Kim, C. Y.

2017-06-01

A transmission line is discussed for application in an underwater spark-discharge technique in the cleaning of a horizontal well by incorporating a power-transmission model into the simulation. The pulsed-spark-discharge technique has been proposed for clogged-well rehabilitation, because it removes incrustations that are attached to well screens by using strong pressure waves that are generated by the rapid expansion of a spark channel. To apply the pulsed-spark-discharge technique to the cleaning of horizontal wells, the coaxial cable between the pulsed power supply and the spark gap as a load needs to be extended to a few hundred meters. Prior to field application, pulsed-spark-discharge experiments were conducted and the role of the transmission line was examined using an improved simulation model. In the model, a non-linear interaction of the spark channel and the capacitor bank is described by the pulse-forming action of the coaxial cable. Based on the accurate physical properties of the water plasma, such as the equation of state and electrical conductivity within the region of interest, the amount of energy contributed to the development of a shock wave was evaluated. The simulation shows that if the initial conditions of the spark channel are the same, no further reduction in strength of the pressure wave occurs, even if the cable length is increased above 50 m. Hence, the degraded peak pressure that was observed in the experiments using the longer cable is attributed to a change in the initial condition of the spark channel. The parametric study suggests that the low initial charging voltage, the high ambient water pressure, and the long cable length yield the low initial spark-channel density, which results in a reduced peak pressure. The simulation of line charging is presented to discuss the principle of disturbing the pre-breakdown process by an extended cable.

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)

Evaluating Students' Conceptual Understanding of Balanced Equations and Stoichiometric Ratios Using a Particulate Drawing

ERIC Educational Resources Information Center

Sanger, Michael J.

2005-01-01

A total of 156 students were asked to provide free-response balanced chemical equations for a classic multiple-choice particulate-drawing question first used by Nurrenbern and Pickering. The balanced equations and the number of students providing each equation are reported in this study. The most common student errors included a confusion between…

Application of ANNs approach for wave-like and heat-like equations

NASA Astrophysics Data System (ADS)

Jafarian, Ahmad; Baleanu, Dumitru

2017-12-01

Artificial neural networks are data processing systems which originate from human brain tissue studies. The remarkable abilities of these networks help us to derive desired results from complicated raw data. In this study, we intend to duplicate an efficient iterative method to the numerical solution of two famous partial differential equations, namely the wave-like and heat-like problems. It should be noted that many physical phenomena such as coupling currents in a flat multi-strand two-layer super conducting cable, non-homogeneous elastic waves in soils and earthquake stresses, are described by initial-boundary value wave and heat partial differential equations with variable coefficients. To the numerical solution of these equations, a combination of the power series method and artificial neural networks approach, is used to seek an appropriate bivariate polynomial solution of the mentioned initial-boundary value problem. Finally, several computer simulations confirmed the theoretical results and demonstrating applicability of the method.

Classical metaphyseal lesions thought to be pathognomonic of child abuse are often artifacts or indicative of metabolic bone disease.

PubMed

Miller, Marvin; Mirkin, L David

2018-06-01

The objective of the present study was to review the histopathology in the original articles by authors Kleinman and Marks that described the specificity of the classical metaphyseal lesion for child abuse and to determine if there were any oversights in the authors' analysis. We reviewed the histopathology of the original studies that equated the classical metaphyseal lesion with child abuse. We compared this with the histopathology of metaphyseal fractures caused by known accidental, severe trauma in children and reviewed the histopathology of artifacts that can sometimes be produced in bone histology preparations. Acute classical metaphyseal lesions showed no hemorrhage, and the chronic classical metaphyseal showed islands of cartilage proliferation at the metaphyses and growth plate, findings consistent with rickets and other metabolic bone disorders. Some of the acute metaphyseal lesions were consistent with artifacts. We believe the original studies that equate the classical metaphyseal lesion with child abuse are flawed. The most compelling observation that challenges the histopathology of the classical metaphyseal lesion as being a fracture is the absence of hemorrhage in the acute classical metaphyseal lesion. We hypothesize that some of the classical metaphyseal lesions were artifacts or represent metabolic bone disorders that were not considered and that these two non-traumatic explanations may have been the basis of the abnormal bone findings. Copyright © 2018 The Authors. Published by Elsevier Ltd.. All rights reserved.

Mixed Quantum/Classical Theory for Molecule-Molecule Inelastic Scattering: Derivations of Equations and Application to N2 + H2 System.

PubMed

Semenov, Alexander; Babikov, Dmitri

2015-12-17

The mixed quantum classical theory, MQCT, for inelastic scattering of two molecules is developed, in which the internal (rotational, vibrational) motion of both collision partners is treated with quantum mechanics, and the molecule-molecule scattering (translational motion) is described by classical trajectories. The resultant MQCT formalism includes a system of coupled differential equations for quantum probability amplitudes, and the classical equations of motion in the mean-field potential. Numerical tests of this theory are carried out for several most important rotational state-to-state transitions in the N2 + H2 system, in a broad range of collision energies. Besides scattering resonances (at low collision energies) excellent agreement with full-quantum results is obtained, including the excitation thresholds, the maxima of cross sections, and even some smaller features, such as slight oscillations of energy dependencies. Most importantly, at higher energies the results of MQCT are nearly identical to the full quantum results, which makes this approach a good alternative to the full-quantum calculations that become computationally expensive at higher collision energies and for heavier collision partners. Extensions of this theory to include vibrational transitions or general asymmetric-top rotor (polyatomic) molecules are relatively straightforward.

On the solution of the generalized wave and generalized sine-Gordon equations

NASA Technical Reports Server (NTRS)

Ablowitz, M. J.; Beals, R.; Tenenblat, K.

1986-01-01

The generalized wave equation and generalized sine-Gordon equations are known to be natural multidimensional differential geometric generalizations of the classical two-dimensional versions. In this paper, a system of linear differential equations is associated with these equations, and it is shown how the direct and inverse problems can be solved for appropriately decaying data on suitable lines. An initial-boundary value problem is solved for these equations.

Time Reparametrization Group and the Long Time Behavior in Quantum Glassy Systems

NASA Astrophysics Data System (ADS)

Kennett, Malcolm P.; Chamon, Claudio

2001-02-01

We study the long time dynamics of a quantum version of the Sherrington-Kirkpatrick model. Time reparametrizations of the dynamical equations have a parallel with renormalization group transformations; in this language the long time behavior of this model is controlled by a reparametrization group ( RpG) fixed point of the classical dynamics. The irrelevance of quantum terms in the dynamical equations in the aging regime explains the classical nature of the out of equilibrium fluctuation-dissipation relation.

The classical equation of state of fully ionized plasmas

NASA Astrophysics Data System (ADS)

Eisa, Dalia Ahmed

2011-03-01

The aim of this paper is to calculate the analytical form of the equation of state until the third virial coefficient of a classical system interacting via an effective potential of fully Ionized Plasmas. The excess osmotic pressure is represented in the forms of a convergent series expansions in terms of the plasma Parameter μ _{ab} = {{{e_a e_b χ } over {DKT}}}, where χ2 is the square of the inverse Debye radius. We consider only the thermal equilibrium plasma.

Transfer function modeling of damping mechanisms in viscoelastic plates

NASA Technical Reports Server (NTRS)

Slater, J. C.; Inman, D. J.

1991-01-01

This work formulates a method for the modeling of material damping characteristics in plates. The Sophie German equation of classical plate theory is modified to incorporate hysteresis effects represented by complex stiffness using the transfer function approach proposed by Golla and Hughes, (1985). However, this procedure is not limited to this representation. The governing characteristic equation is decoupled through separation of variables, yielding a solution similar to that of undamped classical plate theory, allowing solution of the steady state as well as the transient response problem.

Dressing the post-Newtonian two-body problem and classical effective field theory

NASA Astrophysics Data System (ADS)

Kol, Barak; Smolkin, Michael

2009-12-01

We apply a dressed perturbation theory to better organize and economize the computation of high orders of the 2-body effective action of an inspiralling post-Newtonian (PN) gravitating binary. We use the effective field theory approach with the nonrelativistic field decomposition (NRG fields). For that purpose we develop quite generally the dressing theory of a nonlinear classical field theory coupled to pointlike sources. We introduce dressed charges and propagators, but unlike the quantum theory there are no dressed bulk vertices. The dressed quantities are found to obey recursive integral equations which succinctly encode parts of the diagrammatic expansion, and are the classical version of the Schwinger-Dyson equations. Actually, the classical equations are somewhat stronger since they involve only finitely many quantities, unlike the quantum theory. Classical diagrams are shown to factorize exactly when they contain nonlinear worldline vertices, and we classify all the possible topologies of irreducible diagrams for low loop numbers. We apply the dressing program to our post-Newtonian case of interest. The dressed charges consist of the dressed energy-momentum tensor after a nonrelativistic decomposition, and we compute all dressed charges (in the harmonic gauge) appearing up to 2PN in the 2-body effective action (and more). We determine the irreducible skeleton diagrams up to 3PN and we employ the dressed charges to compute several terms beyond 2PN.

Design Equations and Criteria of Orthotropic Composite Panels

DTIC Science & Technology

2013-05-01

33  Appendix A Classical Laminate Theory ( CLT ): ....................................................................... A–1  Appendix...Science London , 1990. NSWCCD-65-TR–2004/16A A–1 Appendix A Classical Laminate Theory ( CLT ): In Section 6 of this report, preliminary design...determined using:  Classical Laminate Theory, CLT , to Predict Equivalent Stiffness Characteristics, First- Ply Strength Note: CLT is valid for

Exact solutions to the Mo-Papas and Landau-Lifshitz equations

NASA Astrophysics Data System (ADS)

Rivera, R.; Villarroel, D.

2002-10-01

Two exact solutions of the Mo-Papas and Landau-Lifshitz equations for a point charge in classical electrodynamics are presented here. Both equations admit as an exact solution the motion of a charge rotating with constant speed in a circular orbit. These equations also admit as an exact solution the motion of two identical charges rotating with constant speed at the opposite ends of a diameter. These exact solutions allow one to obtain, starting from the equation of motion, a definite formula for the rate of radiation. In both cases the rate of radiation can also be obtained, with independence of the equation of motion, from the well known fields of a point charge, that is, from the Maxwell equations. The rate of radiation obtained from the Mo-Papas equation in the one-charge case coincides with the rate of radiation that comes from the Maxwell equations; but in the two-charge case the results do not coincide. On the other hand, the rate of radiation obtained from the Landau-Lifshitz equation differs from the one that follows from the Maxwell equations in both the one-charge and two-charge cases. This last result does not support a recent statement by Rohrlich in favor of considering the Landau-Lifshitz equation as the correct and exact equation of motion for a point charge in classical electrodynamics.

Classical electromagnetic fields from quantum sources in heavy-ion collisions

NASA Astrophysics Data System (ADS)

Holliday, Robert; McCarty, Ryan; Peroutka, Balthazar; Tuchin, Kirill

2017-01-01

Electromagnetic fields are generated in high energy nuclear collisions by spectator valence protons. These fields are traditionally computed by integrating the Maxwell equations with point sources. One might expect that such an approach is valid at distances much larger than the proton size and thus such a classical approach should work well for almost the entire interaction region in the case of heavy nuclei. We argue that, in fact, the contrary is true: due to the quantum diffusion of the proton wave function, the classical approximation breaks down at distances of the order of the system size. We compute the electromagnetic field created by a charged particle described initially as a Gaussian wave packet of width 1 fm and evolving in vacuum according to the Klein-Gordon equation. We completely neglect the medium effects. We show that the dynamics, magnitude and even sign of the electromagnetic field created by classical and quantum sources are different.

Information transport in classical statistical systems

NASA Astrophysics Data System (ADS)

Wetterich, C.

2018-02-01

For "static memory materials" the bulk properties depend on boundary conditions. Such materials can be realized by classical statistical systems which admit no unique equilibrium state. We describe the propagation of information from the boundary to the bulk by classical wave functions. The dependence of wave functions on the location of hypersurfaces in the bulk is governed by a linear evolution equation that can be viewed as a generalized Schrödinger equation. Classical wave functions obey the superposition principle, with local probabilities realized as bilinears of wave functions. For static memory materials the evolution within a subsector is unitary, as characteristic for the time evolution in quantum mechanics. The space-dependence in static memory materials can be used as an analogue representation of the time evolution in quantum mechanics - such materials are "quantum simulators". For example, an asymmetric Ising model on a Euclidean two-dimensional lattice represents the time evolution of free relativistic fermions in two-dimensional Minkowski space.

Predicting bunching costs for the Radio Horse 9 winch

Treesearch

Chris B. LeDoux; Bruce W. Kling; Patrice A. Harou; Patrice A. Harou

1987-01-01

Data from field studies and a prebunching cost simulator have been assembled and converted into a general equation that can be used to estimate the prebunching cost of the Radio Horse 9 winch. The methods can be used to estimate prebunching cost for bunching under the skyline corridor for swinging with cable systems, for bunching to skid trail edge to be picked up by a...

Predicting duff consumption from prescribed burns on conifer clearcuts in western Oregon and western Washington.

Treesearch

Susan N. Little; Roger D. Ottmar; Janet L. Ohmann

1986-01-01

Duff consumption by fire was studied on 15 cable-yarded clearcut units in western Oregon and western Washington. Equations are presented that predict duff consumption (in depth reduction and weight loss) from loading, consumption, and moisture of large fuels, and days since significant precipitation. When more than 25 days elapsed since 1.3 cm rainfall, the effect of...

Extended theory of harmonic maps connects general relativity to chaos and quantum mechanism

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

Ren, Gang; Duan, Yi-Shi

General relativity and quantum mechanism are two separate rules of modern physics explaining how nature works. Both theories are accurate, but the direct connection between two theories was not yet clarified. Recently, researchers blur the line between classical and quantum physics by connecting chaos and entanglement equation. Here in this paper, we showed the Duan's extended HM theory, which has the solution of the general relativity, can also have the solutions of the classic chaos equations and even the solution of Schrödinger equation in quantum physics, suggesting the extended theory of harmonic maps may act as a universal theory ofmore » physics.« less

Extended theory of harmonic maps connects general relativity to chaos and quantum mechanism

DOE PAGES

Ren, Gang; Duan, Yi-Shi

2017-07-20

General relativity and quantum mechanism are two separate rules of modern physics explaining how nature works. Both theories are accurate, but the direct connection between two theories was not yet clarified. Recently, researchers blur the line between classical and quantum physics by connecting chaos and entanglement equation. Here in this paper, we showed the Duan's extended HM theory, which has the solution of the general relativity, can also have the solutions of the classic chaos equations and even the solution of Schrödinger equation in quantum physics, suggesting the extended theory of harmonic maps may act as a universal theory ofmore » physics.« less

SU(N) affine Toda solitons and breathers from transparent Dirac potentials

NASA Astrophysics Data System (ADS)

Thies, Michael

2017-05-01

Transparent scalar and pseudoscalar potentials in the one-dimensional Dirac equation play an important role as self-consistent mean fields in 1  +  1 dimensional four-fermion theories (Gross-Neveu, Nambu-Jona Lasinio models) and quasi-one dimensional superconductors (Bogoliubov-de Gennes equation). Here, we show that they also serve as seed to generate a large class of classical multi-soliton and multi-breather solutions of su(N) affine Toda field theories, including the Lax representation and the corresponding vector. This generalizes previous findings about the relationship between real kinks in the Gross-Neveu model and classical solitons of the sinh-Gordon equation to complex twisted kinks.

IRT Equating of the MCAT. MCAT Monograph.

ERIC Educational Resources Information Center

Hendrickson, Amy B.; Kolen, Michael J.

This study compared various equating models and procedures for a sample of data from the Medical College Admission Test(MCAT), considering how item response theory (IRT) equating results compare with classical equipercentile results and how the results based on use of various IRT models, observed score versus true score, direct versus linked…

On the Mo-Papas equation

NASA Astrophysics Data System (ADS)

Aguirregabiria, J. M.; Chamorro, A.; Valle, M. A.

1982-05-01

A new heuristic derivation of the Mo-Papas equation for charged particles is given. It is shown that this equation cannot be derived for a point particle by closely following Dirac's classical treatment of the problem. The Mo-Papas theory and the Bonnor-Rowe-Marx variable mass dynamics are not compatible.

Mapping quantum-classical Liouville equation: projectors and trajectories.

PubMed

Kelly, Aaron; van Zon, Ramses; Schofield, Jeremy; Kapral, Raymond

2012-02-28

The evolution of a mixed quantum-classical system is expressed in the mapping formalism where discrete quantum states are mapped onto oscillator states, resulting in a phase space description of the quantum degrees of freedom. By defining projection operators onto the mapping states corresponding to the physical quantum states, it is shown that the mapping quantum-classical Liouville operator commutes with the projection operator so that the dynamics is confined to the physical space. It is also shown that a trajectory-based solution of this equation can be constructed that requires the simulation of an ensemble of entangled trajectories. An approximation to this evolution equation which retains only the Poisson bracket contribution to the evolution operator does admit a solution in an ensemble of independent trajectories but it is shown that this operator does not commute with the projection operators and the dynamics may take the system outside the physical space. The dynamical instabilities, utility, and domain of validity of this approximate dynamics are discussed. The effects are illustrated by simulations on several quantum systems.

Effective equations for the quantum pendulum from momentous quantum mechanics

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

Hernandez, Hector H.; Chacon-Acosta, Guillermo; Departamento de Matematicas Aplicadas y Sistemas, Universidad Autonoma Metropolitana-Cuajimalpa, Artificios 40, Mexico D. F. 01120

In this work we study the quantum pendulum within the framework of momentous quantum mechanics. This description replaces the Schroedinger equation for the quantum evolution of the system with an infinite set of classical equations for expectation values of configuration variables, and quantum dispersions. We solve numerically the effective equations up to the second order, and describe its evolution.

Comparing Alternative Kernels for the Kernel Method of Test Equating: Gaussian, Logistic, and Uniform Kernels. Research Report. ETS RR-08-12

ERIC Educational Resources Information Center

Lee, Yi-Hsuan; von Davier, Alina A.

2008-01-01

The kernel equating method (von Davier, Holland, & Thayer, 2004) is based on a flexible family of equipercentile-like equating functions that use a Gaussian kernel to continuize the discrete score distributions. While the classical equipercentile, or percentile-rank, equating method carries out the continuization step by linear interpolation,…

Variational symmetries, conserved quantities and identities for several equations of mathematical physics

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

Donchev, Veliko, E-mail: velikod@ie.bas.bg

2014-03-15

We find variational symmetries, conserved quantities and identities for several equations: envelope equation, Böcher equation, the propagation of sound waves with losses, flow of a gas with losses, and the nonlinear Schrödinger equation with losses or gains, and an electro-magnetic interaction. Most of these equations do not have a variational description with the classical variational principle and we find such a description with the generalized variational principle of Herglotz.

Atlantoaxial Fusion Using C1 Sublaminar Cables and C2 Translaminar Screws.

PubMed

Larsen, Alexandra M Giantini; Grannan, Benjamin L; Koffie, Robert M; Coumans, Jean-Valéry

2018-06-01

Atlantoaxial instability, which can arise in the setting of trauma, degenerative diseases, and neoplasm, is often managed surgically with C1-C2 arthrodesis. Classical C1-C2 fusion techniques require placement of instrumentation in close proximity to the vertebral artery and C2 nerve root. To report a novel C1-C2 fusion technique that utilizes C2 translaminar screws and C1 sublaminar cables to decrease the risk of injury to the vertebral artery and C2 nerve root. To facilitate fixation to the atlas, while minimizing the risk of injury to the vertebral artery and to the C2 nerve root, we sought to determine the feasibility of using a soft cable around the C1 arch and affixing it to a rod connected to C2 laminar screws. We reviewed our experience in 3 patients. We used this technique in patients in whom we anticipated difficult C1 screw placement. Three patients were identified through a review of the senior author's cases. Atlantoaxial instability was associated with trauma in 2 patients and chronic degenerative changes in 1 patient. Common symptoms on presentation included pain and limited range of motion. All patients underwent C1-C2 fusion with C2 translaminar screws with sublaminar cable harnessing of the posterior arch of C1. There were no reports of postoperative complications or hardware failure. We demonstrate a novel, technically straightforward approach for C1-C2 fusion that minimizes risk to the vertebral artery and to the C2 nerve root, while still allowing for semirigid fixation in instances of both traumatic and chronic degenerative atlantoaxial instability.

An Efficient Numerical Approach for Nonlinear Fokker-Planck equations

NASA Astrophysics Data System (ADS)

Otten, Dustin; Vedula, Prakash

2009-03-01

Fokker-Planck equations which are nonlinear with respect to their probability densities that occur in many nonequilibrium systems relevant to mean field interaction models, plasmas, classical fermions and bosons can be challenging to solve numerically. To address some underlying challenges in obtaining numerical solutions, we propose a quadrature based moment method for efficient and accurate determination of transient (and stationary) solutions of nonlinear Fokker-Planck equations. In this approach the distribution function is represented as a collection of Dirac delta functions with corresponding quadrature weights and locations, that are in turn determined from constraints based on evolution of generalized moments. Properties of the distribution function can be obtained by solution of transport equations for quadrature weights and locations. We will apply this computational approach to study a wide range of problems, including the Desai-Zwanzig Model (for nonlinear muscular contraction) and multivariate nonlinear Fokker-Planck equations describing classical fermions and bosons, and will also demonstrate good agreement with results obtained from Monte Carlo and other standard numerical methods.

Catenaries in viscous fluid

NASA Astrophysics Data System (ADS)

Hanna, James; Chakrabarti, Brato

2015-11-01

Slender structures live in fluid flows across many scales, from towed instruments to plant blades to microfluidic valves. The present work details a simple model of a flexible structure in a uniform flow. We present analytical solutions for the translating, axially flowing equilibria of strings subjected to a uniform body force and linear drag forces. This is an extension of the classical catenaries to a five-parameter family of solutions, represented as trajectories in angle-curvature ``phase space.'' Limiting cases include neutrally buoyant towed cables and freely sedimenting flexible filaments. Now at University of California, San Diego.

Statistical mechanics in the context of special relativity. II.

PubMed

Kaniadakis, G

2005-09-01

The special relativity laws emerge as one-parameter (light speed) generalizations of the corresponding laws of classical physics. These generalizations, imposed by the Lorentz transformations, affect both the definition of the various physical observables (e.g., momentum, energy, etc.), as well as the mathematical apparatus of the theory. Here, following the general lines of [Phys. Rev. E 66, 056125 (2002)], we show that the Lorentz transformations impose also a proper one-parameter generalization of the classical Boltzmann-Gibbs-Shannon entropy. The obtained relativistic entropy permits us to construct a coherent and self-consistent relativistic statistical theory, preserving the main features of the ordinary statistical theory, which is recovered in the classical limit. The predicted distribution function is a one-parameter continuous deformation of the classical Maxwell-Boltzmann distribution and has a simple analytic form, showing power law tails in accordance with the experimental evidence. Furthermore, this statistical mechanics can be obtained as the stationary case of a generalized kinetic theory governed by an evolution equation obeying the H theorem and reproducing the Boltzmann equation of the ordinary kinetics in the classical limit.

Thermodynamics Fundamental Equation of a "Non-Ideal" Rubber Band from Experiments

ERIC Educational Resources Information Center

Ritacco, Herna´n A.; Fortunatti, Juan C.; Devoto, Walter; Ferna´ndez-Miconi, Eugenio; Dominguez, Claudia; Sanchez, Miguel D.

2014-01-01

In this paper, we describe laboratory and classroom exercises designed to obtain the "fundamental" equation of a rubber band by combining experiments and theory. The procedure shows students how classical thermodynamics formalism can help to obtain empirical equations of state by constraining and guiding in the construction of the…

The Bernoulli Equation in a Moving Reference Frame

ERIC Educational Resources Information Center

Mungan, Carl E.

2011-01-01

Unlike other standard equations in introductory classical mechanics, the Bernoulli equation is not Galilean invariant. The explanation is that, in a reference frame moving with respect to constrictions or obstacles, those surfaces do work on the fluid, constituting an extra term that needs to be included in the work-energy calculation. A…

A van der Waals Equation of State for a Dilute Boson Gas

ERIC Educational Resources Information Center

Deeney, F. A.; O'Leary, J. P.

2012-01-01

An equation of state of a system is a relationship that connects the thermodynamic variables of the system such as pressure and temperature. Such equations are well known for classical gases but less so for quantum systems. In this paper we develop a van der Waals equation of state for a dilute boson gas that may be used to explain the occurrence…

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

Gevorkyan, A. S., E-mail: g-ashot@sci.am; Sahakyan, V. V.

We study the classical 1D Heisenberg spin glasses in the framework of nearest-neighboring model. Based on the Hamilton equations we obtained the system of recurrence equations which allows to perform node-by-node calculations of a spin-chain. It is shown that calculations from the first principles of classical mechanics lead to ℕℙ hard problem, that however in the limit of the statistical equilibrium can be calculated by ℙ algorithm. For the partition function of the ensemble a new representation is offered in the form of one-dimensional integral of spin-chains’ energy distribution.

The Equivalence of the Radial Return and Mendelson Methods for Integrating the Classical Plasticity Equations

NASA Technical Reports Server (NTRS)

Bednarcyk, Brett A.; Aboudi, Jacob; Arnold, Steven M.

2006-01-01

The radial return and Mendelson methods for integrating the equations of classical plasticity, which appear independently in the literature, are shown to be identical. Both methods are presented in detail as are the specifics of their algorithmic implementation. Results illustrate the methods' equivalence across a range of conditions and address the question of when the methods require iteration in order for the plastic state to remain on the yield surface. FORTRAN code implementations of the radial return and Mendelson methods are provided in the appendix.

Ultrasonic waves in classical gases

NASA Astrophysics Data System (ADS)

Magner, A. G.; Gorenstein, M. I.; Grygoriev, U. V.

2017-12-01

The velocity and absorption coefficient for the plane sound waves in a classical gas are obtained by solving the Boltzmann kinetic equation, which describes the reaction of the single-particle distribution function to a periodic external field. Within the linear response theory, the nonperturbative dispersion equation valid for all sound frequencies is derived and solved numerically. The results are in agreement with the approximate analytical solutions found for both the frequent- and rare-collision regimes. These results are also in qualitative agreement with the experimental data for ultrasonic waves in dilute gases.

Erosion associated with cable and tractor logging in northwestern California

Treesearch

R. M. Rice; P. A. Datzman

1981-01-01

Abstract - Erosion and site conditions were measured at 102 logged plots in northwestern California. Erosion averaged 26.8 m 3 /ha. A log-normal distribution was a better fit to the data. The antilog of the mean of the logarithms of erosion was 3.2 m 3 /ha. The Coast District Erosion Hazard Rating was a poor predictor of erosion related to logging. In a new equation...

Mode and climatic factors effect on energy losses in transient heat modes of transmission lines

NASA Astrophysics Data System (ADS)

Bigun, A. Ya; Sidorov, O. A.; Osipov, D. S.; Girshin, S. S.; Goryunov, V. N.; Petrova, E. V.

2018-01-01

Electrical energy losses increase in modern grids. The losses are connected with an increase in consumption. Existing models of electric power losses estimation considering climatic factors do not allow estimating the cable temperature in real time. Considering weather and mode factors in real time allows to meet effectively and safely the consumer’s needs to minimize energy losses during transmission, to use electric power equipment effectively. These factors increase an interest in the evaluation of the dynamic thermal mode of overhead transmission lines conductors. The article discusses an approximate analytic solution of the heat balance equation in the transient operation mode of overhead lines based on the least squares method. The accuracy of the results obtained is comparable with the results of solving the heat balance equation of transient thermal mode with the Runge-Kutt method. The analysis of mode and climatic factors effect on the cable temperature in a dynamic thermal mode is presented. The calculation of the maximum permissible current for variation of weather conditions is made. The average electric energy losses during the transient process are calculated with the change of wind, air temperature and solar radiation. The parameters having the greatest effect on the transmission capacity are identified.

Generalized Onsager's reciprocal relations for the master and Fokker-Planck equations

NASA Astrophysics Data System (ADS)

Peng, Liangrong; Zhu, Yi; Hong, Liu

2018-06-01

The Onsager's reciprocal relation plays a fundamental role in the nonequilibrium thermodynamics. However, unfortunately, its classical version is valid only within a narrow region near equilibrium due to the linear regression hypothesis, which largely restricts its usage. In this paper, based on the conservation-dissipation formalism, a generalized version of Onsager's relations for the master equations and Fokker-Planck equations was derived. Nonlinear constitutive relations with nonsymmetric and positively stable operators, which become symmetric under the detailed balance condition, constitute key features of this new generalization. Similar conclusions also hold for many other classical models in physics and chemistry, which in turn make the current study as a benchmark for the application of generalized Onsager's relations in nonequilibrium thermodynamics.

Quantum no-singularity theorem from geometric flows

NASA Astrophysics Data System (ADS)

Alsaleh, Salwa; Alasfar, Lina; Faizal, Mir; Ali, Ahmed Farag

2018-04-01

In this paper, we analyze the classical geometric flow as a dynamical system. We obtain an action for this system, such that its equation of motion is the Raychaudhuri equation. This action will be used to quantize this system. As the Raychaudhuri equation is the basis for deriving the singularity theorems, we will be able to understand the effects and such a quantization will have on the classical singularity theorems. Thus, quantizing the geometric flow, we can demonstrate that a quantum space-time is complete (nonsingular). This is because the existence of a conjugate point is a necessary condition for the occurrence of singularities, and we will be able to demonstrate that such conjugate points cannot occur due to such quantum effects.

Geometric Approaches to Quadratic Equations from Other Times and Places.

ERIC Educational Resources Information Center

Allaire, Patricia R.; Bradley, Robert E.

2001-01-01

Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)

Fractional-calculus diffusion equation

PubMed Central

2010-01-01

Background Sequel to the work on the quantization of nonconservative systems using fractional calculus and quantization of a system with Brownian motion, which aims to consider the dissipation effects in quantum-mechanical description of microscale systems. Results The canonical quantization of a system represented classically by one-dimensional Fick's law, and the diffusion equation is carried out according to the Dirac method. A suitable Lagrangian, and Hamiltonian, describing the diffusive system, are constructed and the Hamiltonian is transformed to Schrodinger's equation which is solved. An application regarding implementation of the developed mathematical method to the analysis of diffusion, osmosis, which is a biological application of the diffusion process, is carried out. Schrödinger's equation is solved. Conclusions The plot of the probability function represents clearly the dissipative and drift forces and hence the osmosis, which agrees totally with the macro-scale view, or the classical-version osmosis. PMID:20492677

Spectra of turbulently advected scalars that have small Schmidt number

NASA Astrophysics Data System (ADS)

Hill, Reginald J.

2017-09-01

Exact statistical equations are derived for turbulent advection of a passive scalar having diffusivity much larger than the kinematic viscosity, i.e., small Schmidt number. The equations contain all terms needed for precise direct numerical simulation (DNS) quantification. In the appropriate limit, the equations reduce to the classical theory for which the scalar spectrum is proportional to the energy spectrum multiplied by k-4, which, in turn, results in the inertial-diffusive range power law, k-17 /3. The classical theory was derived for the case of isotropic velocity and scalar fields. The exact equations are simplified for less restrictive cases: (1) locally isotropic scalar fluctuations at dissipation scales with no restriction on symmetry of the velocity field, (2) isotropic velocity field with averaging over all wave-vector directions with no restriction on the symmetry of the scalar, motivated by that average being used for DNS, and (3) isotropic velocity field with axisymmetric scalar fluctuations, motivated by the mean-scalar-gradient-source case. The equations are applied to recently published DNSs of passive scalars for the cases of a freely decaying scalar and a mean-scalar-gradient source. New terms in the exact equations are estimated for those cases and are found to be significant; those terms cause the deviations from the classical theory found by the DNS studies. A new formula for the mean-scalar-gradient case explains the variation of the scalar spectra for the DNS of the smallest Schmidt-number cases. Expansion in Legendre polynomials reveals the effect of axisymmetry. Inertial-diffusive-range formulas for both the zero- and second-order Legendre contributions are given. Exact statistical equations reveal what must be quantified using DNS to determine what causes deviations from asymptotic relationships.

k-Cosymplectic Classical Field Theories: Tulczyjew and Skinner-Rusk Formulations

NASA Astrophysics Data System (ADS)

Rey, Angel M.; Román-Roy, Narciso; Salgado, Modesto; Vilariño, Silvia

2012-06-01

The k-cosymplectic Lagrangian and Hamiltonian formalisms of first-order classical field theories are reviewed and completed. In particular, they are stated for singular and almost-regular systems. Subsequently, several alternative formulations for k-cosymplectic first-order field theories are developed: First, generalizing the construction of Tulczyjew for mechanics, we give a new interpretation of the classical field equations. Second, the Lagrangian and Hamiltonian formalisms are unified by giving an extension of the Skinner-Rusk formulation on classical mechanics.

A quantum-classical theory with nonlinear and stochastic dynamics

NASA Astrophysics Data System (ADS)

Burić, N.; Popović, D. B.; Radonjić, M.; Prvanović, S.

2014-12-01

The method of constrained dynamical systems on the quantum-classical phase space is utilized to develop a theory of quantum-classical hybrid systems. Effects of the classical degrees of freedom on the quantum part are modeled using an appropriate constraint, and the interaction also includes the effects of neglected degrees of freedom. Dynamical law of the theory is given in terms of nonlinear stochastic differential equations with Hamiltonian and gradient terms. The theory provides a successful dynamical description of the collapse during quantum measurement.

Numerical Solution of 3D Poisson-Nernst-Planck Equations Coupled with Classical Density Functional Theory for Modeling Ion and Electron Transport in a Confined Environment

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

Meng, Da; Zheng, Bin; Lin, Guang

2014-08-29

We have developed efficient numerical algorithms for the solution of 3D steady-state Poisson-Nernst-Planck equations (PNP) with excess chemical potentials described by the classical density functional theory (cDFT). The coupled PNP equations are discretized by finite difference scheme and solved iteratively by Gummel method with relaxation. The Nernst-Planck equations are transformed into Laplace equations through the Slotboom transformation. Algebraic multigrid method is then applied to efficiently solve the Poisson equation and the transformed Nernst-Planck equations. A novel strategy for calculating excess chemical potentials through fast Fourier transforms is proposed which reduces computational complexity from O(N2) to O(NlogN) where N is themore » number of grid points. Integrals involving Dirac delta function are evaluated directly by coordinate transformation which yields more accurate result compared to applying numerical quadrature to an approximated delta function. Numerical results for ion and electron transport in solid electrolyte for Li ion batteries are shown to be in good agreement with the experimental data and the results from previous studies.« less

Global Classical Solutions for MHD System

NASA Astrophysics Data System (ADS)

Casella, E.; Secchi, P.; Trebeschi, P.

In this paper we study the equations of magneto-hydrodynamics for a 2D incompressible ideal fluid in the exterior domain and in the half-plane. We prove the existence of a global classical solution in Hölder spaces, by applying Shauder fixed point theorem.

Higuchi equation: derivation, applications, use and misuse.

PubMed

Siepmann, Juergen; Peppas, Nicholas A

2011-10-10

Fifty years ago, the legendary Professor Takeru Higuchi published the derivation of an equation that allowed for the quantification of drug release from thin ointment films, containing finely dispersed drug into a perfect sink. This became the famous Higuchi equation whose fiftieth anniversary we celebrate this year. Despite the complexity of the involved mass transport processes, Higuchi derived a very simple equation, which is easy to use. Based on a pseudo-steady-state approach, a direct proportionality between the cumulative amount of drug released and the square root of time can be demonstrated. In contrast to various other "square root of time" release kinetics, the constant of proportionality in the classical Higuchi equation has a specific, physically realistic meaning. The major benefits of this equation include the possibility to: (i) facilitate device optimization, and (ii) to better understand the underlying drug release mechanisms. The equation can also be applied to other types of drug delivery systems than thin ointment films, e.g., controlled release transdermal patches or films for oral controlled drug delivery. Later, the equation was extended to other geometries and related theories have been proposed. The aim of this review is to highlight the assumptions the derivation of the classical Higuchi equation is based on and to give an overview on the use and potential misuse of this equation as well as of related theories. Copyright © 2011 Elsevier B.V. All rights reserved.

Kinetic theory molecular dynamics and hot dense matter: theoretical foundations.

PubMed

Graziani, F R; Bauer, J D; Murillo, M S

2014-09-01

Electrons are weakly coupled in hot, dense matter that is created in high-energy-density experiments. They are also mildly quantum mechanical and the ions associated with them are classical and may be strongly coupled. In addition, the dynamical evolution of plasmas under these hot, dense matter conditions involve a variety of transport and energy exchange processes. Quantum kinetic theory is an ideal tool for treating the electrons but it is not adequate for treating the ions. Molecular dynamics is perfectly suited to describe the classical, strongly coupled ions but not the electrons. We develop a method that combines a Wigner kinetic treatment of the electrons with classical molecular dynamics for the ions. We refer to this hybrid method as "kinetic theory molecular dynamics," or KTMD. The purpose of this paper is to derive KTMD from first principles and place it on a firm theoretical foundation. The framework that KTMD provides for simulating plasmas in the hot, dense regime is particularly useful since current computational methods are generally limited by their inability to treat the dynamical quantum evolution of the electronic component. Using the N-body von Neumann equation for the electron-proton plasma, three variations of KTMD are obtained. Each variant is determined by the physical state of the plasma (e.g., collisional versus collisionless). The first variant of KTMD yields a closed set of equations consisting of a mean-field quantum kinetic equation for the electron one-particle distribution function coupled to a classical Liouville equation for the protons. The latter equation includes both proton-proton Coulombic interactions and an effective electron-proton interaction that involves the convolution of the electron density with the electron-proton Coulomb potential. The mean-field approach is then extended to incorporate equilibrium electron-proton correlations through the Singwi-Tosi-Land-Sjolander (STLS) ansatz. This is the second variant of KTMD. The STLS contribution produces an effective electron-proton interaction that involves the electron-proton structure factor, thereby extending the usual mean-field theory to correlated but near equilibrium systems. Finally, a third variant of KTMD is derived. It includes dynamical electrons and their correlations coupled to a MD description for the ions. A set of coupled equations for the one-particle electron Wigner function and the electron-electron and electron-proton correlation functions are coupled to a classical Liouville equation for the protons. This latter variation has both time and momentum dependent correlations.

Pair correlation function and nonlinear kinetic equation for a spatially uniform polarizable nonideal plasma

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

Belyi, V.V.; Kukharenko, Y.A.; Wallenborn, J.

Taking into account the first non-Markovian correction to the Balescu-Lenard equation, we have derived an expression for the pair correlation function and a nonlinear kinetic equation valid for a nonideal polarized classical plasma. This last equation allows for the description of the correlational energy evolution and shows the global conservation of energy with dynamical polarization. {copyright} {ital 1996 The American Physical Society.}

On the Solution of Elliptic Partial Differential Equations on Regions with Corners

DTIC Science & Technology

2015-07-09

In this report we investigate the solution of boundary value problems on polygonal domains for elliptic partial differential equations . We observe...that when the problems are formulated as the boundary integral equations of classical potential theory, the solutions are representable by series of...efficient numerical algorithms. The results are illustrated by a number of numerical examples. On the solution of elliptic partial differential equations on

Mini 3D for shallow gas reconnaissance

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

Vallieres, T. des; Enns, D.; Kuehn, H.

1996-12-31

The Mini 3D project was undertaken by TOTAL and ELF with the support of CEPM (Comite d`Etudes Petrolieres et Marines) to define an economical method of obtaining 3D seismic HR data for shallow gas assessment. An experimental 3D survey was carried out with classical site survey techniques in the North Sea. From these data 19 simulations, were produced to compare different acquisition geometries ranging from dual, 600 m long cables to a single receiver. Results show that short offset, low fold and very simple streamer positioning are sufficient to give a reliable 3D image of gas charged bodies. The 3Dmore » data allow a much more accurate risk delineation than 2D HR data. Moreover on financial grounds Mini-3D is comparable in cost to a classical HR 2D survey. In view of these results, such HR 3D should now be the standard for shallow gas surveying.« less

Diophantine Equations as a Context for Technology-Enhanced Training in Conjecturing and Proving

ERIC Educational Resources Information Center

Abramovich, Sergei; Sugden, Stephen J.

2008-01-01

Solving indeterminate algebraic equations in integers is a classic topic in the mathematics curricula across grades. At the undergraduate level, the study of solutions of non-linear equations of this kind can be motivated by the use of technology. This article shows how the unity of geometric contextualization and spreadsheet-based amplification…

Self-equilibrated Tapered Three-stage Tensegrity Mast

NASA Astrophysics Data System (ADS)

Oh, C. L.; Choong, K. K.; Nishimura, T.; Lee, S. W.

2018-04-01

Investigation of tensegrity structures for the space application is ongoing owing to the characteristics of being lightweight and flexible. Tensegrity structures consist of struts and cables are self-stressed and stable under gravitational loading. Form-finding is an important process to obtain the configuration of tensegrity structures that are in self-equilibrated state. Form-finding of tensegrity structures involves a complex computational strategy in solving the geometrical and forces of the structures. This paper aims to form-finding for a tapered three-stage tensegrity mast. The form-finding strategy involves the assemblage of the tensegrity mast, establishment of equilibrium equations and determination of one possible set of coefficient beta. Several cases of configurations with various twist angles with range of 20°-40° are investigated. A configuration with 9 struts and 42 cables satisfying the material elastic conditions was successfully found. The scalable self-equilibrated tensegrity mast is recommended for space applications.

Flow friction of the turbulent coolant flow in cryogenic porous cables

NASA Technical Reports Server (NTRS)

Hendricks, R. C.; Yeroshenko, V. M.; Zaichik, L. I.; Yanovsky, L. S.

1979-01-01

Considered are cryogenic power transmission cables with porous cores. Calculations of the turbulent coolant flow with injection or suction through the porous wall are presented within the framework of a two-layer model. Universal velocity profiles were obtained for the viscous sublayer and flow core. Integrating the velocity profile, the law of flow friction in the pipe with injection has been derived for the case when there is a tangential injection velocity component. The effect of tangential velocity on the relative law of flow friction is analyzed. The applicability of the Prandtl model to the problem under study is discussed. It is shown that the error due to the acceptance of the model increases with the injection parameter and at lower Reynolds numbers; under these circumstances, the influence of convective terms in the turbulent energy equation on the mechanism of turbulent transport should be taken into account.

Quasi-stationary mechanics of elastic continua with bending stiffness wrapping on a pulley system

NASA Astrophysics Data System (ADS)

Kaczmarczyk, S.; Mirhadizadeh, S.

2016-05-01

In many engineering applications elastic continua such as ropes and belts often are subject to bending when they pass over pulleys / sheaves. In this paper the quasi-stationary mechanics of a cable-pulley system is studied. The cable is modelled as a moving Euler- Bernoulli beam. The distribution of tension is non-uniform along its span and due to the bending stiffness the contact points at the pulley-beam boundaries are not unknown. The system is described by a set of nonlinear ordinary differential equations with undetermined boundary conditions. The resulting nonlinear Boundary Value Problem (BVP) with unknown boundaries is solved by converting the problem into the ‘standard’ form defined over a fixed interval. Numerical results obtained for a range of typical configurations with relevant boundary conditions applied demonstrate that due to the effects of bending stiffness the angels of wrap are reduced and the span tensions are increased.

International Symposium on Electromagnetic Compatibility, 25th, Arlington, VA, August 23-25, 1983, Symposium Record

NASA Astrophysics Data System (ADS)

Subjects related to electromagnetic compatibility (EMC) analysis are discussed, taking into account forcing terms of line equations for externally excited transmission lines, E-fields over ground, electromagnetic near fields as a function of electrical size, a program for experimental verification of EMC analysis models, random susceptability of an IC 7400 TTL NAND gate, and a comparison of IEMCAP and SEMCAP. Other topics explored are concerned with EMC measurements, spectrum management, the electromagnetic pulse (EMP), a Navy EMC program, measurement systems, filters, EMC design, electromagnetic vulnerability (EMV) assessment of weapon systems, FCC rules and regulations, shielding, and electromagnetic interference (EMI) in communication systems. Attention is also given to nonsinusoidal functions in radar and communications, transients/electrostatic discharge, open field testing, cables and connectors, interference effects of induced and conducted earth current at dc and ELF, test cells, and cable coupling.

Method and apparatus for shape and end position determination using an optical fiber

NASA Technical Reports Server (NTRS)

Moore, Jason P. (Inventor)

2010-01-01

A method of determining the shape of an unbound optical fiber includes collecting strain data along a length of the fiber, calculating curvature and bending direction data of the fiber using the strain data, curve-fitting the curvature and bending direction data to derive curvature and bending direction functions, calculating a torsion function using the bending direction function, and determining the 3D shape from the curvature, bending direction, and torsion functions. An apparatus for determining the 3D shape of the fiber includes a fiber optic cable unbound with respect to a protective sleeve, strain sensors positioned along the cable, and a controller in communication with the sensors. The controller has an algorithm for determining a 3D shape and end position of the fiber by calculating a set of curvature and bending direction data, deriving curvature, bending, and torsion functions, and solving Frenet-Serret equations using these functions.

Classical r matrix of the su(2 vertical bar 2) super Yang-Mills spin chain

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

Torrielli, Alessandro

2007-05-15

In this note we straightforwardly derive and make use of the quantum R matrix for the su(2 vertical bar 2) super Yang-Mills spin chain in the manifest su(1 vertical bar 2)-invariant formulation, which solves the standard quantum Yang-Baxter equation, in order to obtain the correspondent (undressed) classical r matrix from the first order expansion in the 'deformation' parameter 2{pi}/{radical}({lambda}) and check that this last solves the standard classical Yang-Baxter equation. We analyze its bialgebra structure, its dependence on the spectral parameters, and its pole structure. We notice that it still preserves an su(1 vertical bar 2) subalgebra, thereby admitting anmore » expression in terms of a combination of projectors, which spans only a subspace of su(1 vertical bar 2)xsu(1 vertical bar 2). We study the residue at its simple pole at the origin and comment on the applicability of the classical Belavin-Drinfeld type of analysis.« less

Classical and sequential limit analysis revisited

NASA Astrophysics Data System (ADS)

Leblond, Jean-Baptiste; Kondo, Djimédo; Morin, Léo; Remmal, Almahdi

2018-04-01

Classical limit analysis applies to ideal plastic materials, and within a linearized geometrical framework implying small displacements and strains. Sequential limit analysis was proposed as a heuristic extension to materials exhibiting strain hardening, and within a fully general geometrical framework involving large displacements and strains. The purpose of this paper is to study and clearly state the precise conditions permitting such an extension. This is done by comparing the evolution equations of the full elastic-plastic problem, the equations of classical limit analysis, and those of sequential limit analysis. The main conclusion is that, whereas classical limit analysis applies to materials exhibiting elasticity - in the absence of hardening and within a linearized geometrical framework -, sequential limit analysis, to be applicable, strictly prohibits the presence of elasticity - although it tolerates strain hardening and large displacements and strains. For a given mechanical situation, the relevance of sequential limit analysis therefore essentially depends upon the importance of the elastic-plastic coupling in the specific case considered.

Shape sensing using multi-core fiber optic cable and parametric curve solutions.

PubMed

Moore, Jason P; Rogge, Matthew D

2012-01-30

The shape of a multi-core optical fiber is calculated by numerically solving a set of Frenet-Serret equations describing the path of the fiber in three dimensions. Included in the Frenet-Serret equations are curvature and bending direction functions derived from distributed fiber Bragg grating strain measurements in each core. The method offers advantages over prior art in that it determines complex three-dimensional fiber shape as a continuous parametric solution rather than an integrated series of discrete planar bends. Results and error analysis of the method using a tri-core optical fiber is presented. Maximum error expressed as a percentage of fiber length was found to be 7.2%.

Nonextensive Thomas-Fermi model

NASA Astrophysics Data System (ADS)

Shivamoggi, Bhimsen; Martinenko, Evgeny

2007-11-01

Nonextensive Thomas-Fermi model was father investigated in the following directions: Heavy atom in strong magnetic field. following Shivamoggi work on the extension of Kadomtsev equation we applied nonextensive formalism to father generalize TF model for the very strong magnetic fields (of order 10e12 G). The generalized TF equation and the binding energy of atom were calculated which contain a new nonextensive term dominating the classical one. The binding energy of a heavy atom was also evaluated. Thomas-Fermi equations in N dimensions which is technically the same as in Shivamoggi (1998) ,but behavior is different and in interesting 2 D case nonextesivity prevents from becoming linear ODE as in classical case. Effect of nonextensivity on dielectrical screening reveals itself in the reduction of the envelope radius. It was shown that nonextesivity in each case is responsible for new term dominating classical thermal correction term by order of magnitude, which is vanishing in a limit q->1. Therefore it appears that nonextensive term is ubiquitous for a wide range of systems and father work is needed to understand the origin of it.

Hamilton-Jacobi theory in multisymplectic classical field theories

NASA Astrophysics Data System (ADS)

de León, Manuel; Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso; Vilariño, Silvia

2017-09-01

The geometric framework for the Hamilton-Jacobi theory developed in the studies of Cariñena et al. [Int. J. Geom. Methods Mod. Phys. 3(7), 1417-1458 (2006)], Cariñena et al. [Int. J. Geom. Methods Mod. Phys. 13(2), 1650017 (2015)], and de León et al. [Variations, Geometry and Physics (Nova Science Publishers, New York, 2009)] is extended for multisymplectic first-order classical field theories. The Hamilton-Jacobi problem is stated for the Lagrangian and the Hamiltonian formalisms of these theories as a particular case of a more general problem, and the classical Hamilton-Jacobi equation for field theories is recovered from this geometrical setting. Particular and complete solutions to these problems are defined and characterized in several equivalent ways in both formalisms, and the equivalence between them is proved. The use of distributions in jet bundles that represent the solutions to the field equations is the fundamental tool in this formulation. Some examples are analyzed and, in particular, the Hamilton-Jacobi equation for non-autonomous mechanical systems is obtained as a special case of our results.

Boundary Quantum Knizhnik-Zamolodchikov Equations and Bethe Vectors

NASA Astrophysics Data System (ADS)

Reshetikhin, Nicolai; Stokman, Jasper; Vlaar, Bart

2015-06-01

Solutions to boundary quantum Knizhnik-Zamolodchikov equations are constructed as bilateral sums involving "off-shell" Bethe vectors in case the reflection matrix is diagonal and only the 2-dimensional representation of is involved. We also consider their rational and classical degenerations.

APL-UW Deep Water Propagation 2015-2017: Philippine Sea Data Analysis

DTIC Science & Technology

independent Monte Carlo parabolic equation simulations . The autospectrum of normalized intensity had an excellent match to that of a time-dependent Monte...ambient noise; systems along the Aleutian chain have either no significant trendor a slight increasing trend; systems in the central Pacific Ocean...At the end of the grant, it was determined that the Kauai cable had suffered a break in the shallow near-shore region. Additional contractual

The symmetric = ω -semi-classical orthogonal polynomials of class one

NASA Astrophysics Data System (ADS)

Maroni, P.; Mejri, M.

2008-12-01

We give the system of Laguerre-Freud equations associated with the = ω -semi-classical functionals of class one, where = ω is the divided difference operator. This system is solved in the symmetric case. There are essentially two canonical cases. The corresponding integral representations are given.

Eigensystem analysis of classical relaxation techniques with applications to multigrid analysis

NASA Technical Reports Server (NTRS)

Lomax, Harvard; Maksymiuk, Catherine

1987-01-01

Classical relaxation techniques are related to numerical methods for solution of ordinary differential equations. Eigensystems for Point-Jacobi, Gauss-Seidel, and SOR methods are presented. Solution techniques such as eigenvector annihilation, eigensystem mixing, and multigrid methods are examined with regard to the eigenstructure.

Quantum-mechanical transport equation for atomic systems.

NASA Technical Reports Server (NTRS)

Berman, P. R.

1972-01-01

A quantum-mechanical transport equation (QMTE) is derived which should be applicable to a wide range of problems involving the interaction of radiation with atoms or molecules which are also subject to collisions with perturber atoms. The equation follows the time evolution of the macroscopic atomic density matrix elements of atoms located at classical position R and moving with classical velocity v. It is quantum mechanical in the sense that all collision kernels or rates which appear have been obtained from a quantum-mechanical theory and, as such, properly take into account the energy-level variations and velocity changes of the active (emitting or absorbing) atom produced in collisions with perturber atoms. The present formulation is better suited to problems involving high-intensity external fields, such as those encountered in laser physics.

Global classical solvability and stabilization in a two-dimensional chemotaxis-Navier-Stokes system modeling coral fertilization

NASA Astrophysics Data System (ADS)

Espejo, Elio; Winkler, Michael

2018-04-01

The interplay of chemotaxis, convection and reaction terms is studied in the particular framework of a refined model for coral broadcast spawning, consisting of three equations describing the population densities of unfertilized sperms and eggs and the concentration of a chemical released by the latter, coupled to the incompressible Navier-Stokes equations. Under mild assumptions on the initial data, global existence of classical solutions to an associated initial-boundary value problem in bounded planar domains is established. Moreover, all these solutions are shown to approach a spatially homogeneous equilibrium in the large time limit.

Modifications of the PCPT method for HJB equations

NASA Astrophysics Data System (ADS)

Kossaczký, I.; Ehrhardt, M.; Günther, M.

2016-10-01

In this paper we will revisit the modification of the piecewise constant policy timestepping (PCPT) method for solving Hamilton-Jacobi-Bellman (HJB) equations. This modification is called piecewise predicted policy timestepping (PPPT) method and if properly used, it may be significantly faster. We will quickly recapitulate the algorithms of PCPT, PPPT methods and of the classical implicit method and apply them on a passport option pricing problem with non-standard payoff. We will present modifications needed to solve this problem effectively with the PPPT method and compare the performance with the PCPT method and the classical implicit method.

Nonlinear acoustic wave equations with fractional loss operators.

PubMed

Prieur, Fabrice; Holm, Sverre

2011-09-01

Fractional derivatives are well suited to describe wave propagation in complex media. When introduced in classical wave equations, they allow a modeling of attenuation and dispersion that better describes sound propagation in biological tissues. Traditional constitutive equations from solid mechanics and heat conduction are modified using fractional derivatives. They are used to derive a nonlinear wave equation which describes attenuation and dispersion laws that match observations. This wave equation is a generalization of the Westervelt equation, and also leads to a fractional version of the Khokhlov-Zabolotskaya-Kuznetsov and Burgers' equations. © 2011 Acoustical Society of America

Transition from the mechanics of material points to the mechanics of structured particles

NASA Astrophysics Data System (ADS)

Somsikov, V. M.

2016-01-01

In this paper, necessity of creation of mechanics of structured particles is discussed. The way to create this mechanics within the laws of classical mechanics with the use of energy equation is shown. The occurrence of breaking of time symmetry within the mechanics of structured particles is shown, as well as the introduction of concept of entropy in the framework of classical mechanics. The way to create the mechanics of non-equilibrium systems in the thermodynamic approach is shown. It is also shown that the use of hypothesis of holonomic constraints while deriving the canonical Lagrange equation made it impossible to describe irreversible dynamics. The difference between the mechanics of structured particles and the mechanics of material points is discussed. It is also shown that the matter is infinitely divisible according to the laws of classical mechanics.

Quantum localization of classical mechanics

NASA Astrophysics Data System (ADS)

Batalin, Igor A.; Lavrov, Peter M.

2016-07-01

Quantum localization of classical mechanics within the BRST-BFV and BV (or field-antifield) quantization methods are studied. It is shown that a special choice of gauge fixing functions (or BRST-BFV charge) together with the unitary limit leads to Hamiltonian localization in the path integral of the BRST-BFV formalism. In turn, we find that a special choice of gauge fixing functions being proportional to extremals of an initial non-degenerate classical action together with a very special solution of the classical master equation result in Lagrangian localization in the partition function of the BV formalism.

Leading-order classical Lagrangians for the nonminimal standard-model extension

NASA Astrophysics Data System (ADS)

Reis, J. A. A. S.; Schreck, M.

2018-03-01

In this paper, we derive the general leading-order classical Lagrangian covering all fermion operators of the nonminimal standard-model extension (SME). Such a Lagrangian is considered to be the point-particle analog of the effective field theory description of Lorentz violation that is provided by the SME. At leading order in Lorentz violation, the Lagrangian obtained satisfies the set of five nonlinear equations that govern the map from the field theory to the classical description. This result can be of use for phenomenological studies of classical bodies in gravitational fields.

A Practitioner's Introduction to Equating with Primers on Classical Test Theory and Item Response Theory

ERIC Educational Resources Information Center

Ryan, Joseph; Brockmann, Frank

2009-01-01

Equating is an essential tool in educational assessment due the critical role it plays in several key areas: establishing validity across forms and years; fairness; test security; and, increasingly, continuity in programs that release items or require ongoing development. Although the practice of equating is rooted in long standing practices that…

Quantum Hamilton equations of motion for bound states of one-dimensional quantum systems

NASA Astrophysics Data System (ADS)

Köppe, J.; Patzold, M.; Grecksch, W.; Paul, W.

2018-06-01

On the basis of Nelson's stochastic mechanics derivation of the Schrödinger equation, a formal mathematical structure of non-relativistic quantum mechanics equivalent to the one in classical analytical mechanics has been established in the literature. We recently were able to augment this structure by deriving quantum Hamilton equations of motion by finding the Nash equilibrium of a stochastic optimal control problem, which is the generalization of Hamilton's principle of classical mechanics to quantum systems. We showed that these equations allow a description and numerical determination of the ground state of quantum problems without using the Schrödinger equation. We extend this approach here to deliver the complete discrete energy spectrum and related eigenfunctions for bound states of one-dimensional stationary quantum systems. We exemplify this analytically for the one-dimensional harmonic oscillator and numerically by analyzing a quartic double-well potential, a model of broad importance in many areas of physics. We furthermore point out a relation between the tunnel splitting of such models and mean first passage time concepts applied to Nelson's diffusion paths in the ground state.

Recent advances in capacitance type of blade tip clearance measurements

NASA Technical Reports Server (NTRS)

Barranger, John P.

1988-01-01

Two recent electronic advances at NASA-Lewis that meet the blade tip clearance needs of a wide class of fans, compressors, and turbines are described. The first is a frequency modulated (FM) oscillator that requires only a single low cost ultrahigh frequency operational amplifier. Its carrier frequency is 42.8 MHz when used with a 61 cm long hermetically sealed coaxial cable. The oscillator can be calibrated in the static mode and has a negative peak frequency deviation of 400 kHz for a typical rotor blade. High temperature performance tests of the probe and 13 cm of the adjacent cable show good accuracy up to 600 C, the maximum which produces a clearance error of + or - 10 microns at a clearance of 500 microns. In the second advance, a guarded probe configuration allows a longer cable capacitance. The capacitance of the probe is part of a small time constant feedback in a high speed operational amplifier. The solution of the governing differential equation is applied to a ramp type of input. The results show an amplifier output that contains a term which is proportional to the derivative of the feedback capacitance. The capacitance is obtained by subtracting a balancing reference channel followed by an integration stage.

Motions in Taub-NUT-de Sitter spinning spacetime

NASA Astrophysics Data System (ADS)

Banu, Akhtara

2012-09-01

We investigate the geodesic motion of pseudo-classical spinning particles in the Taub-NUT-de Sitter spacetime. We obtain the conserved quantities from the solutions of the generalized Killing equations for spinning spaces. Applying the formalism the motion of a pseudo-classical Dirac fermion is analyzed on a cone and plane.

Constrained variational calculus for higher order classical field theories

NASA Astrophysics Data System (ADS)

Campos, Cédric M.; de León, Manuel; Martín de Diego, David

2010-11-01

We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner-Rusk formalism. Some examples of applications are studied, in particular to the geometrical description of optimal control theory for partial differential equations.

Electrons in strong electromagnetic fields: spin effects and radiation reaction (Conference Presentation)

NASA Astrophysics Data System (ADS)

Bauke, Heiko; Wen, Meng; Keitel, Christoph H.

2017-05-01

Various different classical models of electrons including their spin degree of freedom are commonly applied to describe the coupled dynamics of relativistic electron motion and spin precession in strong electromagnetic fields. The spin dynamics is usually governed by the Thomas-Bargmann-Michel-Telegdi equation [1, 2] in these models, while the electron's orbital motion follows the (modified) Lorentz force and a spin-dependent Stern-Gerlach force. Various classical models can lead to different or even contradicting predictions how the spin degree of freedom modifies the electron's orbital motion when the electron moves in strong electromagnetic fields. This discrepancy is rooted in the model-specific energy dependency of the spin induced relativistic Stern-Gerlach force acting on the electron. The Frenkel model [3, 4] and the classical Foldy-Wouthuysen model 5 are compared exemplarily against each other and against the quantum mechanical Dirac equation in order to identify parameter regimes where these classical models make different predictions [6, 7]. Our theoretical results allow for experimental tests of these models. In the setup of the longitudinal Stern-Gerlach effect, the Frenkel model and classical Foldy-Wouthuysen model lead in the relativistic limit to qualitatively different spin effects on the electron trajectory. Furthermore, it is demonstrated that in tightly focused beams in the near infrared the effect of the Stern-Gerlach force of the Frenkel model becomes sufficiently large to be potentially detectable in an experiment. Among the classical spin models, the Frenkel model is certainly prominent for its long history and its wide application. Our results, however, suggest that the classical Foldy-Wouthuysen model is superior as it is qualitatively in better agreement with the quantum mechanical Dirac equation. In ultra strong laser setups at parameter regimes where effects of the Stern-Gerlach force become relevant also radiation reaction effects are expected to set in. We incorporate radiation reaction classically via the Landau-Lifshitz equation and demonstrate that although radiation reaction effects can have a significant effect on the electron trajectory, the Frenkel model and the classical Foldy-Wouthuysen model remain distinguishable also if radiation reaction effects are taken into account. Our calculations are also suitable to verify the Landau-Lifshitz equation for the radiation reaction of electrons and other spin one-half particles. 1. Thomas, L. H., "I. The kinematics of an electron with an axis," The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 3(13), 1-22 (1927). 2. Bargmann, V., Michel, L., and Telegdi, V. L., "Precession of the polarization of particles moving in a homogeneous electromagnetic field," Phys. Rev. Lett. 2(10), 435-436 (1959). 3. Frenkel, J., "Die Elektrodynamik des rotierenden Elektrons," Z. Phys. 37(4-5), 243-262 (1926). 4. Frenkel, J., "Spinning electrons," Nature (London) 117(2949), 653-654 (1926). 5. Silenko, A. J., "Foldy-Wouthyusen transformation and semiclassical limit for relativistic particles in strong external fields," Phys. Rev. A 77(1), 012116 (2008). 6. Wen, M., Bauke, H., and Keitel, C. H., "Identifying the Stern-Gerlach force of classical electron dynamics," Sci. Rep. 6, 31624 (2016). 7. Wen, M., Keitel, C. H., and Bauke, H., "Spin one-half particles in strong electromagnetic fields: spin effects and radiation reaction," arXiv:1610.08951 (2016).

Knotted optical vortices in exact solutions to Maxwell's equations

NASA Astrophysics Data System (ADS)

de Klerk, Albertus J. J. M.; van der Veen, Roland I.; Dalhuisen, Jan Willem; Bouwmeester, Dirk

2017-05-01

We construct a family of exact solutions to Maxwell's equations in which the points of zero intensity form knotted lines topologically equivalent to a given but arbitrary algebraic link. These lines of zero intensity, more commonly referred to as optical vortices, and their topology are preserved as time evolves and the fields have finite energy. To derive explicit expressions for these new electromagnetic fields that satisfy the nullness property, we make use of the Bateman variables for the Hopf field as well as complex polynomials in two variables whose zero sets give rise to algebraic links. The class of algebraic links includes not only all torus knots and links thereof, but also more intricate cable knots. While the unknot has been considered before, the solutions presented here show that more general knotted structures can also arise as optical vortices in exact solutions to Maxwell's equations.

Lorentz Atom Revisited by Solving the Abraham-Lorentz Equation of Motion

NASA Astrophysics Data System (ADS)

Bosse, Jürgen

2017-08-01

By solving the non-relativistic Abraham-Lorentz (AL) equation, I demonstrate that the AL equation of motion is not suited for treating the Lorentz atom, because a steady-state solution does not exist. The AL equation serves as a tool, however, for deducing the appropriate parameters Ω and Γ to be used with the equation of forced oscillations in modelling the Lorentz atom. The electric polarisability, which many authors "derived" from the AL equation in recent years, is shown to violate Kramers-Kronig relations rendering obsolete the extracted photon-absorption rate, for example. Fortunately, errors turn out to be small quantitatively, as long as the light frequency ω is neither too close to nor too far from the resonance frequency Ω. The polarisability and absorption cross section are derived for the Lorentz atom by purely classical reasoning and are shown to agree with the quantum mechanical calculations of the same quantities. In particular, oscillator parameters Ω and Γ deduced by treating the atom as a quantum oscillator are found to be equivalent to those derived from the classical AL equation. The instructive comparison provides a deep insight into understanding the great success of Lorentz's model that was suggested long before the advent of quantum theory.

Some factors determining the effective resistance between strands in flat cables (or superconducting filaments in tapes)

NASA Astrophysics Data System (ADS)

Takács, S.; Iwakuma, M.; Funaki, K.

2000-04-01

Two effects are considered which can influence the effective resistance between crossing strands on flat cables or filaments in twisted tapes. As analogous cases, the one-layer Rutherford-type cable with classical superconductors and the tapes with twisted BSCCO filaments in a silver matrix in perpendicular magnetic fields are considered as a model. At first, the amount of the central core between the strands and the silver matrix between the filaments increases the effective conductance compared with the direct current paths, which is supposed to be proportional to the touching area of filaments. The increase factor is about two and can be easily suppressed by other effects, such as the contact resistance between the superconductor and the matrix. However, due to the strong anisotropy of critical parameters for high temperature superconductors, this effect can partially compensate the influence of the usually weaker critical current density perpendicular to the tape. The second effect is connected with the existence of the induced voltage between any points of crossing filaments. This leads to an additional effective conductance, proportional to the square of the total number of the filaments. This contribution is prevailing for the anisotropic superconductors. Therefore, to obtain low ac coupling losses in BSCCO tapes, structures with smaller filament number are required. This case is analogous to round structures, leading to ac losses proportional to the square of the layer number in the field direction.

Classical conformal blocks and accessory parameters from isomonodromic deformations

NASA Astrophysics Data System (ADS)

Lencsés, Máté; Novaes, Fábio

2018-04-01

Classical conformal blocks appear in the large central charge limit of 2D Virasoro conformal blocks. In the AdS3 /CFT2 correspondence, they are related to classical bulk actions and used to calculate entanglement entropy and geodesic lengths. In this work, we discuss the identification of classical conformal blocks and the Painlevé VI action showing how isomonodromic deformations naturally appear in this context. We recover the accessory parameter expansion of Heun's equation from the isomonodromic τ -function. We also discuss how the c = 1 expansion of the τ -function leads to a novel approach to calculate the 4-point classical conformal block.

Arcing on dc power systems

NASA Technical Reports Server (NTRS)

Moores, Greg; Heller, R. P.; Sutanto, Surja; Dugal-Whitehead, Norma R.

1992-01-01

Unexpected and undesirable arcing on dc power systems can produce hazardous situations aboard space flights. The potential for fire and shock might exist in a situation where there is a broken conductor, a loose power connection, or a break in the insulation of the power cable. Such arcing has been found to be reproducible in a laboratory environment. Arcing tests show that the phenomena can last for several seconds and yet be undetectable by present protection schemes used in classical power relaying and remote power controller applications. This paper characterizes the arcing phenomena and suggests future research that is needed.

Combinatorial Dyson-Schwinger equations and inductive data types

NASA Astrophysics Data System (ADS)

Kock, Joachim

2016-06-01

The goal of this contribution is to explain the analogy between combinatorial Dyson-Schwinger equations and inductive data types to a readership of mathematical physicists. The connection relies on an interpretation of combinatorial Dyson-Schwinger equations as fixpoint equations for polynomial functors (established elsewhere by the author, and summarised here), combined with the now-classical fact that polynomial functors provide semantics for inductive types. The paper is expository, and comprises also a brief introduction to type theory.

Maximum Principle for General Controlled Systems Driven by Fractional Brownian Motions

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

Han Yuecai; Hu Yaozhong; Song Jian, E-mail: jsong2@math.rutgers.edu

2013-04-15

We obtain a maximum principle for stochastic control problem of general controlled stochastic differential systems driven by fractional Brownian motions (of Hurst parameter H>1/2). This maximum principle specifies a system of equations that the optimal control must satisfy (necessary condition for the optimal control). This system of equations consists of a backward stochastic differential equation driven by both fractional Brownian motions and the corresponding underlying standard Brownian motions. In addition to this backward equation, the maximum principle also involves the Malliavin derivatives. Our approach is to use conditioning and Malliavin calculus. To arrive at our maximum principle we need tomore » develop some new results of stochastic analysis of the controlled systems driven by fractional Brownian motions via fractional calculus. Our approach of conditioning and Malliavin calculus is also applied to classical system driven by standard Brownian motions while the controller has only partial information. As a straightforward consequence, the classical maximum principle is also deduced in this more natural and simpler way.« less

Rational solutions of CYBE for simple compact real Lie algebras

NASA Astrophysics Data System (ADS)

Pop, Iulia; Stolin, Alexander

2007-04-01

In [A.A. Stolin, On rational solutions of Yang-Baxter equation for sl(n), Math. Scand. 69 (1991) 57-80; A.A. Stolin, On rational solutions of Yang-Baxter equation. Maximal orders in loop algebra, Comm. Math. Phys. 141 (1991) 533-548; A. Stolin, A geometrical approach to rational solutions of the classical Yang-Baxter equation. Part I, in: Walter de Gruyter & Co. (Ed.), Symposia Gaussiana, Conf. Alg., Berlin, New York, 1995, pp. 347-357] a theory of rational solutions of the classical Yang-Baxter equation for a simple complex Lie algebra g was presented. We discuss this theory for simple compact real Lie algebras g. We prove that up to gauge equivalence all rational solutions have the form X(u,v)={Ω}/{u-v}+t1∧t2+⋯+t∧t2n, where Ω denotes the quadratic Casimir element of g and {ti} are linearly independent elements in a maximal torus t of g. The quantization of these solutions is also emphasized.

Semi-classical statistical description of Fröhlich condensation.

PubMed

Preto, Jordane

2017-06-01

Fröhlich's model equations describing phonon condensation in open systems of biological relevance are reinvestigated within a semi-classical statistical framework. The main assumptions needed to deduce Fröhlich's rate equations are identified and it is shown how they lead us to write an appropriate form for the corresponding master equation. It is shown how solutions of the master equation can be numerically computed and can highlight typical features of the condensation effect. Our approach provides much more information compared to the existing ones as it allows to investigate the time evolution of the probability density function instead of following single averaged quantities. The current work is also motivated, on the one hand, by recent experimental evidences of long-lived excited modes in the protein structure of hen-egg white lysozyme, which were reported as a consequence of the condensation effect, and, on the other hand, by a growing interest in investigating long-range effects of electromagnetic origin and their influence on the dynamics of biochemical reactions.

Interaction of the sonic boom with atmospheric turbulence

NASA Technical Reports Server (NTRS)

Rusak, Zvi; Cole, Julian D.

1994-01-01

Theoretical research was carried out to study the effect of free-stream turbulence on sonic boom pressure fields. A new transonic small-disturbance model to analyze the interactions of random disturbances with a weak shock was developed. The model equation has an extended form of the classic small-disturbance equation for unsteady transonic aerodynamics. An alternative approach shows that the pressure field may be described by an equation that has an extended form of the classic nonlinear acoustics equation that describes the propagation of sound beams with narrow angular spectrum. The model shows that diffraction effects, nonlinear steepening effects, focusing and caustic effects and random induced vorticity fluctuations interact simultaneously to determine the development of the shock wave in space and time and the pressure field behind it. A finite-difference algorithm to solve the mixed type elliptic-hyperbolic flows around the shock wave was also developed. Numerical calculations of shock wave interactions with various deterministic and random fluctuations will be presented in a future report.

Space-time models based on random fields with local interactions

NASA Astrophysics Data System (ADS)

Hristopulos, Dionissios T.; Tsantili, Ivi C.

2016-08-01

The analysis of space-time data from complex, real-life phenomena requires the use of flexible and physically motivated covariance functions. In most cases, it is not possible to explicitly solve the equations of motion for the fields or the respective covariance functions. In the statistical literature, covariance functions are often based on mathematical constructions. In this paper, we propose deriving space-time covariance functions by solving “effective equations of motion”, which can be used as statistical representations of systems with diffusive behavior. In particular, we propose to formulate space-time covariance functions based on an equilibrium effective Hamiltonian using the linear response theory. The effective space-time dynamics is then generated by a stochastic perturbation around the equilibrium point of the classical field Hamiltonian leading to an associated Langevin equation. We employ a Hamiltonian which extends the classical Gaussian field theory by including a curvature term and leads to a diffusive Langevin equation. Finally, we derive new forms of space-time covariance functions.

Lagrangian geometrical optics of nonadiabatic vector waves and spin particles

DOE PAGES

Ruiz, D. E.; Dodin, I. Y.

2015-07-29

Linear vector waves, both quantum and classical, experience polarization-driven bending of ray trajectories and polarization dynamics that can be interpreted as the precession of the "wave spin". Here, both phenomena are governed by an effective gauge Hamiltonian vanishing in leading-order geometrical optics. This gauge Hamiltonian can be recognized as a generalization of the Stern-Gerlach Hamiltonian that is commonly known for spin-1/2 quantum particles. The corresponding reduced Lagrangians for continuous nondissipative waves and their geometrical-optics rays are derived from the fundamental wave Lagrangian. The resulting Euler-Lagrange equations can describe simultaneous interactions of N resonant modes, where N is arbitrary, and leadmore » to equations for the wave spin, which happens to be an (N 2 - 1)-dimensional spin vector. As a special case, classical equations for a Dirac particle (N = 2) are deduced formally, without introducing additional postulates or interpretations, from the Dirac quantum Lagrangian with the Pauli term. The model reproduces the Bargmann-Michel-Telegdi equations with added Stern-Gerlach force.« less

Loop Quantum Cosmology.

PubMed

Bojowald, Martin

2008-01-01

Quantum gravity is expected to be necessary in order to understand situations in which classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e., the fact that the backward evolution of a classical spacetime inevitably comes to an end after a finite amount of proper time. This presents a breakdown of the classical picture and requires an extended theory for a meaningful description. Since small length scales and high curvatures are involved, quantum effects must play a role. Not only the singularity itself but also the surrounding spacetime is then modified. One particular theory is loop quantum cosmology, an application of loop quantum gravity to homogeneous systems, which removes classical singularities. Its implications can be studied at different levels. The main effects are introduced into effective classical equations, which allow one to avoid the interpretational problems of quantum theory. They give rise to new kinds of early-universe phenomenology with applications to inflation and cyclic models. To resolve classical singularities and to understand the structure of geometry around them, the quantum description is necessary. Classical evolution is then replaced by a difference equation for a wave function, which allows an extension of quantum spacetime beyond classical singularities. One main question is how these homogeneous scenarios are related to full loop quantum gravity, which can be dealt with at the level of distributional symmetric states. Finally, the new structure of spacetime arising in loop quantum gravity and its application to cosmology sheds light on more general issues, such as the nature of time. Supplementary material is available for this article at 10.12942/lrr-2008-4.

A space necklace about the earth

NASA Technical Reports Server (NTRS)

Polyakov, G.

1977-01-01

A space elevator is forecasted for the first quarter of the 21st century, that will consist of a cable attached at the earth's equator, suspended in space by an artificial satellite in geosynchronous orbit. It is stated that such a transport system will supplement rockets as the railway supplements aircraft. Specific aspects of the system are examined, including provisions for artificial gravity, the development special composite construction materials exhibiting high strength and low mass, and spacecraft launching from the elevator.

A stochastic differential equation analysis of cerebrospinal fluid dynamics.

PubMed

Raman, Kalyan

2011-01-18

Clinical measurements of intracranial pressure (ICP) over time show fluctuations around the deterministic time path predicted by a classic mathematical model in hydrocephalus research. Thus an important issue in mathematical research on hydrocephalus remains unaddressed--modeling the effect of noise on CSF dynamics. Our objective is to mathematically model the noise in the data. The classic model relating the temporal evolution of ICP in pressure-volume studies to infusions is a nonlinear differential equation based on natural physical analogies between CSF dynamics and an electrical circuit. Brownian motion was incorporated into the differential equation describing CSF dynamics to obtain a nonlinear stochastic differential equation (SDE) that accommodates the fluctuations in ICP. The SDE is explicitly solved and the dynamic probabilities of exceeding critical levels of ICP under different clinical conditions are computed. A key finding is that the probabilities display strong threshold effects with respect to noise. Above the noise threshold, the probabilities are significantly influenced by the resistance to CSF outflow and the intensity of the noise. Fluctuations in the CSF formation rate increase fluctuations in the ICP and they should be minimized to lower the patient's risk. The nonlinear SDE provides a scientific methodology for dynamic risk management of patients. The dynamic output of the SDE matches the noisy ICP data generated by the actual intracranial dynamics of patients better than the classic model used in prior research.

Modeling of delays in PKPD: classical approaches and a tutorial for delay differential equations.

PubMed

Koch, Gilbert; Krzyzanski, Wojciech; Pérez-Ruixo, Juan Jose; Schropp, Johannes

2014-08-01

In pharmacokinetics/pharmacodynamics (PKPD) the measured response is often delayed relative to drug administration, individuals in a population have a certain lifespan until they maturate or the change of biomarkers does not immediately affects the primary endpoint. The classical approach in PKPD is to apply transit compartment models (TCM) based on ordinary differential equations to handle such delays. However, an alternative approach to deal with delays are delay differential equations (DDE). DDEs feature additional flexibility and properties, realize more complex dynamics and can complementary be used together with TCMs. We introduce several delay based PKPD models and investigate mathematical properties of general DDE based models, which serve as subunits in order to build larger PKPD models. Finally, we review current PKPD software with respect to the implementation of DDEs for PKPD analysis.

Periodic solutions of second-order nonlinear difference equations containing a small parameter. II - Equivalent linearization

NASA Technical Reports Server (NTRS)

Mickens, R. E.

1985-01-01

The classical method of equivalent linearization is extended to a particular class of nonlinear difference equations. It is shown that the method can be used to obtain an approximation of the periodic solutions of these equations. In particular, the parameters of the limit cycle and the limit points can be determined. Three examples illustrating the method are presented.

Some new solutions for the Derrida-Lebowitz-Speer-Spohn equation

NASA Astrophysics Data System (ADS)

Ramírez, J.; Romero, J. L.; Tracinà, R.

2013-09-01

The well-known Derrida-Lebowitz-Speer-Spohn equation is investigated. By using specific ansätze and the classical symmetries of the equation, several families of new exact solutions have been found. In particular, there appear traveling waves that include compactons and soliton-compactons. Some other solutions conserve the mass and exhibit diffusion and convection processes from an instantaneous source and localized peakons.

Hidden Statistics of Schroedinger Equation

NASA Technical Reports Server (NTRS)

Zak, Michail

2011-01-01

Work was carried out in determination of the mathematical origin of randomness in quantum mechanics and creating a hidden statistics of Schr dinger equation; i.e., to expose the transitional stochastic process as a "bridge" to the quantum world. The governing equations of hidden statistics would preserve such properties of quantum physics as superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods.

Numerical method based on the lattice Boltzmann model for the Fisher equation.

PubMed

Yan, Guangwu; Zhang, Jianying; Dong, Yinfeng

2008-06-01

In this paper, a lattice Boltzmann model for the Fisher equation is proposed. First, the Chapman-Enskog expansion and the multiscale time expansion are used to describe higher-order moment of equilibrium distribution functions and a series of partial differential equations in different time scales. Second, the modified partial differential equation of the Fisher equation with the higher-order truncation error is obtained. Third, comparison between numerical results of the lattice Boltzmann models and exact solution is given. The numerical results agree well with the classical ones.

Symmetry Reductions of Fourth-Order Nonlinear Diffusion Equations: Lubrication Model and Some Generalizations

NASA Astrophysics Data System (ADS)

Gandarias, M. L.; Medina, E.

Fourth-order nonlinear diffusion equations appear frequently in the description of physical processes, among these, the lubrication equation ut = (unuxxxx)x or the corresponding modified version ut = unuxxxx play an important role in the study of the interface movements. In this work we analyze the generalizations of the above equations given by ut = (f(u)uxxxx)x, ut = (f(u)uxxxx, and we find that if f(u) = un or f(u) = e-u the equations admit extra classical symmetries. The corresponding reductions are performed and some solutions are characterized.

Analytical solution for the advection-dispersion transport equation in layered media

USDA-ARS?s Scientific Manuscript database

The advection-dispersion transport equation with first-order decay was solved analytically for multi-layered media using the classic integral transform technique (CITT). The solution procedure used an associated non-self-adjoint advection-diffusion eigenvalue problem that had the same form and coef...

Evaporation in Capillary Porous Media at the Perfect Piston-Like Invasion Limit: Evidence of Nonlocal Equilibrium Effects

NASA Astrophysics Data System (ADS)

Attari Moghaddam, Alireza; Prat, Marc; Tsotsas, Evangelos; Kharaghani, Abdolreza

2017-12-01

The classical continuum modeling of evaporation in capillary porous media is revisited from pore network simulations of the evaporation process. The computed moisture diffusivity is characterized by a minimum corresponding to the transition between liquid and vapor transport mechanisms confirming previous interpretations. Also the study suggests an explanation for the scattering generally observed in the moisture diffusivity obtained from experimental data. The pore network simulations indicate a noticeable nonlocal equilibrium effect leading to a new interpretation of the vapor pressure-saturation relationship classically introduced to obtain the one-equation continuum model of evaporation. The latter should not be understood as a desorption isotherm as classically considered but rather as a signature of a nonlocal equilibrium effect. The main outcome of this study is therefore that nonlocal equilibrium two-equation model must be considered for improving the continuum modeling of evaporation.

Quantum Transmission Conditions for Diffusive Transport in Graphene with Steep Potentials

NASA Astrophysics Data System (ADS)

Barletti, Luigi; Negulescu, Claudia

2018-05-01

We present a formal derivation of a drift-diffusion model for stationary electron transport in graphene, in presence of sharp potential profiles, such as barriers and steps. Assuming the electric potential to have steep variations within a strip of vanishing width on a macroscopic scale, such strip is viewed as a quantum interface that couples the classical regions at its left and right sides. In the two classical regions, where the potential is assumed to be smooth, electron and hole transport is described in terms of semiclassical kinetic equations. The diffusive limit of the kinetic model is derived by means of a Hilbert expansion and a boundary layer analysis, and consists of drift-diffusion equations in the classical regions, coupled by quantum diffusive transmission conditions through the interface. The boundary layer analysis leads to the discussion of a four-fold Milne (half-space, half-range) transport problem.

Classical Coset Hamiltonian for the Electronic Motion and its Application to Anderson Localization and Hammett Equation

NASA Astrophysics Data System (ADS)

Xing, Guan; Wu, Guo-Zhen

2001-02-01

A classical coset Hamiltonian is introduced for the system of one electron in multi-sites. By this Hamiltonian, the dynamical behaviour of the electronic motion can be readily simulated. The simulation reproduces the retardation of the electron density decay in a lattice with site energies randomly distributed - an analogy with Anderson localization. This algorithm is also applied to reproduce the Hammett equation which relates the reaction rate with the property of the substitutions in the organic chemical reactions. The advantages and shortcomings of this algorithm, as contrasted with traditional quantum methods such as the molecular orbital theory, are also discussed.

Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories

NASA Astrophysics Data System (ADS)

Román-Roy, Narciso

2009-11-01

This review paper is devoted to presenting the standard multisymplectic formulation for describing geometrically classical field theories, both the regular and singular cases. First, the main features of the Lagrangian formalism are revisited and, second, the Hamiltonian formalism is constructed using Hamiltonian sections. In both cases, the variational principles leading to the Euler-Lagrange and the Hamilton-De Donder-Weyl equations, respectively, are stated, and these field equations are given in different but equivalent geometrical ways in each formalism. Finally, both are unified in a new formulation (which has been developed in the last years), following the original ideas of Rusk and Skinner for mechanical systems.

Thermal Stress Analysis of a Continuous and Pulsed End-Pumped Nd:YAG Rod Crystal Using Non-Classic Conduction Heat Transfer Theory

NASA Astrophysics Data System (ADS)

Mojahedi, Mahdi; Shekoohinejad, Hamidreza

2018-02-01

In this paper, temperature distribution in the continuous and pulsed end-pumped Nd:YAG rod crystal is determined using nonclassical and classical heat conduction theories. In order to find the temperature distribution in crystal, heat transfer differential equations of crystal with consideration of boundary conditions are derived based on non-Fourier's model and temperature distribution of the crystal is achieved by an analytical method. Then, by transferring non-Fourier differential equations to matrix equations, using finite element method, temperature and stress of every point of crystal are calculated in the time domain. According to the results, a comparison between classical and nonclassical theories is represented to investigate rupture power values. In continuous end pumping with equal input powers, non-Fourier theory predicts greater temperature and stress compared to Fourier theory. It also shows that with an increase in relaxation time, crystal rupture power decreases. Despite of these results, in single rectangular pulsed end-pumping condition, with an equal input power, Fourier theory indicates higher temperature and stress rather than non-Fourier theory. It is also observed that, when the relaxation time increases, maximum amounts of temperature and stress decrease.

New general pore size distribution model by classical thermodynamics application: Activated carbon

USGS Publications Warehouse

Lordgooei, M.; Rood, M.J.; Rostam-Abadi, M.

2001-01-01

A model is developed using classical thermodynamics to characterize pore size distributions (PSDs) of materials containing micropores and mesopores. The thermal equation of equilibrium adsorption (TEEA) is used to provide thermodynamic properties and relate the relative pore filling pressure of vapors to the characteristic pore energies of the adsorbent/adsorbate system for micropore sizes. Pore characteristic energies are calculated by averaging of interaction energies between adsorbate molecules and adsorbent pore walls as well as considering adsorbate-adsorbate interactions. A modified Kelvin equation is used to characterize mesopore sizes by considering variation of the adsorbate surface tension and by excluding the adsorbed film layer for the pore size. The modified-Kelvin equation provides similar pore filling pressures as predicted by density functional theory. Combination of these models provides a complete PSD of the adsorbent for the micropores and mesopores. The resulting PSD is compared with the PSDs from Jaroniec and Choma and Horvath and Kawazoe models as well as a first-order approximation model using Polanyi theory. The major importance of this model is its basis on classical thermodynamic properties, less simplifying assumptions in its derivation compared to other methods, and ease of use.

Efficient spectral computation of the stationary states of rotating Bose-Einstein condensates by preconditioned nonlinear conjugate gradient methods

NASA Astrophysics Data System (ADS)

Antoine, Xavier; Levitt, Antoine; Tang, Qinglin

2017-08-01

We propose a preconditioned nonlinear conjugate gradient method coupled with a spectral spatial discretization scheme for computing the ground states (GS) of rotating Bose-Einstein condensates (BEC), modeled by the Gross-Pitaevskii Equation (GPE). We first start by reviewing the classical gradient flow (also known as imaginary time (IMT)) method which considers the problem from the PDE standpoint, leading to numerically solve a dissipative equation. Based on this IMT equation, we analyze the forward Euler (FE), Crank-Nicolson (CN) and the classical backward Euler (BE) schemes for linear problems and recognize classical power iterations, allowing us to derive convergence rates. By considering the alternative point of view of minimization problems, we propose the preconditioned steepest descent (PSD) and conjugate gradient (PCG) methods for the GS computation of the GPE. We investigate the choice of the preconditioner, which plays a key role in the acceleration of the convergence process. The performance of the new algorithms is tested in 1D, 2D and 3D. We conclude that the PCG method outperforms all the previous methods, most particularly for 2D and 3D fast rotating BECs, while being simple to implement.

Classical analogous of quantum cosmological perfect fluid models

NASA Astrophysics Data System (ADS)

Batista, A. B.; Fabris, J. C.; Gonçalves, S. V. B.; Tossa, J.

2001-05-01

Quantization in the minisuperspace of a gravity system coupled to a perfect fluid, leads to a solvable model which implies singularity free solutions through the construction of a superposition of the wavefunctions. We show that such models are equivalent to a classical system where, besides the perfect fluid, a repulsive fluid with an equation of state pQ= ρQ is present. This leads to speculate on the true nature of this quantization procedure. A perturbative analysis of the classical system reveals the condition for the stability of the classical system in terms of the existence of an anti-gravity phase.

Application of variational and Galerkin equations to linear and nonlinear finite element analysis

NASA Technical Reports Server (NTRS)

Yu, Y.-Y.

1974-01-01

The paper discusses the application of the variational equation to nonlinear finite element analysis. The problem of beam vibration with large deflection is considered. The variational equation is shown to be flexible in both the solution of a general problem and in the finite element formulation. Difficulties are shown to arise when Galerkin's equations are used in the consideration of the finite element formulation of two-dimensional linear elasticity and of the linear classical beam.

The existence of periodic solutions for nonlinear beam equations on Td by a para-differential method

NASA Astrophysics Data System (ADS)

Chen, Bochao; Li, Yong; Gao, Yixian

2018-05-01

This paper focuses on the construction of periodic solutions of nonlinear beam equations on the $d$-dimensional tori. For a large set of frequencies, we demonstrate that an equivalent form of the nonlinear equations can be obtained by a para-differential conjugation. Given the non-resonant conditions on each finite dimensional subspaces, it is shown that the periodic solutions can be constructed for the block diagonal equation by a classical iteration scheme.

The Ostrovsky-Vakhnenko equation by a Riemann-Hilbert approach

NASA Astrophysics Data System (ADS)

Boutet de Monvel, Anne; Shepelsky, Dmitry

2015-01-01

We present an inverse scattering transform (IST) approach for the (differentiated) Ostrovsky-Vakhnenko equation This equation can also be viewed as the short wave model for the Degasperis-Procesi (sDP) equation. Our IST approach is based on an associated Riemann-Hilbert problem, which allows us to give a representation for the classical (smooth) solution, to get the principal term of its long time asymptotics, and also to describe loop soliton solutions. Dedicated to Johannes Sjöstrand with gratitude and admiration.

Basic results on the equations of magnetohydrodynamics of partially ionized inviscid plasmas

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

Nunez, Manuel

2009-10-15

The equations of evolution of partially ionized plasmas have been far more studied in one of their many simplifications than in its original form. They present a relation between the velocity of each species, plus the magnetic and electric fields, which yield as an analog of Ohm's law a certain elliptic equation. Therefore, the equations represent a functional evolution system, not a classical one. Nonetheless, a priori estimates and theorems of existence may be obtained in appropriate Sobolev spaces.

Siewert solutions of transcendental equations, generalized Lambert functions and physical applications

NASA Astrophysics Data System (ADS)

Barsan, Victor

2018-05-01

Several classes of transcendental equations, mainly eigenvalue equations associated to non-relativistic quantum mechanical problems, are analyzed. Siewert's systematic approach of such equations is discussed from the perspective of the new results recently obtained in the theory of generalized Lambert functions and of algebraic approximations of various special or elementary functions. Combining exact and approximate analytical methods, quite precise analytical outputs are obtained for apparently untractable problems. The results can be applied in quantum and classical mechanics, magnetism, elasticity, solar energy conversion, etc.

Integral equations in the study of polar and ionic interaction site fluids

PubMed Central

Howard, Jesse J.

2011-01-01

In this review article we consider some of the current integral equation approaches and application to model polar liquid mixtures. We consider the use of multidimensional integral equations and in particular progress on the theory and applications of three dimensional integral equations. The IEs we consider may be derived from equilibrium statistical mechanical expressions incorporating a classical Hamiltonian description of the system. We give example including salt solutions, inhomogeneous solutions and systems including proteins and nucleic acids. PMID:22383857

Disentangling the response of streamflow to forest management and climate

NASA Astrophysics Data System (ADS)

Dymond, S.; Miniat, C.; Bladon, K. D.; Keppeler, E.; Caldwell, P. V.

2016-12-01

Paired watershed studies have showcased the relationships between forests, management, and streamflow. However, classical analyses of paired-watershed studies have done little to disentangle the effects of management from overarching climatic signals, potentially masking the interaction between management and climate. Such approaches may confound our understanding of how forest management impacts streamflow. Here we use a 50-year record of streamflow and climate data from the Caspar Creek Experimental Watersheds (CCEW), California, USA to separate the effects of forest management and climate on streamflow. CCEW has two treatment watersheds that have been harvested in the past 50 years. We used a nonlinear mixed model to combine the pre-treatment relationship between streamflow and climate and the post-treatment relationship via an interaction between climate and management into one equation. Our results show that precipitation and potential evapotranspiration alone can account for >95% of the variability in pre-treatment streamflow. Including management scenarios into the model explained most of the variability in streamflow (R2 > 0.98). While forest harvesting altered streamflow in both of our modeled watersheds, removing 66% of the vegetation via selection logging using a tractor yarding system over the entire watershed had a more substantial impact on streamflow than clearcutting small portions of a watershed using cable-yarding. These results suggest that forest harvesting may result in differing impacts on streamflow and highlights the need to incorporate climate into streamflow analyses of paired-watershed studies.

Quadratically Convergent Method for Simultaneously Approaching the Roots of Polynomial Solutions of a Class of Differential Equations

NASA Astrophysics Data System (ADS)

Recchioni, Maria Cristina

2001-12-01

This paper investigates the application of the method introduced by L. Pasquini (1989) for simultaneously approaching the zeros of polynomial solutions to a class of second-order linear homogeneous ordinary differential equations with polynomial coefficients to a particular case in which these polynomial solutions have zeros symmetrically arranged with respect to the origin. The method is based on a family of nonlinear equations which is associated with a given class of differential equations. The roots of the nonlinear equations are related to the roots of the polynomial solutions of differential equations considered. Newton's method is applied to find the roots of these nonlinear equations. In (Pasquini, 1994) the nonsingularity of the roots of these nonlinear equations is studied. In this paper, following the lines in (Pasquini, 1994), the nonsingularity of the roots of these nonlinear equations is studied. More favourable results than the ones in (Pasquini, 1994) are proven in the particular case of polynomial solutions with symmetrical zeros. The method is applied to approximate the roots of Hermite-Sobolev type polynomials and Freud polynomials. A lower bound for the smallest positive root of Hermite-Sobolev type polynomials is given via the nonlinear equation. The quadratic convergence of the method is proven. A comparison with a classical method that uses the Jacobi matrices is carried out. We show that the algorithm derived by the proposed method is sometimes preferable to the classical QR type algorithms for computing the eigenvalues of the Jacobi matrices even if these matrices are real and symmetric.

Use of heat as a groundwater tracer in fractured rock hydrology

NASA Astrophysics Data System (ADS)

Bour, Olivier; Le Borgne, Tanguy; Klepikova, Maria V.; Read, Tom; Selker, John S.; Bense, Victor F.; Le Lay, Hugo; Hochreutener, Rebecca; Lavenant, Nicolas

2015-04-01

Crystalline rocks aquifers are often difficult to characterize since flows are mainly localized in few fractures. In particular, the geometry and the connections of the main flow paths are often only partly constrained with classical hydraulic tests. Here, we show through few examples how heat can be used to characterize groundwater flows in fractured rocks at the borehole, inter-borehole and watershed scale. Estimating flows from temperature measurements requires heat advection to be the dominant process of heat transport, but this condition is generally met in fractured rock at least within the few structures where flow is highly channelized. At the borehole scale, groundwater temperature variations with depth can be used to locate permeable fractures and to estimates borehole flows. Measurements can be done with classical multi-parameters probes, but also with recent technologies such as Fiber Optic Distributed Temperature Sensing (FO-DTS) which allows to measure temperature over long distances with an excellent spatial and temporal resolution. In addition, we show how a distributed borehole flowmeter can be achieved using an armored fiber-optic cable and measuring the difference in temperature between a heated and unheated cable that is a function of the fluid velocity. At the inter-borehole scale, temperature changes during cross-borehole hydraulic tests allow to identify the connections and the hydraulic properties of the main flow paths between boreholes. At the aquifer scale, groundwater temperature may be monitored to record temperature changes and estimate groundwater origin. In the example chosen, the main water supply comes from a depth of at least 300 meters through relatively deep groundwater circulation within a major permeable fault zone. The influence of groundwater extraction is clearly identified through groundwater temperature monitoring. These examples illustrate the advantages and limitations of using heat and groundwater temperature measurements for fractured rock hydrology.

Towards a wave theory of charged beam transport: A collection of thoughts

NASA Technical Reports Server (NTRS)

Dattoli, G.; Mari, C.; Torre, A.

1992-01-01

We formulate in a rigorous way a wave theory of charged beam linear transport. The Wigner distribution function is introduced and provides the link with classical mechanics. Finally, the von Neumann equation is shown to coincide with the Liouville equation for the nonlinear transport.

Some Properties of Estimated Scale Invariant Covariance Structures.

ERIC Educational Resources Information Center

Dijkstra, T. K.

1990-01-01

An example of scale invariance is provided via the LISREL model that is subject only to classical normalizations and zero constraints on the parameters. Scale invariance implies that the estimated covariance matrix must satisfy certain equations, and the nature of these equations depends on the fitting function used. (TJH)

Enzyme Kinetics and the Michaelis-Menten Equation

ERIC Educational Resources Information Center

Biaglow, Andrew; Erickson, Keith; McMurran, Shawnee

2010-01-01

The concepts presented in this article represent the cornerstone of classical mathematical biology. The central problem of the article relates to enzyme kinetics, which is a biochemical system. However, the theoretical underpinnings that lead to the formation of systems of time-dependent ordinary differential equations have been applied widely to…

A correlated Walks' theory for DNA denaturation

NASA Astrophysics Data System (ADS)

Mejdani, R.

1994-08-01

We have shown that by using a correlated Walks' theory for the lattice gas model on a one-dimensional lattice, we can study, beside the saturation curves obtained before for the enzyme kinetics, also the DNA denaturation process. In the limit of no interactions between sites the equation for melting curves of DNA reduces to the random model equation. Thus our leads naturally to this classical equation in the limiting case.

Algebraic Riccati equations in zero-sum differential games

NASA Technical Reports Server (NTRS)

Johnson, T. L.; Chao, A.

1974-01-01

The procedure for finding the closed-loop Nash equilibrium solution of two-player zero-sum linear time-invariant differential games with quadratic performance criteria and classical information pattern may be reduced in most cases to the solution of an algebraic Riccati equation. Based on the results obtained by Willems, necessary and sufficient conditions for existence of solutions to these equations are derived, and explicit conditions for a scalar example are given.

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

Hayashi, A.; Hashimoto, T.; Horibe, M.

In quantum teleportation, neither Alice nor Bob acquires any classical knowledge on teleported states. The teleportation protocol is said to be oblivious to both parties. In remote state preparation (RSP), it is assumed that Alice is given complete classical knowledge on the state that is to be prepared by Bob. Recently, Leung and Shor [e-print quant-ph/0201008] showed that the same amount of classical information as that in teleportation needs to be transmitted in any exact and deterministic RSP protocol that is oblivious to Bob. Assuming that the dimension of subsystems in the prior-entangled state is the same as the dimensionmore » of the input space, we study similar RSP protocols, but not necessarily oblivious to Bob. We show that in this case Bob's quantum operation can be safely assumed to be a unitary transformation. We then derive an equation that is a necessary and sufficient condition for such a protocol to exist. By studying this equation, we show that one-qubit RSP requires two classical bits of communication, which is the same amount as in teleportation, even if the protocol is not assumed oblivious to Bob. For higher dimensions, it is still an open question whether the amount of classical communication can be reduced by abandoning oblivious conditions.« less

Fully adaptive propagation of the quantum-classical Liouville equation

NASA Astrophysics Data System (ADS)

Horenko, Illia; Weiser, Martin; Schmidt, Burkhard; Schütte, Christof

2004-05-01

In mixed quantum-classical molecular dynamics few but important degrees of freedom of a dynamical system are modeled quantum-mechanically while the remaining ones are treated within the classical approximation. Rothe methods established in the theory of partial differential equations are used to control both temporal and spatial discretization errors on grounds of a global tolerance criterion. The TRAIL (trapezoidal rule for adaptive integration of Liouville dynamics) scheme [I. Horenko and M. Weiser, J. Comput. Chem. 24, 1921 (2003)] has been extended to account for nonadiabatic effects in molecular dynamics described by the quantum-classical Liouville equation. In the context of particle methods, the quality of the spatial approximation of the phase-space distributions is maximized while the numerical condition of the least-squares problem for the parameters of particles is minimized. The resulting dynamical scheme is based on a simultaneous propagation of moving particles (Gaussian and Dirac deltalike trajectories) in phase space employing a fully adaptive strategy to upgrade Dirac to Gaussian particles and, vice versa, downgrading Gaussians to Dirac-type trajectories. This allows for the combination of Monte-Carlo-based strategies for the sampling of densities and coherences in multidimensional problems with deterministic treatment of nonadiabatic effects. Numerical examples demonstrate the application of the method to spin-boson systems in different dimensionality. Nonadiabatic effects occurring at conical intersections are treated in the diabatic representation. By decreasing the global tolerance, the numerical solution obtained from the TRAIL scheme are shown to converge towards exact results.

Fully adaptive propagation of the quantum-classical Liouville equation.

PubMed

Horenko, Illia; Weiser, Martin; Schmidt, Burkhard; Schütte, Christof

2004-05-15

In mixed quantum-classical molecular dynamics few but important degrees of freedom of a dynamical system are modeled quantum-mechanically while the remaining ones are treated within the classical approximation. Rothe methods established in the theory of partial differential equations are used to control both temporal and spatial discretization errors on grounds of a global tolerance criterion. The TRAIL (trapezoidal rule for adaptive integration of Liouville dynamics) scheme [I. Horenko and M. Weiser, J. Comput. Chem. 24, 1921 (2003)] has been extended to account for nonadiabatic effects in molecular dynamics described by the quantum-classical Liouville equation. In the context of particle methods, the quality of the spatial approximation of the phase-space distributions is maximized while the numerical condition of the least-squares problem for the parameters of particles is minimized. The resulting dynamical scheme is based on a simultaneous propagation of moving particles (Gaussian and Dirac deltalike trajectories) in phase space employing a fully adaptive strategy to upgrade Dirac to Gaussian particles and, vice versa, downgrading Gaussians to Dirac-type trajectories. This allows for the combination of Monte-Carlo-based strategies for the sampling of densities and coherences in multidimensional problems with deterministic treatment of nonadiabatic effects. Numerical examples demonstrate the application of the method to spin-boson systems in different dimensionality. Nonadiabatic effects occurring at conical intersections are treated in the diabatic representation. By decreasing the global tolerance, the numerical solution obtained from the TRAIL scheme are shown to converge towards exact results.

Displacement of Tethered Hydro-Acoustic Modems by Uniform Horizontal Currents

DTIC Science & Technology

2009-12-01

smooth and plane surfaces (in incompressible flow ) in air and in water (From [4]) ..............22  Figure 13.  Drag of streamline bodies, tested in...from a stationary sea- surface buoy or Unmanned Surface Vehicle (USV) weighted by a dense object at the free end (Figure 2). The equations of static...forces on the free end are caused by an attached ballast or float. The moored cable has a free -moving sub- surface buoy positioned at a water depth

Self-energy-modified Poisson-Nernst-Planck equations: WKB approximation and finite-difference approaches.

PubMed

Xu, Zhenli; Ma, Manman; Liu, Pei

2014-07-01

We propose a modified Poisson-Nernst-Planck (PNP) model to investigate charge transport in electrolytes of inhomogeneous dielectric environment. The model includes the ionic polarization due to the dielectric inhomogeneity and the ion-ion correlation. This is achieved by the self energy of test ions through solving a generalized Debye-Hückel (DH) equation. We develop numerical methods for the system composed of the PNP and DH equations. Particularly, toward the numerical challenge of solving the high-dimensional DH equation, we developed an analytical WKB approximation and a numerical approach based on the selective inversion of sparse matrices. The model and numerical methods are validated by simulating the charge diffusion in electrolytes between two electrodes, for which effects of dielectrics and correlation are investigated by comparing the results with the prediction by the classical PNP theory. We find that, at the length scale of the interface separation comparable to the Bjerrum length, the results of the modified equations are significantly different from the classical PNP predictions mostly due to the dielectric effect. It is also shown that when the ion self energy is in weak or mediate strength, the WKB approximation presents a high accuracy, compared to precise finite-difference results.

Modeling the Gross-Pitaevskii Equation Using the Quantum Lattice Gas Method

NASA Astrophysics Data System (ADS)

Oganesov, Armen

We present an improved Quantum Lattice Gas (QLG) algorithm as a mesoscopic unitary perturbative representation of the mean field Gross Pitaevskii (GP) equation for Bose-Einstein Condensates (BECs). The method employs an interleaved sequence of unitary collide and stream operators. QLG is applicable to many different scalar potentials in the weak interaction regime and has been used to model the Korteweg-de Vries (KdV), Burgers and GP equations. It can be implemented on both quantum and classical computers and is extremely scalable. We present results for 1D soliton solutions with positive and negative internal interactions, as well as vector solitons with inelastic scattering. In higher dimensions we look at the behavior of vortex ring reconnection. A further improvement is considered with a proper operator splitting technique via a Fourier transformation. This is great for quantum computers since the quantum FFT is exponentially faster than its classical counterpart which involves non-local data on the entire lattice (Quantum FFT is the backbone of the Shor algorithm for quantum factorization). We also present an imaginary time method in which we transform the Schrodinger equation into a diffusion equation for recovering ground state initial conditions of a quantum system suitable for the QLG algorithm.

Dynamics of open quantum systems by interpolation of von Neumann and classical master equations, and its application to quantum annealing

NASA Astrophysics Data System (ADS)

Kadowaki, Tadashi

2018-02-01

We propose a method to interpolate dynamics of von Neumann and classical master equations with an arbitrary mixing parameter to investigate the thermal effects in quantum dynamics. The two dynamics are mixed by intervening to continuously modify their solutions, thus coupling them indirectly instead of directly introducing a coupling term. This maintains the quantum system in a pure state even after the introduction of thermal effects and obtains not only a density matrix but also a state vector representation. Further, we demonstrate that the dynamics of a two-level system can be rewritten as a set of standard differential equations, resulting in quantum dynamics that includes thermal relaxation. These equations are equivalent to the optical Bloch equations at the weak coupling and asymptotic limits, implying that the dynamics cause thermal effects naturally. Numerical simulations of ferromagnetic and frustrated systems support this idea. Finally, we use this method to study thermal effects in quantum annealing, revealing nontrivial performance improvements for a spin glass model over a certain range of annealing time. This result may enable us to optimize the annealing time of real annealing machines.

Dam break problem for the focusing nonlinear Schrödinger equation and the generation of rogue waves

NASA Astrophysics Data System (ADS)

El, G. A.; Khamis, E. G.; Tovbis, A.

2016-09-01

We propose a novel, analytically tractable, scenario of the rogue wave formation in the framework of the small-dispersion focusing nonlinear Schrödinger (NLS) equation with the initial condition in the form of a rectangular barrier (a ‘box’). We use the Whitham modulation theory combined with the nonlinear steepest descent for the semi-classical inverse scattering transform, to describe the evolution and interaction of two counter-propagating nonlinear wave trains—the dispersive dam break flows—generated in the NLS box problem. We show that the interaction dynamics results in the emergence of modulated large-amplitude quasi-periodic breather lattices whose amplitude profiles are closely approximated by the Akhmediev and Peregrine breathers within certain space-time domain. Our semi-classical analytical results are shown to be in excellent agreement with the results of direct numerical simulations of the small-dispersion focusing NLS equation.

Aging dynamics of quantum spin glasses of rotors

NASA Astrophysics Data System (ADS)

Kennett, Malcolm P.; Chamon, Claudio; Ye, Jinwu

2001-12-01

We study the long time dynamics of quantum spin glasses of rotors using the nonequilibrium Schwinger-Keldysh formalism. These models are known to have a quantum phase transition from a paramagnetic to a spin-glass phase, which we approach by looking at the divergence of the spin-relaxation rate at the transition point. In the aging regime, we determine the dynamical equations governing the time evolution of the spin response and correlation functions, and show that all terms in the equations that arise solely from quantum effects are irrelevant at long times under time reparametrization group (RPG) transformations. At long times, quantum effects enter only through the renormalization of the parameters in the dynamical equations for the classical counterpart of the rotor model. Consequently, quantum effects only modify the out-of-equilibrium fluctuation-dissipation relation (OEFDR), i.e. the ratio X between the temperature and the effective temperature, but not the form of the classical OEFDR.

Real time visualization of quantum walk

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

Miyazaki, Akihide; Hamada, Shinji; Sekino, Hideo

2014-02-20

Time evolution of quantum particles like electrons is described by time-dependent Schrödinger equation (TDSE). The TDSE is regarded as the diffusion equation of electrons with imaginary diffusion coefficients. And the TDSE is solved by quantum walk (QW) which is regarded as a quantum version of a classical random walk. The diffusion equation is solved in discretized space/time as in the case of classical random walk with additional unitary transformation of internal degree of freedom typical for quantum particles. We call the QW for solution of the TDSE a Schrödinger walk (SW). For observation of one quantum particle evolution under amore » given potential in atto-second scale, we attempt a successive computation and visualization of the SW. Using Pure Data programming, we observe the correct behavior of a probability distribution under the given potential in real time for observers of atto-second scale.« less

Prebifurcation periodic ghost orbits in semiclassical quantization

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

Kus, M.; Haake, F.; Delande, D.

1993-10-04

Classical periodic orbits are stationary-phase points in path integral representations of quantum propagators. We show that complex solutions of the stationary-phase equation, not corresponding to real classical periodic orbits, give additional contributions to the propagator which can be important, especially near bifurcations. We reveal the existence and relevance of such periodic ghost orbits for a kicked top.

Detectors Ensure Function, Safety of Aircraft Wiring

NASA Technical Reports Server (NTRS)

2013-01-01

Pedro Medelius waited patiently in his lab at Kennedy Space Center. He had just received word that a colleague was bringing over a cable from a Space Shuttle solid rocket booster to test Medelius new invention. Medelius was calm until his colleague arrived, with about 30 other people. "Talk about testing under pressure," says Medelius. "There were people there from the Navy, the Air Force, and the Federal Aviation Administration." After the group s arrival, Medelius took a deep breath and connected his Standing Wave Reflectometer (SWR) to the cable. He wiggled the cable around, and the display showed a fault (a short or open circuit in wire) about an inch and a half inside the connector on the cable. His colleague questioned the results, because he had already checked that area on the cable. Medelius used the SWR to check again but got the same result. "That is when we took the cable apart and looked inside," Medelius says. "Lo and behold, that was exactly where the fault was." The impetus for Medelius new wire inspection technology came about in 1999 when one of the space shuttles lost power due to a fault somewhere in its more than 200 miles of electrical wiring. "The backup circuit was activated and prevented a major dysfunction, but nevertheless, there was a problem with the wiring," Medelius describes. Even though technicians used a device called a multimeter to measure the electrical current to find which wire had a fault, it could not pinpoint exactly where on the wire the fault was located. For that, technicians had to visually inspect the wire. "Sometimes they would have to remove the whole wire assembly and visually inspect every single wire. It was a very tedious operation because the wires are behind cabinets. They go all over the place in the shuttle," says Medelius. "NASA needed an instrument capable of telling them exactly where the faults were occurring." To meet NASA s needs for a highly precise device to inspect electrical power bundles, wires, and connectors, Medelius devised the SWR. "It came down to what was affected when a wire is short circuited or opened," he says. "We worked out a few equations based on physical principles." The SWR proved very sensitive, and the technology was patented.

Capacitance-type blade-tip clearance measurement system using a dual amplifier with ramp/dc inputs and integration

NASA Technical Reports Server (NTRS)

Sarma, Garimella R.; Barranger, John P.

1992-01-01

The analysis and prototype results of a dual-amplifier circuit for measuring blade-tip clearance in turbine engines are presented. The capacitance between the blade tip and mounted capacitance electrode within a guard ring of a probe forms one of the feedback elements of an operational amplifier (op amp). The differential equation governing the circuit taking into consideration the nonideal features of the op amp was formulated and solved for two types of inputs (ramp and dc) that are of interest for the application. Under certain time-dependent constraints, it is shown that (1) with a ramp input the circuit has an output voltage proportional to the static tip clearance capacitance, and (2) with a dc input, the output is proportional to the derivative of the clearance capacitance, and subsequent integration recovers the dynamic capacitance. The technique accommodates long cable lengths and environmentally induced changes in cable and probe parameters. System implementation for both static and dynamic measurements having the same high sensitivity is also presented.

Capacitance-type blade-tip clearance measurement system using a dual amplifier with ramp/dc inputs and integration

NASA Astrophysics Data System (ADS)

Sarma, Garimella R.; Barranger, John P.

1992-10-01

The analysis and prototype results of a dual-amplifier circuit for measuring blade-tip clearance in turbine engines are presented. The capacitance between the blade tip and mounted capacitance electrode within a guard ring of a probe forms one of the feedback elements of an operational amplifier (op amp). The differential equation governing the circuit taking into consideration the nonideal features of the op amp was formulated and solved for two types of inputs (ramp and dc) that are of interest for the application. Under certain time-dependent constraints, it is shown that (1) with a ramp input the circuit has an output voltage proportional to the static tip clearance capacitance, and (2) with a dc input, the output is proportional to the derivative of the clearance capacitance, and subsequent integration recovers the dynamic capacitance. The technique accommodates long cable lengths and environmentally induced changes in cable and probe parameters. System implementation for both static and dynamic measurements having the same high sensitivity is also presented.

Advanced Space Transportation Program (ASTP)

NASA Image and Video Library

2000-09-07

The `once upon a time' science fiction concept of a space elevator has been envisioned and studied as a real mass transportation system in the latter part of the 21st century. David Smitherman of NASA's Marshall Space Flight Center's Advanced Projects Office has compiled plans for such an elevator. The space elevator concept is a structure extending from the surface of the Earth to geostationary Earth orbit (GEO) at 35,786 km in altitude. The tower would be approximately 50 km tall with a cable tethered to the top. Its center mass would be at GEO such that the entire structure orbits the Earth in sync with the Earth's rotation maintaining a stationary position over its base attachment at the equator. Electromagnetic vehicles traveling along the cable could serve as a mass transportation system for transporting people, payloads, and power between space and Earth. This illustration by artist Pat Rawling shows the concept of a space elevator as viewed from the geostationary transfer station looking down the length of the elevator towards the Earth.

Soliton solution and gauge equivalence for an integrable nonlocal complex modified Korteweg-de Vries equation

NASA Astrophysics Data System (ADS)

Ma, Li-Yuan; Shen, Shou-Feng; Zhu, Zuo-Nong

2017-10-01

In this paper, we prove that an integrable nonlocal complex modified Korteweg-de Vries (mKdV) equation introduced by Ablowitz and Musslimani [Nonlinearity 29, 915-946 (2016)] is gauge equivalent to a spin-like model. From the gauge equivalence, one can see that there exists significant difference between the nonlocal complex mKdV equation and the classical complex mKdV equation. Through constructing the Darboux transformation for nonlocal complex mKdV equation, a variety of exact solutions including dark soliton, W-type soliton, M-type soliton, and periodic solutions are derived.

Analytical solutions to time-fractional partial differential equations in a two-dimensional multilayer annulus

NASA Astrophysics Data System (ADS)

Chen, Shanzhen; Jiang, Xiaoyun

2012-08-01

In this paper, analytical solutions to time-fractional partial differential equations in a multi-layer annulus are presented. The final solutions are obtained in terms of Mittag-Leffler function by using the finite integral transform technique and Laplace transform technique. In addition, the classical diffusion equation (α=1), the Helmholtz equation (α→0) and the wave equation (α=2) are discussed as special cases. Finally, an illustrative example problem for the three-layer semi-circular annular region is solved and numerical results are presented graphically for various kind of order of fractional derivative.

The Scaling Group of the 1-D Invisicid Euler Equations

NASA Astrophysics Data System (ADS)

Schmidt, Emma; Ramsey, Scott; Boyd, Zachary; Baty, Roy

2017-11-01

The one dimensional (1-D) compressible Euler equations in non-ideal media support scale invariant solutions under a variety of initial conditions. Famous scale invariant solutions include the Noh, Sedov, Guderley, and collapsing cavity hydrodynamic test problems. We unify many classical scale invariant solutions under a single scaling group analysis. The scaling symmetry group generator provides a framework for determining all scale invariant solutions emitted by the 1-D Euler equations for arbitrary geometry, initial conditions, and equation of state. We approach the Euler equations from a geometric standpoint, and conduct scaling analyses for a broad class of materials.

On solutions of the fifth-order dispersive equations with porous medium type non-linearity

NASA Astrophysics Data System (ADS)

Kocak, Huseyin; Pinar, Zehra

2018-07-01

In this work, we focus on obtaining the exact solutions of the fifth-order semi-linear and non-linear dispersive partial differential equations, which have the second-order diffusion-like (porous-type) non-linearity. The proposed equations were not studied in the literature in the sense of the exact solutions. We reveal solutions of the proposed equations using the classical Riccati equations method. The obtained exact solutions, which can play a key role to simulate non-linear waves in the medium with dispersion and diffusion, are illustrated and discussed in details.

Application of active distribute temperature sensing and fiber optic as sensors to determinate the unsaturated hydraulic conductivity curve

NASA Astrophysics Data System (ADS)

Zubelzu, Sergio; Rodriguez-Sinobas, Leonor; Sobrino, Fernando

2017-04-01

The development of methodologies for the characterization of soil water content through the use of distribute temperature sensing and fiber optic cable has allowed for modelling with high temporal and spatial accuracy water movement in soils. One of the advantage of using fiber optic as a sensor, compared with the traditional point water probes, is the possibility to measure the variable continuously along the cable every 0.125 m (up to a cable length of 1500) and every second. Traditionally, applications based on fiber optic as a soil water sensor apply the active heated fiber optic technique AHFO to follow the evolution soil water content during and after irrigation events or for hydrologic characterization. However, this paper accomplishes an original experience by using AHFO as a sensor to characterize the soil hydraulic conductivity curve in subsaturated conditions. The non lineal nature between the hidraulic conductivity curve and soil water, showing high slope in the range close to saturation ) favors the AHFO a most suitable sensor due to its ability to measure the variable at small time and length intervals. Thus, it is possible to obtain accurate and a large number of data to be used to estimate the hydraulic conductivity curve from de water flow general equation by numerical methods. Results are promising and showed the feasibility of this technique to estimate the hydraulic conductivity curve for subsaturated soils .

When is an Inhibitory Synapse Effective?

NASA Astrophysics Data System (ADS)

Qian, Ning; Sejnowski, Terrence J.

1990-10-01

Interactions between excitatory and inhibitory synaptic inputs on dendrites determine the level of activity in neurons. Models based on the cable equation predict that silent shunting inhibition can strongly veto the effect of an excitatory input. The cable model assumes that ionic concentrations do not change during the electrical activity, which may not be a valid assumption, especially for small structures such as dendritic spines. We present here an analysis and computer simulations to show that for large Cl^- conductance changes, the more general Nernst-Planck electrodiffusion model predicts that shunting inhibition on spines should be much less effective than that predicted by the cable model. This is a consequence of the large changes in the intracellular ionic concentration of Cl^- that can occur in small structures, which would alter the reversal potential and reduce the driving force for Cl^-. Shunting inhibition should therefore not be effective on spines, but it could be significantly more effective on the dendritic shaft at the base of the spine. In contrast to shunting inhibition, hyperpolarizing synaptic inhibition mediated by K^+ currents can be very effective in reducing the excitatory synaptic potentials on the same spine if the excitatory conductance change is less than 10 nS. We predict that if the inhibitory synapses found on cortical spines are to be effective, then they should be mediated by K^+ through GABA_B receptors.

Forces on nuclei moving on autoionizing molecular potential energy surfaces.

PubMed

Moiseyev, Nimrod

2017-01-14

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

Convective flows of generalized time-nonlocal nanofluids through a vertical rectangular channel

NASA Astrophysics Data System (ADS)

Ahmed, Najma; Vieru, Dumitru; Fetecau, Constantin; Shah, Nehad Ali

2018-05-01

Time-nonlocal generalized model of the natural convection heat transfer and nanofluid flows through a rectangular vertical channel with wall conditions of the Robin type are studied. The generalized mathematical model with time-nonlocality is developed by considering the fractional constitutive equations for the shear stress and thermal flux defined with the time-fractional Caputo derivative. The Caputo power-law non-local kernel provides the damping to the velocity and temperature gradient; therefore, transport processes are influenced by the histories at all past and present times. Analytical solutions for dimensionless velocity and temperature fields are obtained by using the Laplace transform coupled with the finite sine-cosine Fourier transform which is suitable to problems with boundary conditions of the Robin type. Particularizing the fractional thermal and velocity parameters, solutions for three simplified models are obtained (classical linear momentum equation with damped thermal flux; fractional shear stress constitutive equation with classical Fourier's law for thermal flux; classical shear stress and thermal flux constitutive equations). It is found that the thermal histories strongly influence the thermal transport for small values of time t. Also, the thermal transport can be enhanced if the thermal fractional parameter decreases or by increasing the nanoparticles' volume fraction. The velocity field is influenced on the one hand by the temperature of the fluid and on the other by the damping of the velocity gradient introduced by the fractional derivative. Also, the transport motions of the channel walls influence the motion of the fluid layers located near them.

First year of practical experiences of the new Arctic AWIPEV-COSYNA cabled Underwater Observatory in Kongsfjorden, Spitsbergen

NASA Astrophysics Data System (ADS)

Fischer, Philipp; Schwanitz, Max; Loth, Reiner; Posner, Uwe; Brand, Markus; Schröder, Friedhelm

2017-04-01

A combined year-round assessment of selected oceanographic data and a macrobiotic community assessment was performed from October 2013 to November 2014 in the littoral zone of the Kongsfjorden polar fjord system on the western coast of Svalbard (Norway). State of the art remote controlled cabled underwater observatory technology was used for daily vertical profiles of temperature, salinity, and turbidity together with a stereo-optical assessment of the macrobiotic community, including fish. The results reveal a distinct seasonal cycle in total species abundances, with a significantly higher total abundance and species richness during the polar winter when no light is available underwater compared to the summer months when 24 h light is available. During the winter months, a temporally highly segmented community was observed with respect to species occurrence, with single species dominating the winter community for restricted times. In contrast, the summer community showed an overall lower total abundance as well as a significantly lower number of species. The study clearly demonstrates the high potential of cable connected remote controlled digital sampling devices, especially in remote areas, such as polar fjord systems, with harsh environmental conditions and limited accessibility. A smart combination of such new digital sampling methods with classic sampling procedures can provide a possibility to significantly extend the sampling time and frequency, especially in remote and difficult to access areas. This can help to provide a sufficient data density and therefore statistical power for a sound scientific analysis without increasing the invasive sampling pressure in ecologically sensitive environments.

On integrability of the Killing equation

NASA Astrophysics Data System (ADS)

Houri, Tsuyoshi; Tomoda, Kentaro; Yasui, Yukinori

2018-04-01

Killing tensor fields have been thought of as describing the hidden symmetry of space(-time) since they are in one-to-one correspondence with polynomial first integrals of geodesic equations. Since many problems in classical mechanics can be formulated as geodesic problems in curved space and spacetime, solving the defining equation for Killing tensor fields (the Killing equation) is a powerful way to integrate equations of motion. Thus it has been desirable to formulate the integrability conditions of the Killing equation, which serve to determine the number of linearly independent solutions and also to restrict the possible forms of solutions tightly. In this paper, we show the prolongation for the Killing equation in a manner that uses Young symmetrizers. Using the prolonged equations, we provide the integrability conditions explicitly.

30 CFR 77.605 - Breaking trailing cable and power cable connections.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 30 Mineral Resources 1 2010-07-01 2010-07-01 false Breaking trailing cable and power cable... OF UNDERGROUND COAL MINES Trailing Cables § 77.605 Breaking trailing cable and power cable connections. Trailing cable and power cable connections between cables and to power sources shall not be made...

30 CFR 77.605 - Breaking trailing cable and power cable connections.

Code of Federal Regulations, 2013 CFR

2013-07-01

... 30 Mineral Resources 1 2013-07-01 2013-07-01 false Breaking trailing cable and power cable... OF UNDERGROUND COAL MINES Trailing Cables § 77.605 Breaking trailing cable and power cable connections. Trailing cable and power cable connections between cables and to power sources shall not be made...

30 CFR 77.605 - Breaking trailing cable and power cable connections.

Code of Federal Regulations, 2011 CFR

2011-07-01

... 30 Mineral Resources 1 2011-07-01 2011-07-01 false Breaking trailing cable and power cable... OF UNDERGROUND COAL MINES Trailing Cables § 77.605 Breaking trailing cable and power cable connections. Trailing cable and power cable connections between cables and to power sources shall not be made...

30 CFR 77.605 - Breaking trailing cable and power cable connections.

Code of Federal Regulations, 2012 CFR

2012-07-01

... 30 Mineral Resources 1 2012-07-01 2012-07-01 false Breaking trailing cable and power cable... OF UNDERGROUND COAL MINES Trailing Cables § 77.605 Breaking trailing cable and power cable connections. Trailing cable and power cable connections between cables and to power sources shall not be made...

30 CFR 77.605 - Breaking trailing cable and power cable connections.

Code of Federal Regulations, 2014 CFR

2014-07-01

... 30 Mineral Resources 1 2014-07-01 2014-07-01 false Breaking trailing cable and power cable... OF UNDERGROUND COAL MINES Trailing Cables § 77.605 Breaking trailing cable and power cable connections. Trailing cable and power cable connections between cables and to power sources shall not be made...

Causal Diffusion and the Survival of Charge Fluctuations

NASA Astrophysics Data System (ADS)

Abdel-Aziz, Mohamed; Gavin, Sean

2004-10-01

Diffusion may obliterate fluctuation signals of the QCD phase transition in nuclear collisions at SPS and RHIC energies. We propose a hyperbolic diffusion equation to study the dissipation of net charge fluctuations [1]. This equation is needed in a relativistic context, because the classic parabolic diffusion equation violates causality. We find that causality substantially limits the extent to which diffusion can dissipate these fluctuations. [1] M. Abdel-Aziz and S. Gavin, nucl-th/0404058

CLASSICAL AREAS OF PHENOMENOLOGY: Material parameter equation for rotating elliptical spherical cloaks

NASA Astrophysics Data System (ADS)

Ma, Hua; Qu, Shao-Bo; Xu, Zhuo; Zhang, Jie-Qiu; Wang, Jia-Fu

2009-01-01

By using the coordinate transformation method, we have deduced the material parameter equation for rotating elliptical spherical cloaks and carried out simulation as well. The results indicate that the rotating elliptical spherical cloaking shell, which is made of meta-materials whose permittivity and permeability are governed by the equation deduced in this paper, can achieve perfect invisibility by excluding electromagnetic fields from the internal region without disturbing any external field.

Advanced classical thermodynamics

NASA Astrophysics Data System (ADS)

Emanuel, George

The theoretical and mathematical foundations of thermodynamics are presented in an advanced text intended for graduate engineering students. Chapters are devoted to definitions and postulates, the fundamental equation, equilibrium, the application of Jacobian theory to thermodynamics, the Maxwell equations, stability, the theory of real gases, critical-point theory, and chemical thermodynamics. Diagrams, graphs, tables, and sample problems are provided.

Exact solution of a quantum forced time-dependent harmonic oscillator

NASA Technical Reports Server (NTRS)

Yeon, Kyu Hwang; George, Thomas F.; Um, Chung IN

1992-01-01

The Schrodinger equation is used to exactly evaluate the propagator, wave function, energy expectation values, uncertainty values, and coherent state for a harmonic oscillator with a time dependent frequency and an external driving time dependent force. These quantities represent the solution of the classical equation of motion for the time dependent harmonic oscillator.

Spin-Orbit Coupling and the Conservation of Angular Momentum

ERIC Educational Resources Information Center

Hnizdo, V.

2012-01-01

In nonrelativistic quantum mechanics, the total (i.e. orbital plus spin) angular momentum of a charged particle with spin that moves in a Coulomb plus spin-orbit-coupling potential is conserved. In a classical nonrelativistic treatment of this problem, in which the Lagrange equations determine the orbital motion and the Thomas equation yields the…

Verifying the Hanging Chain Model

ERIC Educational Resources Information Center

Karls, Michael A.

2013-01-01

The wave equation with variable tension is a classic partial differential equation that can be used to describe the horizontal displacements of a vertical hanging chain with one end fixed and the other end free to move. Using a web camera and TRACKER software to record displacement data from a vibrating hanging chain, we verify a modified version…

The Quantum Arnold Transformation for the damped harmonic oscillator: from the Caldirola-Kanai model toward the Bateman model

NASA Astrophysics Data System (ADS)

López-Ruiz, F. F.; Guerrero, J.; Aldaya, V.; Cossío, F.

2012-08-01

Using a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations (LSODE), including systems with friction linear in velocity such as the damped harmonic oscillator, can be related to the quantum free-particle dynamical system. This implies that symmetries and simple computations in the free particle can be exported to the LSODE-system. The quantum Arnold transformation is given explicitly for the damped harmonic oscillator, and an algebraic connection between the Caldirola-Kanai model for the damped harmonic oscillator and the Bateman system will be sketched out.

Expected values and variances of Bragg peak intensities measured in a nanocrystalline powder diffraction experiment

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

Öztürk, Hande; Noyan, I. Cevdet

A rigorous study of sampling and intensity statistics applicable for a powder diffraction experiment as a function of crystallite size is presented. Our analysis yields approximate equations for the expected value, variance and standard deviations for both the number of diffracting grains and the corresponding diffracted intensity for a given Bragg peak. The classical formalism published in 1948 by Alexander, Klug & Kummer [J. Appl. Phys.(1948),19, 742–753] appears as a special case, limited to large crystallite sizes, here. It is observed that both the Lorentz probability expression and the statistics equations used in the classical formalism are inapplicable for nanocrystallinemore » powder samples.« less

Expected values and variances of Bragg peak intensities measured in a nanocrystalline powder diffraction experiment

DOE PAGES

Öztürk, Hande; Noyan, I. Cevdet

2017-08-24

A rigorous study of sampling and intensity statistics applicable for a powder diffraction experiment as a function of crystallite size is presented. Our analysis yields approximate equations for the expected value, variance and standard deviations for both the number of diffracting grains and the corresponding diffracted intensity for a given Bragg peak. The classical formalism published in 1948 by Alexander, Klug & Kummer [J. Appl. Phys.(1948),19, 742–753] appears as a special case, limited to large crystallite sizes, here. It is observed that both the Lorentz probability expression and the statistics equations used in the classical formalism are inapplicable for nanocrystallinemore » powder samples.« less

Asymptotic theory of neutral stability of the Couette flow of a vibrationally excited gas

NASA Astrophysics Data System (ADS)

Grigor'ev, Yu. N.; Ershov, I. V.

2017-01-01

An asymptotic theory of the neutral stability curve for a supersonic plane Couette flow of a vibrationally excited gas is developed. The initial mathematical model consists of equations of two-temperature viscous gas dynamics, which are used to derive a spectral problem for a linear system of eighth-order ordinary differential equations within the framework of the classical linear stability theory. Unified transformations of the system for all shear flows are performed in accordance with the classical Lin scheme. The problem is reduced to an algebraic secular equation with separation into the "inviscid" and "viscous" parts, which is solved numerically. It is shown that the thus-calculated neutral stability curves agree well with the previously obtained results of the direct numerical solution of the original spectral problem. In particular, the critical Reynolds number increases with excitation enhancement, and the neutral stability curve is shifted toward the domain of higher wave numbers. This is also confirmed by means of solving an asymptotic equation for the critical Reynolds number at the Mach number M ≤ 4.

Pore size distribution calculation from 1H NMR signal and N2 adsorption-desorption techniques

NASA Astrophysics Data System (ADS)

Hassan, Jamal

2012-09-01

The pore size distribution (PSD) of nano-material MCM-41 is determined using two different approaches: N2 adsorption-desorption and 1H NMR signal of water confined in silica nano-pores of MCM-41. The first approach is based on the recently modified Kelvin equation [J.V. Rocha, D. Barrera, K. Sapag, Top. Catal. 54(2011) 121-134] which deals with the known underestimation in pore size distribution for the mesoporous materials such as MCM-41 by introducing a correction factor to the classical Kelvin equation. The second method employs the Gibbs-Thompson equation, using NMR, for melting point depression of liquid in confined geometries. The result shows that both approaches give similar pore size distribution to some extent, and also the NMR technique can be considered as an alternative direct method to obtain quantitative results especially for mesoporous materials. The pore diameter estimated for the nano-material used in this study was about 35 and 38 Å for the modified Kelvin and NMR methods respectively. A comparison between these methods and the classical Kelvin equation is also presented.

Classical Affine W-Algebras and the Associated Integrable Hamiltonian Hierarchies for Classical Lie Algebras

NASA Astrophysics Data System (ADS)

De Sole, Alberto; Kac, Victor G.; Valeri, Daniele

2018-06-01

We prove that any classical affine W-algebra W (g, f), where g is a classical Lie algebra and f is an arbitrary nilpotent element of g, carries an integrable Hamiltonian hierarchy of Lax type equations. This is based on the theories of generalized Adler type operators and of generalized quasideterminants, which we develop in the paper. Moreover, we show that under certain conditions, the product of two generalized Adler type operators is a Lax type operator. We use this fact to construct a large number of integrable Hamiltonian systems, recovering, as a special case, all KdV type hierarchies constructed by Drinfeld and Sokolov.

Equations of motion for the variable mass flow-variable exhaust velocity rocket

NASA Technical Reports Server (NTRS)

Tempelman, W. H.

1972-01-01

An equation of motion for a one dimensional rocket is derived as a function of the mass flow rate into the acceleration chamber and the velocity distribution along the chamber, thereby including the transient flow changes in the chamber. The derivation of the mass density requires the introduction of the special time coordinate. The equation of motion is derived from both classical force and momentum approaches and is shown to be consistent with the standard equation expressed in terms of flow parameters at the exit to the acceleration chamber.

Magnonic analog of relativistic Zitterbewegung in an antiferromagnetic spin chain

NASA Astrophysics Data System (ADS)

Wang, Weiwei; Gu, Chenjie; Zhou, Yan; Fangohr, Hans

2017-07-01

We theoretically investigate the spin-wave (magnon) excitations in a classical antiferromagnetic spin chain with easy-axis anisotropy. We obtain a Dirac-like equation by linearizing the Landau-Lifshitz-Gilbert equation in this antiferromagnetic system, in contrast to the ferromagnetic system in which a Schrödinger-type equation is derived. The Hamiltonian operator in the Dirac-like equation is a pseudo-Hermitian. We compute and demonstrate relativistic Zitterbewegung (trembling motion) in the antiferromagnetic spin chain by measuring the expectation values of the wave-packet position.

Structural interactions in ionic liquids linked to higher-order Poisson-Boltzmann equations

NASA Astrophysics Data System (ADS)

Blossey, R.; Maggs, A. C.; Podgornik, R.

2017-06-01

We present a derivation of generalized Poisson-Boltzmann equations starting from classical theories of binary fluid mixtures, employing an approach based on the Legendre transform as recently applied to the case of local descriptions of the fluid free energy. Under specific symmetry assumptions, and in the linearized regime, the Poisson-Boltzmann equation reduces to a phenomenological equation introduced by Bazant et al. [Phys. Rev. Lett. 106, 046102 (2011)], 10.1103/PhysRevLett.106.046102, whereby the structuring near the surface is determined by bulk coefficients.

Schrödinger equation revisited

PubMed Central

Schleich, Wolfgang P.; Greenberger, Daniel M.; Kobe, Donald H.; Scully, Marlan O.

2013-01-01

The time-dependent Schrödinger equation is a cornerstone of quantum physics and governs all phenomena of the microscopic world. However, despite its importance, its origin is still not widely appreciated and properly understood. We obtain the Schrödinger equation from a mathematical identity by a slight generalization of the formulation of classical statistical mechanics based on the Hamilton–Jacobi equation. This approach brings out most clearly the fact that the linearity of quantum mechanics is intimately connected to the strong coupling between the amplitude and phase of a quantum wave. PMID:23509260

Static and Dynamic Characteristics of a Long-Span Cable-Stayed Bridge with CFRP Cables

PubMed Central

Xie, Xu; Li, Xiaozhang; Shen, Yonggang

2014-01-01

In this study, the scope of CFRP cables in cable-stayed bridges is studied by establishing a numerical model of a 1400-m span of the same. The mechanical properties and characteristics of CFRP stay cables and of a cable-stayed bridge with CFRP cables are here subjected to comprehensive analysis. The anomalies in the damping properties of free vibration, nonlinear parametric vibration and wind fluctuating vibration between steel cables and CFRP cables are determined. The structural stiffness, wind resistance and traffic vibration of the cable-stayed bridge with CFRP cables are also analyzed. It was found that the static performances of a cable-stayed bridge with CFRP cables and steel cables are basically the same. The natural frequencies of CFRP cables do not coincide with the major natural frequencies of the cable-stayed bridge, so the likelihood of CFRP cable-bridge coupling vibration is minuscule. For CFRP cables, the response amplitudes of both parametric vibration and wind fluctuating vibration are smaller than those of steel cables. It can be concluded from the research that the use of CFRP cables does not change the dynamic characteristics of the vehicle-bridge coupling vibration. Therefore, they can be used in long-span cable-stayed bridges with an excellent mechanical performance. PMID:28788710

Static and Dynamic Characteristics of a Long-Span Cable-Stayed Bridge with CFRP Cables.

PubMed

Xie, Xu; Li, Xiaozhang; Shen, Yonggang

2014-06-23

In this study, the scope of CFRP cables in cable-stayed bridges is studied by establishing a numerical model of a 1400-m span of the same. The mechanical properties and characteristics of CFRP stay cables and of a cable-stayed bridge with CFRP cables are here subjected to comprehensive analysis. The anomalies in the damping properties of free vibration, nonlinear parametric vibration and wind fluctuating vibration between steel cables and CFRP cables are determined. The structural stiffness, wind resistance and traffic vibration of the cable-stayed bridge with CFRP cables are also analyzed. It was found that the static performances of a cable-stayed bridge with CFRP cables and steel cables are basically the same. The natural frequencies of CFRP cables do not coincide with the major natural frequencies of the cable-stayed bridge, so the likelihood of CFRP cable-bridge coupling vibration is minuscule. For CFRP cables, the response amplitudes of both parametric vibration and wind fluctuating vibration are smaller than those of steel cables. It can be concluded from the research that the use of CFRP cables does not change the dynamic characteristics of the vehicle-bridge coupling vibration. Therefore, they can be used in long-span cable-stayed bridges with an excellent mechanical performance.

Duration of classicality in highly degenerate interacting Bosonic systems

DOE PAGES

Sikivie, Pierre; Todarello, Elisa M.

2017-04-28

We study sets of oscillators that have high quantum occupancy and that interact by exchanging quanta. It is shown by analytical arguments and numerical simulation that such systems obey classical equations of motion only on time scales of order their relaxation time τ and not longer than that. The results are relevant to the cosmology of axions and axion-like particles.

An amateur's contribution to the design of Telford's Menai Suspension Bridge: a commentary on Gilbert (1826) ‘On the mathematical theory of suspension bridges’

PubMed Central

Calladine, C. R.

2015-01-01

Davies Gilbert's work on the catenary is notable on two counts. First, it influenced Thomas Telford in formulating his final design for the Menai Strait suspension bridge (1826); and second, it established for the first time the form of the ‘catenary of equal strength’. The classical catenary is a uniform flexible chain or cable hanging freely under gravity between supports. The ‘catenary of equal strength’ is the form of a cable whose cross-sectional area is made proportional to the tension at each point, so that the tensile stress is uniform throughout. In this paper I provide a sketch of the lives and achievements of Gilbert and Telford, and of their interaction over the Menai Bridge. There follows a commentary on Gilbert's 1826 paper, and on his two related publications; and a brief sketch of the earlier history of the catenary. I then describe the development of the suspension bridge up to the present time. Finally, I discuss relations between mathematical analysts and practical engineers. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society. PMID:25750153

An amateur's contribution to the design of Telford's Menai Suspension Bridge: a commentary on Gilbert (1826) 'On the mathematical theory of suspension bridges'.

PubMed

Calladine, C R

2015-04-13

Davies Gilbert's work on the catenary is notable on two counts. First, it influenced Thomas Telford in formulating his final design for the Menai Strait suspension bridge (1826); and second, it established for the first time the form of the 'catenary of equal strength'. The classical catenary is a uniform flexible chain or cable hanging freely under gravity between supports. The 'catenary of equal strength' is the form of a cable whose cross-sectional area is made proportional to the tension at each point, so that the tensile stress is uniform throughout. In this paper I provide a sketch of the lives and achievements of Gilbert and Telford, and of their interaction over the Menai Bridge. There follows a commentary on Gilbert's 1826 paper, and on his two related publications; and a brief sketch of the earlier history of the catenary. I then describe the development of the suspension bridge up to the present time. Finally, I discuss relations between mathematical analysts and practical engineers. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.

Application of gradient elasticity to benchmark problems of beam vibrations

NASA Astrophysics Data System (ADS)

Kateb, K. M.; Almitani, K. H.; Alnefaie, K. A.; Abu-Hamdeh, N. H.; Papadopoulos, P.; Askes, H.; Aifantis, E. C.

2016-04-01

The gradient approach, specifically gradient elasticity theory, is adopted to revisit certain typical configurations on mechanical vibrations. New results on size effects and scale-dependent behavior not captured by classical elasticity are derived, aiming at illustrating the usefulness of this approach to applications in advanced technologies. In particular, elastic prismatic straight beams in bending are discussed using two different governing equations: the gradient elasticity bending moment equation (fourth order) and the gradient elasticity deflection equation (sixth order). Different boundary/support conditions are examined. One problem considers the free vibrations of a cantilever beam loaded by an end force. A second problem is concerned with a simply supported beam disturbed by a concentrated force in the middle of the beam. Both problems are solved analytically. Exact free vibration frequencies and mode shapes are derived and presented. The difference between the gradient elasticity solution and its classical counterpart is revealed. The size ratio c/L (c denotes internal length and L is the length of the beam) induces significant effects on vibration frequencies. For both beam configurations, it turns out that as the ratio c/L increases, the vibration frequencies decrease, a fact which implies lower beam stiffness. Numerical examples show this behavior explicitly and recover the classical vibration behavior for vanishing size ratio c/L.

Lamb wave extraction of dispersion curves in micro/nano-plates using couple stress theories

NASA Astrophysics Data System (ADS)

Ghodrati, Behnam; Yaghootian, Amin; Ghanbar Zadeh, Afshin; Mohammad-Sedighi, Hamid

2018-01-01

In this paper, Lamb wave propagation in a homogeneous and isotropic non-classical micro/nano-plates is investigated. To consider the effect of material microstructure on the wave propagation, three size-dependent models namely indeterminate-, modified- and consistent couple stress theories are used to extract the dispersion equations. In the mentioned theories, a parameter called 'characteristic length' is used to consider the size of material microstructure in the governing equations. To generalize the parametric studies and examine the effect of thickness, propagation wavelength, and characteristic length on the behavior of miniature plate structures, the governing equations are nondimensionalized by defining appropriate dimensionless parameters. Then the dispersion curves for phase and group velocities are plotted in terms of a wide frequency-thickness range to study the lamb waves propagation considering microstructure effects in very high frequencies. According to the illustrated results, it was observed that the couple stress theories in the Cosserat type material predict more rigidity than the classical theory; so that in a plate with constant thickness, by increasing the thickness to characteristic length ratio, the results approach to the classical theory, and by reducing this ratio, wave propagation speed in the plate is significantly increased. In addition, it is demonstrated that for high-frequency Lamb waves, it converges to dispersive Rayleigh wave velocity.

A reformulation of mechanics and electrodynamics.

PubMed

Pinheiro, Mario J

2017-07-01

Classical mechanics, as commonly taught in engineering and science, are confined to the conventional Newtonian theory. But classical mechanics has not really changed in substance since Newton formulation, describing simultaneous rotation and translation of objects with somewhat complicate drawbacks, risking interpretation of forces in non-inertial frames. In this work we introduce a new variational principle for out-of-equilibrium, rotating systems, obtaining a set of two first order differential equations that introduces a thermodynamic-mechanistic time into Newton's dynamical equation, and revealing the same formal symplectic structure shared by classical mechanics, fluid mechanics and thermodynamics. The results is a more consistent formulation of dynamics and electrodynamics, explaining natural phenomena as the outcome from a balance between energy and entropy, embedding translational with rotational motion into a single equation, showing centrifugal and Coriolis force as derivatives from the transport of angular momentum, and offering a natural method to handle variational problems, as shown with the brachistochrone problem. In consequence, a new force term appears, the topological torsion current, important for spacecraft dynamics. We describe a set of solved problems showing the potential of a competing technique, with significant interest to electrodynamics as well. We expect this new approach to have impact in a large class of scientific and technological problems.

30 CFR 77.601 - Trailing cables or portable cables; temporary splices.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 30 Mineral Resources 1 2010-07-01 2010-07-01 false Trailing cables or portable cables; temporary... OF UNDERGROUND COAL MINES Trailing Cables § 77.601 Trailing cables or portable cables; temporary splices. Temporary splices in trailing cables or portable cables shall be made in a workmanlike manner and...

Revised standards for statistical evidence.

PubMed

Johnson, Valen E

2013-11-26

Recent advances in Bayesian hypothesis testing have led to the development of uniformly most powerful Bayesian tests, which represent an objective, default class of Bayesian hypothesis tests that have the same rejection regions as classical significance tests. Based on the correspondence between these two classes of tests, it is possible to equate the size of classical hypothesis tests with evidence thresholds in Bayesian tests, and to equate P values with Bayes factors. An examination of these connections suggest that recent concerns over the lack of reproducibility of scientific studies can be attributed largely to the conduct of significance tests at unjustifiably high levels of significance. To correct this problem, evidence thresholds required for the declaration of a significant finding should be increased to 25-50:1, and to 100-200:1 for the declaration of a highly significant finding. In terms of classical hypothesis tests, these evidence standards mandate the conduct of tests at the 0.005 or 0.001 level of significance.

Wave chaos in the elastic disk.

PubMed

Sondergaard, Niels; Tanner, Gregor

2002-12-01

The relation between the elastic wave equation for plane, isotropic bodies and an underlying classical ray dynamics is investigated. We study, in particular, the eigenfrequencies of an elastic disk with free boundaries and their connection to periodic rays inside the circular domain. Even though the problem is separable, wave mixing between the shear and pressure component of the wave field at the boundary leads to an effective stochastic part in the ray dynamics. This introduces phenomena typically associated with classical chaos as, for example, an exponential increase in the number of periodic orbits. Classically, the problem can be decomposed into an integrable part and a simple binary Markov process. Similarly, the wave equation can, in the high-frequency limit, be mapped onto a quantum graph. Implications of this result for the level statistics are discussed. Furthermore, a periodic trace formula is derived from the scattering matrix based on the inside-outside duality between eigenmodes and scattering solutions and periodic orbits are identified by Fourier transforming the spectral density.

Autonomous rotor heat engine

NASA Astrophysics Data System (ADS)

Roulet, Alexandre; Nimmrichter, Stefan; Arrazola, Juan Miguel; Seah, Stella; Scarani, Valerio

2017-06-01

The triumph of heat engines is their ability to convert the disordered energy of thermal sources into useful mechanical motion. In recent years, much effort has been devoted to generalizing thermodynamic notions to the quantum regime, partly motivated by the promise of surpassing classical heat engines. Here, we instead adopt a bottom-up approach: we propose a realistic autonomous heat engine that can serve as a test bed for quantum effects in the context of thermodynamics. Our model draws inspiration from actual piston engines and is built from closed-system Hamiltonians and weak bath coupling terms. We analytically derive the performance of the engine in the classical regime via a set of nonlinear Langevin equations. In the quantum case, we perform numerical simulations of the master equation. Finally, we perform a dynamic and thermodynamic analysis of the engine's behavior for several parameter regimes in both the classical and quantum case and find that the latter exhibits a consistently lower efficiency due to additional noise.

Gravitational tides in the outer planets. I - Implications of classical tidal theory. II - Interior calculations and estimation of the tidal dissipation factor

NASA Technical Reports Server (NTRS)

Ioannou, Petros J.; Lindzen, Richard S.

1993-01-01

Classical tidal theory is applied to the atmospheres of the outer planets. The tidal geopotential due to satellites of the outer planets is discussed, and the solution of Laplace's tidal equation for Hough modes appropriate to tides on the outer planets is examined. The vertical structure of tidal modes is described, noting that only relatively high-order meridional mode numbers can propagate vertically with growing amplitude. Expected magnitudes for tides in the visible atmosphere of Jupiter are discussed. The classical theory is extended to planetary interiors taking the effects of spherically and self-gravity into account. The thermodynamic structure of Jupiter is described and the WKB theory of the vertical structure equation is presented. The regions for which inertial, gravity, and acoustic oscillations are possible are delineated. The case of a planet with a neutral interior is treated, discussing the various atmospheric boundary conditions and showing that the tidal response is small.

Quantization and Quantum-Like Phenomena: A Number Amplitude Approach

NASA Astrophysics Data System (ADS)

Robinson, T. R.; Haven, E.

2015-12-01

Historically, quantization has meant turning the dynamical variables of classical mechanics that are represented by numbers into their corresponding operators. Thus the relationships between classical variables determine the relationships between the corresponding quantum mechanical operators. Here, we take a radically different approach to this conventional quantization procedure. Our approach does not rely on any relations based on classical Hamiltonian or Lagrangian mechanics nor on any canonical quantization relations, nor even on any preconceptions of particle trajectories in space and time. Instead we examine the symmetry properties of certain Hermitian operators with respect to phase changes. This introduces harmonic operators that can be identified with a variety of cyclic systems, from clocks to quantum fields. These operators are shown to have the characteristics of creation and annihilation operators that constitute the primitive fields of quantum field theory. Such an approach not only allows us to recover the Hamiltonian equations of classical mechanics and the Schrödinger wave equation from the fundamental quantization relations, but also, by freeing the quantum formalism from any physical connotation, makes it more directly applicable to non-physical, so-called quantum-like systems. Over the past decade or so, there has been a rapid growth of interest in such applications. These include, the use of the Schrödinger equation in finance, second quantization and the number operator in social interactions, population dynamics and financial trading, and quantum probability models in cognitive processes and decision-making. In this paper we try to look beyond physical analogies to provide a foundational underpinning of such applications.

Critical behavior of dilute NaCl in H2O

USGS Publications Warehouse

Pitzer, Kenneth S.; Bischoff, J.L.; Rosenbauer, R.J.

1987-01-01

The compositions of the saturated vapor and liquid phases are measured for the system NaCl-H2O at 380??C, which is close to the critical point of pure water. The shape of the phase equilibrium curve is classical, which confirms a conclusion reached earlier on the basis of less accurate data. This implies that the long-range forces introduced by the NaCl suppress the non-classical effects present in pure H2O. An empirical equation of a classical type fits these data. ?? 1987.

A Method for the Construction of Hereditary Constitutive Equations of Laminates Bases on a Hereditary Constitutive Equation for a Layer

NASA Astrophysics Data System (ADS)

Dumansky, Alexander M.; Tairova, Lyudmila P.

2008-09-01

A method for the construction of hereditary constitutive equation is proposed for the laminate on the basis of hereditary constitutive equations of a layer. The method is developed from the assumption that in the directions of axes of orthotropy the layer follows elastic behavior, and obeys hereditary constitutive equations under shear. The constitutive equations of the laminate are constructed on the basis of classical laminate theory and algebra of resolvent operators. Effective matrix algorithm and relationships of operator algebra are used to derive visco-elastic stiffness and compliance of the laminate. The example of construction of hereditary constitutive equations of cross-ply carbon fiber-reinforced plastic is presented.

The Operational Equations of State. 5: The APA - Equation of State

DTIC Science & Technology

2013-09-01

Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law , no person shall be subject to any penalty for...physical measurements. Thermodynamic consistency means that theEOS is totally consistent with the first and second laws of thermodynamics. Remember...form equation 1. From that standpoint, the EOS reminds the classical Boyle- Mariotte-Gay- Lussac model (when the heat capacity must be function of

On A Theory of Rates

DTIC Science & Technology

2005-02-01

and the jump function one. 51 F. Predator and Prey The Lotka - Volterra equations,[Ball 1985] dx dt = AxBxy; (209) dy dt = Cx+Dxy; are classical di...that neither set of these rate di¤erential equations look like the Lotka - Volterra equa- tions. We might want to account for a predator starving to...h 1 kpeatx i ktencounter y; 53 which gets us closer to the form of the Lotka - Volterra equations, especially for the asexual reproduction forms

47 CFR 36.153 - Assignment of Cable and Wire Facilities (C&WF) to categories.

Code of Federal Regulations, 2014 CFR

2014-10-01

... 47 Telecommunication 2 2014-10-01 2014-10-01 false Assignment of Cable and Wire Facilities (C&WF... Telecommunications Property Cable and Wire Facilities § 36.153 Assignment of Cable and Wire Facilities (C&WF) to categories. (a) Cable consists of: Aerial cable, underground cable, buried cable, submarine cable, deep sea...

47 CFR 36.153 - Assignment of Cable and Wire Facilities (C&WF) to categories.

Code of Federal Regulations, 2012 CFR

2012-10-01

... 47 Telecommunication 2 2012-10-01 2012-10-01 false Assignment of Cable and Wire Facilities (C&WF... Telecommunications Property Cable and Wire Facilities § 36.153 Assignment of Cable and Wire Facilities (C&WF) to categories. (a) Cable consists of: Aerial cable, underground cable, buried cable, submarine cable, deep sea...

47 CFR 36.153 - Assignment of Cable and Wire Facilities (C&WF) to categories.

Code of Federal Regulations, 2013 CFR

2013-10-01

... 47 Telecommunication 2 2013-10-01 2013-10-01 false Assignment of Cable and Wire Facilities (C&WF... Telecommunications Property Cable and Wire Facilities § 36.153 Assignment of Cable and Wire Facilities (C&WF) to categories. (a) Cable consists of: Aerial cable, underground cable, buried cable, submarine cable, deep sea...

Reliability and Characterization of High Voltage Power Capacitors

DTIC Science & Technology

2014-03-01

Cable The HVPS cable is a specialized coaxial cable that utilizes a high voltage bayonet connector. The cable itself has a voltage rating in excess...the( LabVIEW(program( GPIB( CABLE ( HVPS( HVPS( COAXIAL ( CABLE ( BNC( COAXIAL ( CABLE ( BNC( COAXIAL ( CABLE ( CAPACITOR(‘C’(DATA( CAPACITOR(‘A’(DATA( Circuit...16   F.   CABLES AND CONNECTORS ...................................................................16

From classical to quantum mechanics: ``How to translate physical ideas into mathematical language''

NASA Astrophysics Data System (ADS)

Bergeron, H.

2001-09-01

Following previous works by E. Prugovečki [Physica A 91A, 202 (1978) and Stochastic Quantum Mechanics and Quantum Space-time (Reidel, Dordrecht, 1986)] on common features of classical and quantum mechanics, we develop a unified mathematical framework for classical and quantum mechanics (based on L2-spaces over classical phase space), in order to investigate to what extent quantum mechanics can be obtained as a simple modification of classical mechanics (on both logical and analytical levels). To obtain this unified framework, we split quantum theory in two parts: (i) general quantum axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoints operators, and so on) and (ii) quantum mechanics proper that specifies the Hilbert space as L2(Rn); the Heisenberg rule [pi,qj]=-iℏδij with p=-iℏ∇, the free Hamiltonian H=-ℏ2Δ/2m and so on. We show that general quantum axiomatics (up to a supplementary "axiom of classicity") can be used as a nonstandard mathematical ground to formulate physical ideas and equations of ordinary classical statistical mechanics. So, the question of a "true quantization" with "ℏ" must be seen as an independent physical problem not directly related with quantum formalism. At this stage, we show that this nonstandard formulation of classical mechanics exhibits a new kind of operation that has no classical counterpart: this operation is related to the "quantization process," and we show why quantization physically depends on group theory (the Galilei group). This analytical procedure of quantization replaces the "correspondence principle" (or canonical quantization) and allows us to map classical mechanics into quantum mechanics, giving all operators of quantum dynamics and the Schrödinger equation. The great advantage of this point of view is that quantization is based on concrete physical arguments and not derived from some "pure algebraic rule" (we exhibit also some limit of the correspondence principle). Moreover spins for particles are naturally generated, including an approximation of their interaction with magnetic fields. We also recover by this approach the semi-classical formalism developed by E. Prugovečki [Stochastic Quantum Mechanics and Quantum Space-time (Reidel, Dordrecht, 1986)].

A functional equation for the specular reflection of rays.

PubMed

Le Bot, A

2002-10-01

This paper aims to generalize the "radiosity method" when applied to specular reflection. Within the field of thermics, the radiosity method is also called the "standard procedure." The integral equation for incident energy, which is usually derived for diffuse reflection, is replaced by a more appropriate functional equation. The latter is used to solve some specific problems and it is shown that all the classical features of specular reflection, for example, the existence of image sources, are embodied within this equation. This equation can be solved with the ray-tracing technique, despite the implemented mathematics being quite different. Several interesting features of the energy field are presented.

Modified harmonic balance method for the solution of nonlinear jerk equations

NASA Astrophysics Data System (ADS)

Rahman, M. Saifur; Hasan, A. S. M. Z.

2018-03-01

In this paper, a second approximate solution of nonlinear jerk equations (third order differential equation) can be obtained by using modified harmonic balance method. The method is simpler and easier to carry out the solution of nonlinear differential equations due to less number of nonlinear equations are required to solve than the classical harmonic balance method. The results obtained from this method are compared with those obtained from the other existing analytical methods that are available in the literature and the numerical method. The solution shows a good agreement with the numerical solution as well as the analytical methods of the available literature.

A molecular dynamics study of intramolecular proton transfer reaction of malonaldehyde in solutions based upon mixed quantum-classical approximation. I. Proton transfer reaction in water

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

Yamada, Atsushi; Kojima, Hidekazu; Okazaki, Susumu, E-mail: okazaki@apchem.nagoya-u.ac.jp

2014-08-28

In order to investigate proton transfer reaction in solution, mixed quantum-classical molecular dynamics calculations have been carried out based on our previously proposed quantum equation of motion for the reacting system [A. Yamada and S. Okazaki, J. Chem. Phys. 128, 044507 (2008)]. Surface hopping method was applied to describe forces acting on the solvent classical degrees of freedom. In a series of our studies, quantum and solvent effects on the reaction dynamics in solutions have been analysed in detail. Here, we report our mixed quantum-classical molecular dynamics calculations for intramolecular proton transfer of malonaldehyde in water. Thermally activated proton transfermore » process, i.e., vibrational excitation in the reactant state followed by transition to the product state and vibrational relaxation in the product state, as well as tunneling reaction can be described by solving the equation of motion. Zero point energy is, of course, included, too. The quantum simulation in water has been compared with the fully classical one and the wave packet calculation in vacuum. The calculated quantum reaction rate in water was 0.70 ps{sup −1}, which is about 2.5 times faster than that in vacuum, 0.27 ps{sup −1}. This indicates that the solvent water accelerates the reaction. Further, the quantum calculation resulted in the reaction rate about 2 times faster than the fully classical calculation, which indicates that quantum effect enhances the reaction rate, too. Contribution from three reaction mechanisms, i.e., tunneling, thermal activation, and barrier vanishing reactions, is 33:46:21 in the mixed quantum-classical calculations. This clearly shows that the tunneling effect is important in the reaction.« less

Hamiltonian structure of classical N-body systems of finite-size particles subject to EM interactions

NASA Astrophysics Data System (ADS)

Cremaschini, C.; Tessarotto, M.

2012-01-01

An open issue in classical relativistic mechanics is the consistent treatment of the dynamics of classical N-body systems of mutually interacting particles. This refers, in particular, to charged particles subject to EM interactions, including both binary interactions and self-interactions ( EM-interacting N- body systems). The correct solution to the question represents an overriding prerequisite for the consistency between classical and quantum mechanics. In this paper it is shown that such a description can be consistently obtained in the context of classical electrodynamics, for the case of a N-body system of classical finite-size charged particles. A variational formulation of the problem is presented, based on the N -body hybrid synchronous Hamilton variational principle. Covariant Lagrangian and Hamiltonian equations of motion for the dynamics of the interacting N-body system are derived, which are proved to be delay-type ODEs. Then, a representation in both standard Lagrangian and Hamiltonian forms is proved to hold, the latter expressed by means of classical Poisson Brackets. The theory developed retains both the covariance with respect to the Lorentz group and the exact Hamiltonian structure of the problem, which is shown to be intrinsically non-local. Different applications of the theory are investigated. The first one concerns the development of a suitable Hamiltonian approximation of the exact equations that retains finite delay-time effects characteristic of the binary interactions and self-EM-interactions. Second, basic consequences concerning the validity of Dirac generator formalism are pointed out, with particular reference to the instant-form representation of Poincaré generators. Finally, a discussion is presented both on the validity and possible extension of the Dirac generator formalism as well as the failure of the so-called Currie "no-interaction" theorem for the non-local Hamiltonian system considered here.

Modeling vibration response and damping of cables and cabled structures

NASA Astrophysics Data System (ADS)

Spak, Kaitlin S.; Agnes, Gregory S.; Inman, Daniel J.

2015-02-01

In an effort to model the vibration response of cabled structures, the distributed transfer function method is developed to model cables and a simple cabled structure. The model includes shear effects, tension, and hysteretic damping for modeling of helical stranded cables, and includes a method for modeling cable attachment points using both linear and rotational damping and stiffness. The damped cable model shows agreement with experimental data for four types of stranded cables, and the damped cabled beam model shows agreement with experimental data for the cables attached to a beam structure, as well as improvement over the distributed mass method for cabled structure modeling.

Quantized Vector Potential and the Photon Wave-function

NASA Astrophysics Data System (ADS)

Meis, C.; Dahoo, P. R.

2017-12-01

The vector potential function {\\overrightarrow{α }}kλ (\\overrightarrow{r},t) for a k-mode and λ-polarization photon, with the quantized amplitude α 0k (ω k ) = ξω k , satisfies the classical wave propagation equation as well as the Schrodinger’s equation with the relativistic massless Hamiltonian \\mathop{H}\\limits∼ =-i\\hslash c\\overrightarrow{\

Power loss of an oscillating electric dipole in a quantum plasma

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

Ghaderipoor, L.; Mehramiz, A.

2012-12-15

A system of linearized quantum plasma equations (quantum hydrodynamic model) has been used for investigating the dispersion equation for electrostatic waves in the plasma. Furthermore, dispersion relations and their modifications due to quantum effects are used for calculating the power loss of an oscillating electric dipole. Finally, the results are compared in quantum and classical regimes.

Modifying Spearman's Attenuation Equation to Yield Partial Corrections for Measurement Error--With Application to Sample Size Calculations

ERIC Educational Resources Information Center

Nicewander, W. Alan

2018-01-01

Spearman's correction for attenuation (measurement error) corrects a correlation coefficient for measurement errors in either-or-both of two variables, and follows from the assumptions of classical test theory. Spearman's equation removes all measurement error from a correlation coefficient which translates into "increasing the reliability of…

Magnetic Bianchi type II string cosmological model in loop quantum cosmology

NASA Astrophysics Data System (ADS)

Rikhvitsky, Victor; Saha, Bijan; Visinescu, Mihai

2014-07-01

The loop quantum cosmology of the Bianchi type II string cosmological model in the presence of a homogeneous magnetic field is studied. We present the effective equations which provide modifications to the classical equations of motion due to quantum effects. The numerical simulations confirm that the big bang singularity is resolved by quantum gravity effects.

On a model for the Navier-Stokes equations using magnetization variables

NASA Astrophysics Data System (ADS)

Pooley, Benjamin C.

2018-04-01

It is known that in a classical setting, the Navier-Stokes equations can be reformulated in terms of so-called magnetization variables w that satisfy Our main focus is the proof of global well-posedness in H 1 / 2 for a new variant of (1), where Pw is replaced by w in the second nonlinear term:

30 CFR 75.607 - Breaking trailing cable and power cable connections.

Code of Federal Regulations, 2013 CFR

2013-07-01

... 30 Mineral Resources 1 2013-07-01 2013-07-01 false Breaking trailing cable and power cable....607 Breaking trailing cable and power cable connections. [Statutory Provisions] Trailing cable and power cable connections to junction boxes shall not be made or broken under load. ...

30 CFR 75.607 - Breaking trailing cable and power cable connections.

Code of Federal Regulations, 2014 CFR

2014-07-01

... 30 Mineral Resources 1 2014-07-01 2014-07-01 false Breaking trailing cable and power cable....607 Breaking trailing cable and power cable connections. [Statutory Provisions] Trailing cable and power cable connections to junction boxes shall not be made or broken under load. ...

30 CFR 75.607 - Breaking trailing cable and power cable connections.

Code of Federal Regulations, 2012 CFR

2012-07-01

... 30 Mineral Resources 1 2012-07-01 2012-07-01 false Breaking trailing cable and power cable....607 Breaking trailing cable and power cable connections. [Statutory Provisions] Trailing cable and power cable connections to junction boxes shall not be made or broken under load. ...

30 CFR 75.607 - Breaking trailing cable and power cable connections.

Code of Federal Regulations, 2011 CFR

2011-07-01

... 30 Mineral Resources 1 2011-07-01 2011-07-01 false Breaking trailing cable and power cable....607 Breaking trailing cable and power cable connections. [Statutory Provisions] Trailing cable and power cable connections to junction boxes shall not be made or broken under load. ...

Towards the quantization of Eddington-inspired-Born-Infeld theory

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

Bouhmadi-López, Mariam; Chen, Che-Yu, E-mail: mbl@ubi.pt, E-mail: b97202056@gmail.com

2016-11-01

The quantum effects close to the classical big rip singularity within the Eddington-inspired-Born-Infeld theory (EiBI) are investigated through quantum geometrodynamics. It is the first time that this approach is applied to a modified theory constructed upon Palatini formalism. The Wheeler-DeWitt (WDW) equation is obtained and solved based on an alternative action proposed in ref. [1], under two different factor ordering choices. This action is dynamically equivalent to the original EiBI action while it is free of square root of the spacetime curvature. We consider a homogeneous, isotropic and spatially flat universe, which is assumed to be dominated by a phantommore » perfect fluid whose equation of state is a constant. We obtain exact solutions of the WDW equation based on some specific conditions. In more general cases, we propose a qualitative argument with the help of a Wentzel-Kramers-Brillouin (WKB) approximation to get further solutions. Besides, we also construct an effective WDW equation by simply promoting the classical Friedmann equations. We find that for all the approaches considered, the DeWitt condition hinting singularity avoidance is satisfied. Therefore the big rip singularity is expected to be avoided through the quantum approach within the EiBI theory.« less

The quantum realm of the ''Little Sibling'' of the Big Rip singularity

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

Albarran, Imanol; Bouhmadi-López, Mariam; Cabral, Francisco

We analyse the quantum behaviour of the ''Little Sibling'' of the Big Rip singularity (LSBR) [1]. The quantisation is carried within the geometrodynamical approach given by the Wheeler-DeWitt (WDW) equation. The classical model is based on a Friedmann-Lemaître-Robertson-Walker Universe filled by a perfect fluid that can be mapped to a scalar field with phantom character. We analyse the WDW equation in two setups. In the first step, we consider the scale factor as the single degree of freedom, which from a classical perspective parametrises both the geometry and the matter content given by the perfect fluid. We then solve themore » WDW equation within a WKB approximation, for two factor ordering choices. On the second approach, we consider the WDW equation with two degrees of freedom: the scale factor and a scalar field. We solve the WDW equation, with the Laplace-Beltrami factor-ordering, using a Born-Oppenheimer approximation. In both approaches, we impose the DeWitt (DW) condition as a potential criterion for singularity avoidance. We conclude that in all the cases analysed the DW condition can be verified, which might be an indication that the LSBR can be avoided or smoothed in the quantum approach.« less

30 CFR 75.607 - Breaking trailing cable and power cable connections.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 30 Mineral Resources 1 2010-07-01 2010-07-01 false Breaking trailing cable and power cable... LABOR COAL MINE SAFETY AND HEALTH MANDATORY SAFETY STANDARDS-UNDERGROUND COAL MINES Trailing Cables § 75.607 Breaking trailing cable and power cable connections. [Statutory Provisions] Trailing cable and...

Bosonic Loop Diagrams as Perturbative Solutions of the Classical Field Equations in ϕ4-Theory

NASA Astrophysics Data System (ADS)

Finster, Felix; Tolksdorf, Jürgen

2012-05-01

Solutions of the classical ϕ4-theory in Minkowski space-time are analyzed in a perturbation expansion in the nonlinearity. Using the language of Feynman diagrams, the solution of the Cauchy problem is expressed in terms of tree diagrams which involve the retarded Green's function and have one outgoing leg. In order to obtain general tree diagrams, we set up a "classical measurement process" in which a virtual observer of a scattering experiment modifies the field and detects suitable energy differences. By adding a classical stochastic background field, we even obtain all loop diagrams. The expansions are compared with the standard Feynman diagrams of the corresponding quantum field theory.

The Reliability and Precision of Total Scores and IRT Estimates as a Function of Polytomous IRT Parameters and Latent Trait Distribution

ERIC Educational Resources Information Center

Culpepper, Steven Andrew

2013-01-01

A classic topic in the fields of psychometrics and measurement has been the impact of the number of scale categories on test score reliability. This study builds on previous research by further articulating the relationship between item response theory (IRT) and classical test theory (CTT). Equations are presented for comparing the reliability and…

Chemical Potential for the Interacting Classical Gas and the Ideal Quantum Gas Obeying a Generalized Exclusion Principle

ERIC Educational Resources Information Center

Sevilla, F. J.; Olivares-Quiroz, L.

2012-01-01

In this work, we address the concept of the chemical potential [mu] in classical and quantum gases towards the calculation of the equation of state [mu] = [mu](n, T) where n is the particle density and "T" the absolute temperature using the methods of equilibrium statistical mechanics. Two cases seldom discussed in elementary textbooks are…

Quantum propagation in single mode fiber

NASA Technical Reports Server (NTRS)

Joneckis, Lance G.; Shapiro, Jeffrey H.

1994-01-01

This paper presents a theory for quantum light propagation in a single-mode fiber which includes the effects of the Kerr nonlinearity, group-velocity dispersion, and linear loss. The theory reproduces the results of classical self-phase modulation, quantum four-wave mixing, and classical solution physics, within their respective regions of validity. It demonstrates the crucial role played by the Kerr-effect material time constant, in limiting the quantum phase shifts caused by the broadband zero-point fluctuations that accompany any quantized input field. Operator moment equations - approximated, numerically, via a terminated cumulant expansion - are used to obtain results for homodyne-measurement noise spectra when dispersion is negligible. More complicated forms of these equations can be used to incorporate dispersion into the noise calculations.

The analysis of cable forces based on natural frequency

NASA Astrophysics Data System (ADS)

Suangga, Made; Hidayat, Irpan; Juliastuti; Bontan, Darwin Julius

2017-12-01

A cable is a flexible structural member that is effective at resisting tensile forces. Cables are used in a variety of structures that employ their unique characteristics to create efficient design tension members. The condition of the cable forces in the cable supported structure is an important indication of judging whether the structure is in good condition. Several methods have been developed to measure on site cable forces. Vibration technique using correlation between natural frequency and cable forces is a simple method to determine in situ cable forces, however the method need accurate information on the boundary condition, cable mass, and cable length. The natural frequency of the cable is determined using FFT (Fast Fourier Transform) Technique to the acceleration record of the cable. Based on the natural frequency obtained, the cable forces then can be determine by analytical or by finite element program. This research is focus on the vibration techniques to determine the cable forces, to understand the physical parameter effect of the cable and also modelling techniques to the natural frequency and cable forces.

Causal implications of viscous damping in compressible fluid flows

PubMed

Jordan; Meyer; Puri

2000-12-01

Classically, a compressible, isothermal, viscous fluid is regarded as a mathematical continuum and its motion is governed by the linearized continuity, Navier-Stokes, and state equations. Unfortunately, solutions of this system are of a diffusive nature and hence do not satisfy causality. However, in the case of a half-space of fluid set to motion by a harmonically vibrating plate the classical equation of motion can, under suitable conditions, be approximated by the damped wave equation. Since this equation is hyperbolic, the resulting solutions satisfy causal requirements. In this work the Laplace transform and other analytical and numerical tools are used to investigate this apparent contradiction. To this end the exact solutions, as well as their special and limiting cases, are found and compared for the two models. The effects of the physical parameters on the solutions and associated quantities are also studied. It is shown that propagating wave fronts are only possible under the hyperbolic model and that the concept of phase speed has different meanings in the two formulations. In addition, discontinuities and shock waves are noted and a physical system is modeled under both formulations. Overall, it is shown that the hyperbolic form gives a more realistic description of the physical problem than does the classical theory. Lastly, a simple mechanical analog is given and connections to viscoelastic fluids are noted. In particular, the research presented here supports the notion that linear compressible, isothermal, viscous fluids can, at least in terms of causality, be better characterized as a type of viscoelastic fluid.

On the Analysis of Multistep-Out-of-Grid Method for Celestial Mechanics Tasks

NASA Astrophysics Data System (ADS)

Olifer, L.; Choliy, V.

2016-09-01

Occasionally, there is a necessity in high-accurate prediction of celestial body trajectory. The most common way to do that is to solve Kepler's equation analytically or to use Runge-Kutta or Adams integrators to solve equation of motion numerically. For low-orbit satellites, there is a critical need in accounting geopotential and another forces which influence motion. As the result, the right side of equation of motion becomes much bigger, and classical integrators will not be quite effective. On the other hand, there is a multistep-out-of-grid (MOG) method which combines Runge-Kutta and Adams methods. The MOG method is based on using m on-grid values of the solution and n × m off-grid derivative estimations. Such method could provide stable integrators of maximum possible order, O (hm+mn+n-1). The main subject of this research was to implement and analyze the MOG method for solving satellite equation of motion with taking into account Earth geopotential model (ex. EGM2008 (Pavlis at al., 2008)) and with possibility to add other perturbations such as atmospheric drag or solar radiation pressure. Simulations were made for satellites on low orbit and with various eccentricities (from 0.1 to 0.9). Results of the MOG integrator were compared with results of Runge-Kutta and Adams integrators. It was shown that the MOG method has better accuracy than classical ones of the same order and less right-hand value estimations when is working on high orders. That gives it some advantage over "classical" methods.

Regular black holes from semi-classical down to Planckian size

NASA Astrophysics Data System (ADS)

Spallucci, Euro; Smailagic, Anais

In this paper, we review various models of curvature singularity free black holes (BHs). In the first part of the review, we describe semi-classical solutions of the Einstein equations which, however, contains a “quantum” input through the matter source. We start by reviewing the early model by Bardeen where the metric is regularized by-hand through a short-distance cutoff, which is justified in terms of nonlinear electro-dynamical effects. This toy-model is useful to point-out the common features shared by all regular semi-classical black holes. Then, we solve Einstein equations with a Gaussian source encoding the quantum spread of an elementary particle. We identify, the a priori arbitrary, Gaussian width with the Compton wavelength of the quantum particle. This Compton-Gauss model leads to the estimate of a terminal density that a gravitationally collapsed object can achieve. We identify this density to be the Planck density, and reformulate the Gaussian model assuming this as its peak density. All these models, are physically reliable as long as the BH mass is big enough with respect to the Planck mass. In the truly Planckian regime, the semi-classical approximation breaks down. In this case, a fully quantum BH description is needed. In the last part of this paper, we propose a nongeometrical quantum model of Planckian BHs implementing the Holographic Principle and realizing the “classicalization” scenario recently introduced by Dvali and collaborators. The classical relation between the mass and radius of the BH emerges only in the classical limit, far away from the Planck scale.

Scattering of massless scalar waves by magnetically charged black holes in Einstein-Yang-Mills-Higgs theory

NASA Astrophysics Data System (ADS)

Gußmann, Alexander

2017-03-01

The existence of the classical black hole solutions of the Einstein-Yang-Mills-Higgs equations with non-Abelian Yang-Mills-Higgs hair implies that not all classical stationary magnetically charged black holes can be uniquely described by their asymptotic characteristics. In fact, in a certain domain of parameters, there exist different spherically-symmetric, non-rotating and asymptotically-flat classical black hole solutions of the Einstein-Yang-Mills-Higgs equations which have the same ADM mass and the same magnetic charge but significantly different geometries in the near-horizon regions. (These are black hole solutions which are described by a Reissner-Nordström metric on the one hand and the black hole solutions with non-Abelian Yang-Mills-Higgs hair which are described by a metric which is not of Reissner-Nordström form on the other hand). One can experimentally distinguish such black holes with the same asymptotic characteristics but different near-horizon geometries classically by probing the near-horizon regions of the black holes. We argue that one way to probe the near-horizon region of a black hole which allows one to distinguish magnetically charged black holes with the same asymptotic characteristics but different near-horizon geometries is by classical scattering of waves. Using the example of a minimally-coupled massless probe scalar field scattered by magnetically charged black holes which can be obtained as solutions of the Einstein-Yang-Mills-Higgs equations with a Higgs triplet and gauge group SU(2) in the limit of an infinite Higgs self-coupling constant we show how, in this case, the scattering cross sections differ for the magnetically charged black holes with different near-horizon geometries but the same asymptotic characteristics. We find in particular that the characteristic glory peaks in the cross sections are located at different scattering angles.

Thermodynamics of an Attractive 2D Fermi Gas

NASA Astrophysics Data System (ADS)

Fenech, K.; Dyke, P.; Peppler, T.; Lingham, M. G.; Hoinka, S.; Hu, H.; Vale, C. J.

2016-01-01

Thermodynamic properties of matter are conveniently expressed as functional relations between variables known as equations of state. Here we experimentally determine the compressibility, density, and pressure equations of state for an attractive 2D Fermi gas in the normal phase as a function of temperature and interaction strength. In 2D, interacting gases exhibit qualitatively different features to those found in 3D. This is evident in the normalized density equation of state, which peaks at intermediate densities corresponding to the crossover from classical to quantum behavior.

GL/sub 3/-invariant solutions of the Yang-Baxter equation and associated quantum systems

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

Kulish, P.P.; Reshetikin N.Y.

1986-09-01

GL/sub 3/-invariant, finite-dimensional solutions of the Yang-Baxter equations acting in the tensor product of two irreducible representations of the group GL/sub 3/ are investigated. A number of relations are obtained for the transfer matrices which demonstrate the connection of representation theory and the Bethe Ansatz in GL/sub 3/invariant models. Some of the most interesting quantum and classical integrable systems connected with GL/sub 3/-invariant solutions of the Yang-Baxter equation are presented.

GL/sub 3/-invariant solutions of the Yang-Baxter equation and associated quantum systems

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

Kulish, P.P.; Reshetikhin, N.Yu.

1986-09-10

GL/sub 3/-invariant, finite-dimensional solutions of the Yang-Baxter equations acting in the tensor product of two irreducible representations of the group GL/sub 3/ are investigated. A number of relations are obtained for the transfer matrices which demonstrate the connection of representation theory and the Bethe Ansatz in GL/sub 3/-invariant models. Some of the most interesting quantum and classical integrable systems connected with GL/sub 3/-invariant solutions of the Yang-Baxter equation are presented.

GL/sub 3/-invariant solutions of the Yang-Baxter equation and associated quantum systems

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

Kulish, P.P.; Reshetikhin, N.Yu.

1987-05-20

The authors investigate the GL/sub 3/-invariant finite-dimensional solutions of the Yang-Baxter equation acting in the tensor product of two irreducible representations of the GL/sub 3/ group. Relationships obtained for the transfer matrices demonstrate the link between representation theory and the Bethe ansatz in GL/sub 3/-invariant models. Some examples of quantum and classical integrable systems associated with GL/sub 3/-invariant solutions of the Yang-Baxter equation are given.

Simulation of quantum dynamics based on the quantum stochastic differential equation.

PubMed

Li, Ming

2013-01-01

The quantum stochastic differential equation derived from the Lindblad form quantum master equation is investigated. The general formulation in terms of environment operators representing the quantum state diffusion is given. The numerical simulation algorithm of stochastic process of direct photodetection of a driven two-level system for the predictions of the dynamical behavior is proposed. The effectiveness and superiority of the algorithm are verified by the performance analysis of the accuracy and the computational cost in comparison with the classical Runge-Kutta algorithm.

Numerical integration of asymptotic solutions of ordinary differential equations

NASA Technical Reports Server (NTRS)

Thurston, Gaylen A.

1989-01-01

Classical asymptotic analysis of ordinary differential equations derives approximate solutions that are numerically stable. However, the analysis also leads to tedious expansions in powers of the relevant parameter for a particular problem. The expansions are replaced with integrals that can be evaluated by numerical integration. The resulting numerical solutions retain the linear independence that is the main advantage of asymptotic solutions. Examples, including the Falkner-Skan equation from laminar boundary layer theory, illustrate the method of asymptotic analysis with numerical integration.

Applications of Multiconductor Transmission Line Theory to the Prediction of Cable Coupling. Volume 6. A Digital Computer Program for Determining Terminal Currents Induced in a Multiconductor Transmission Line by an Incident Electromagnetic Field

DTIC Science & Technology

1978-02-01

115 6.1.3 Comparison of the Two Solutions -------------------- 131 6.2 Example II...the nonuniform field specification option. - -------------- 149 A-I Illustration of common mode and differential mode currents...Ax subsection in Figure 2-2 in the limit as Ax+0 as a set of 2n coupled, complex, ordinary differential equations [1], V(x) + JwLI(x) = Vs(x) (2-1a) l

Analytical and numerical solutions of the equation for the beam propagation in a photovoltaic-photorefractive media

NASA Astrophysics Data System (ADS)

Lin, Ji; Wang, Hou

2013-07-01

We use the classical Lie-group method to study the evolution equation describing a photovoltaic-photorefractive media with the effects of diffusion process and the external electric field. We reduce it to some similarity equations firstly, and then obtain some analytically exact solutions including the soliton solution, the exponential solution and the oscillatory solution. We also obtain the numeric solitons from these similarity equations. Moreover, We show theoretically that these solutions have two types of trajectories. One type is a straight line. The other is a parabolic curve, which indicates these solitons have self-deflection.

Orientation of doubly rotated quartz plates.

PubMed

Sherman, J R

1989-01-01

A derivation from classical spherical trigonometry of equations to compute the orientation of doubly-rotated quartz blanks from Bragg X-ray data is discussed. These are usually derived by compact and efficient vector methods, which are reviewed briefly. They are solved by generating a quadratic equation with numerical coefficients. Two methods exist for performing the computation from measurements against two planes: a direct solution by a quadratic equation and a process of convergent iteration. Both have a spurious solution. Measurement against three lattice planes yields a set of three linear equations the solution of which is an unambiguous result.

The inverse problem of using the information of historical data to estimate model errors is one of the science frontier research topics. In this study, we investigate such a problem using the classic Lorenz (1963) equation as a prediction model.

NASA Astrophysics Data System (ADS)

Wan, S.; He, W.

2016-12-01

The inverse problem of using the information of historical data to estimate model errors is one of the science frontier research topics. In this study, we investigate such a problem using the classic Lorenz (1963) equation as a prediction model and the Lorenz equation with a periodic evolutionary function as an accurate representation of reality to generate "observational data." On the basis of the intelligent features of evolutionary modeling (EM), including self-organization, self-adaptive and self-learning, the dynamic information contained in the historical data can be identified and extracted by computer automatically. Thereby, a new approach is proposed to estimate model errors based on EM in the present paper. Numerical tests demonstrate the ability of the new approach to correct model structural errors. In fact, it can actualize the combination of the statistics and dynamics to certain extent.

Efficient solution of the Wigner-Liouville equation using a spectral decomposition of the force field

NASA Astrophysics Data System (ADS)

Van de Put, Maarten L.; Sorée, Bart; Magnus, Wim

2017-12-01

The Wigner-Liouville equation is reformulated using a spectral decomposition of the classical force field instead of the potential energy. The latter is shown to simplify the Wigner-Liouville kernel both conceptually and numerically as the spectral force Wigner-Liouville equation avoids the numerical evaluation of the highly oscillatory Wigner kernel which is nonlocal in both position and momentum. The quantum mechanical evolution is instead governed by a term local in space and non-local in momentum, where the non-locality in momentum has only a limited range. An interpretation of the time evolution in terms of two processes is presented; a classical evolution under the influence of the averaged driving field, and a probability-preserving quantum-mechanical generation and annihilation term. Using the inherent stability and reduced complexity, a direct deterministic numerical implementation using Chebyshev and Fourier pseudo-spectral methods is detailed. For the purpose of illustration, we present results for the time-evolution of a one-dimensional resonant tunneling diode driven out of equilibrium.

Exhaustive Classification of the Invariant Solutions for a Specific Nonlinear Model Describing Near Planar and Marginally Long-Wave Unstable Interfaces for Phase Transition

NASA Astrophysics Data System (ADS)

Ahangari, Fatemeh

2018-05-01

Problems of thermodynamic phase transition originate inherently in solidification, combustion and various other significant fields. If the transition region among two locally stable phases is adequately narrow, the dynamics can be modeled by an interface motion. This paper is devoted to exhaustive analysis of the invariant solutions for a modified Kuramoto-Sivashinsky equation in two spatial and one temporal dimensions is presented. This nonlinear partial differential equation asymptotically characterizes near planar interfaces, which are marginally long-wave unstable. For this purpose, by applying the classical symmetry method for this model the classical symmetry operators are attained. Moreover, the structure of the Lie algebra of symmetries is discussed and the optimal system of subalgebras, which yields the preliminary classification of group invariant solutions is constructed. Mainly, the Lie invariants corresponding to the infinitesimal symmetry generators as well as associated similarity reduced equations are also pointed out. Furthermore, the nonclassical symmetries of this nonlinear PDE are also comprehensively investigated.

A many-body states picture of electronic friction: The case of multiple orbitals and multiple electronic states

NASA Astrophysics Data System (ADS)

Dou, Wenjie; Subotnik, Joseph E.

2016-08-01

We present a very general form of electronic friction as present when a molecule with multiple orbitals hybridizes with a metal electrode. To develop this picture of friction, we embed the quantum-classical Liouville equation (QCLE) within a classical master equation (CME). Thus, this article extends our previous work analyzing the case of one electronic level, as we may now treat the case of multiple levels and many electronic molecular states. We show that, in the adiabatic limit, where electron transitions are much faster than nuclear motion, the QCLE-CME reduces to a Fokker-Planck equation, such that nuclei feel an average force as well as friction and a random force—as caused by their interaction with the metallic electrons. Finally, we show numerically and analytically that our frictional results agree with other published results calculated using non-equilibrium Green's functions. Numerical recipes for solving this QCLE-CME will be provided in a subsequent paper.

A many-body states picture of electronic friction: The case of multiple orbitals and multiple electronic states

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

Dou, Wenjie; Subotnik, Joseph E.

We present a very general form of electronic friction as present when a molecule with multiple orbitals hybridizes with a metal electrode. To develop this picture of friction, we embed the quantum-classical Liouville equation (QCLE) within a classical master equation (CME). Thus, this article extends our previous work analyzing the case of one electronic level, as we may now treat the case of multiple levels and many electronic molecular states. We show that, in the adiabatic limit, where electron transitions are much faster than nuclear motion, the QCLE-CME reduces to a Fokker-Planck equation, such that nuclei feel an average forcemore » as well as friction and a random force—as caused by their interaction with the metallic electrons. Finally, we show numerically and analytically that our frictional results agree with other published results calculated using non-equilibrium Green’s functions. Numerical recipes for solving this QCLE-CME will be provided in a subsequent paper.« less

The equation of motion for a radiating charged particle without self-interaction term

NASA Astrophysics Data System (ADS)

Herrera, L.

1990-03-01

The motion of a radiating charged particle is studied from the point of view of relativistic classical mechanics. Thus, the resulting equation of motion emerges from equating the total rate of change of momentum to the external force, without the introduction of a “self-force” term. Doing so, one is forced to abandon either one, or both, of the following restrictions: (a) the external force is non-dissipative, (b) the proper mass of the particle is constant. By abandoning (a) we obtain the Mo and Papas equation of motion, whereas allowing variations in the proper mass one is led, uniquely, to the Bonnor equation. A new equation of motion is proposed by abandoning both (a) and (b).

Quantum spatial propagation of squeezed light in a degenerate parametric amplifier

NASA Technical Reports Server (NTRS)

Deutsch, Ivan H.; Garrison, John C.

1992-01-01

Differential equations which describe the steady state spatial evolution of nonclassical light are established using standard quantum field theoretic techniques. A Schroedinger equation for the state vector of the optical field is derived using the quantum analog of the slowly varying envelope approximation (SVEA). The steady state solutions are those that satisfy the time independent Schroedinger equation. The resulting eigenvalue problem then leads to the spatial propagation equations. For the degenerate parametric amplifier this method shows that the squeezing parameter obey nonlinear differential equations coupled by the amplifier gain and phase mismatch. The solution to these differential equations is equivalent to one obtained from the classical three wave mixing steady state solution to the parametric amplifier with a nondepleted pump.

Factorization and the synthesis of optimal feedback kernels for differential-delay systems

NASA Technical Reports Server (NTRS)

Milman, Mark M.; Scheid, Robert E.

1987-01-01

A combination of ideas from the theories of operator Riccati equations and Volterra factorizations leads to the derivation of a novel, relatively simple set of hyperbolic equations which characterize the optimal feedback kernel for the finite-time regulator problem for autonomous differential-delay systems. Analysis of these equations elucidates the underlying structure of the feedback kernel and leads to the development of fast and accurate numerical methods for its computation. Unlike traditional formulations based on the operator Riccati equation, the gain is characterized by means of classical solutions of the derived set of equations. This leads to the development of approximation schemes which are analogous to what has been accomplished for systems of ordinary differential equations with given initial conditions.

On the use of the GRACE normal equation of inter-satellite tracking data for estimation of soil moisture and groundwater in Australia

NASA Astrophysics Data System (ADS)

Tangdamrongsub, Natthachet; Han, Shin-Chan; Decker, Mark; Yeo, In-Young; Kim, Hyungjun

2018-03-01

An accurate estimation of soil moisture and groundwater is essential for monitoring the availability of water supply in domestic and agricultural sectors. In order to improve the water storage estimates, previous studies assimilated terrestrial water storage variation (ΔTWS) derived from the Gravity Recovery and Climate Experiment (GRACE) into land surface models (LSMs). However, the GRACE-derived ΔTWS was generally computed from the high-level products (e.g. time-variable gravity fields, i.e. level 2, and land grid from the level 3 product). The gridded data products are subjected to several drawbacks such as signal attenuation and/or distortion caused by a posteriori filters and a lack of error covariance information. The post-processing of GRACE data might lead to the undesired alteration of the signal and its statistical property. This study uses the GRACE least-squares normal equation data to exploit the GRACE information rigorously and negate these limitations. Our approach combines GRACE's least-squares normal equation (obtained from ITSG-Grace2016 product) with the results from the Community Atmosphere Biosphere Land Exchange (CABLE) model to improve soil moisture and groundwater estimates. This study demonstrates, for the first time, an importance of using the GRACE raw data. The GRACE-combined (GC) approach is developed for optimal least-squares combination and the approach is applied to estimate the soil moisture and groundwater over 10 Australian river basins. The results are validated against the satellite soil moisture observation and the in situ groundwater data. Comparing to CABLE, we demonstrate the GC approach delivers evident improvement of water storage estimates, consistently from all basins, yielding better agreement on seasonal and inter-annual timescales. Significant improvement is found in groundwater storage while marginal improvement is observed in surface soil moisture estimates.

Theory and practice of solving ordinary differential equations (ODEs). [Runge-Kutta method; lectures in Spanish

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

Shampine, L.F.

1978-04-01

Between January 23 and 27, 1978, several lectures were presented at the Instituto de Investigaciones en Matematicas Aplicadas y en Sistemas, National University of Mexico, Mexico City. The author concentrated on the Runge--Kutta method of solving differential equations because its details are simple and it is illustrative of classical perturbation and asymptotic methods.

Mixed quantum/classical theory of rotationally and vibrationally inelastic scattering in space-fixed and body-fixed reference frames

NASA Astrophysics Data System (ADS)

Semenov, Alexander; Babikov, Dmitri

2013-11-01

We formulated the mixed quantum/classical theory for rotationally and vibrationally inelastic scattering process in the diatomic molecule + atom system. Two versions of theory are presented, first in the space-fixed and second in the body-fixed reference frame. First version is easy to derive and the resultant equations of motion are transparent, but the state-to-state transition matrix is complex-valued and dense. Such calculations may be computationally demanding for heavier molecules and/or higher temperatures, when the number of accessible channels becomes large. In contrast, the second version of theory requires some tedious derivations and the final equations of motion are rather complicated (not particularly intuitive). However, the state-to-state transitions are driven by real-valued sparse matrixes of much smaller size. Thus, this formulation is the method of choice from the computational point of view, while the space-fixed formulation can serve as a test of the body-fixed equations of motion, and the code. Rigorous numerical tests were carried out for a model system to ensure that all equations, matrixes, and computer codes in both formulations are correct.

On Entropy Production in the Madelung Fluid and the Role of Bohm's Potential in Classical Diffusion

NASA Astrophysics Data System (ADS)

Heifetz, Eyal; Tsekov, Roumen; Cohen, Eliahu; Nussinov, Zohar

2016-07-01

The Madelung equations map the non-relativistic time-dependent Schrödinger equation into hydrodynamic equations of a virtual fluid. While the von Neumann entropy remains constant, we demonstrate that an increase of the Shannon entropy, associated with this Madelung fluid, is proportional to the expectation value of its velocity divergence. Hence, the Shannon entropy may grow (or decrease) due to an expansion (or compression) of the Madelung fluid. These effects result from the interference between solutions of the Schrödinger equation. Growth of the Shannon entropy due to expansion is common in diffusive processes. However, in the latter the process is irreversible while the processes in the Madelung fluid are always reversible. The relations between interference, compressibility and variation of the Shannon entropy are then examined in several simple examples. Furthermore, we demonstrate that for classical diffusive processes, the "force" accelerating diffusion has the form of the positive gradient of the quantum Bohm potential. Expressing then the diffusion coefficient in terms of the Planck constant reveals the lower bound given by the Heisenberg uncertainty principle in terms of the product between the gas mean free path and the Brownian momentum.

Multiscale modeling and computation of optically manipulated nano devices

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

Bao, Gang, E-mail: baog@zju.edu.cn; Liu, Di, E-mail: richardl@math.msu.edu; Luo, Songting, E-mail: luos@iastate.edu

2016-07-01

We present a multiscale modeling and computational scheme for optical-mechanical responses of nanostructures. The multi-physical nature of the problem is a result of the interaction between the electromagnetic (EM) field, the molecular motion, and the electronic excitation. To balance accuracy and complexity, we adopt the semi-classical approach that the EM field is described classically by the Maxwell equations, and the charged particles follow the Schrödinger equations quantum mechanically. To overcome the numerical challenge of solving the high dimensional multi-component many-body Schrödinger equations, we further simplify the model with the Ehrenfest molecular dynamics to determine the motion of the nuclei, andmore » use the Time-Dependent Current Density Functional Theory (TD-CDFT) to calculate the excitation of the electrons. This leads to a system of coupled equations that computes the electromagnetic field, the nuclear positions, and the electronic current and charge densities simultaneously. In the regime of linear responses, the resonant frequencies initiating the out-of-equilibrium optical-mechanical responses can be formulated as an eigenvalue problem. A self-consistent multiscale method is designed to deal with the well separated space scales. The isomerization of azobenzene is presented as a numerical example.« less

Evaluation of the pentose phosphate pathway from 14CO2 data. Fallibility of a classic equation when applied to non-homogeneous tissues.

PubMed

Larrabee, M G

1990-11-15

A classic equation that has frequently been used to estimate the fraction of glucose metabolized by the pentose phosphate pathway, using 14CO2 data, is more simply re-derived with careful consideration of the assumptions involved and the conditions under which it is applicable. The equation is shown to be unreliable for non-homogeneous tissues, depending on the fraction of triose phosphate converted to CO2. The formula in question is as follows: ([1]CO2/G-[6]CO2/G)/(1-[6]CO2/G) = 3Fmet./(1 + 2Fmet.) where [1]CO2 and [6]CO2 are output rates of carbons 1 and 6 of glucose respectively to CO2, G is the rate of glucose uptake and Fmet. is the fraction of the glucose that is metabolized to CO2 and triose phosphate by the pentose phosphate pathway, allowing for recycling of an appropriate fraction of the fructose-6-phosphate produced by the pathway. This analysis illustrates the importance of suitably testing any equation that assumes homogeneity before application to non-homogeneous tissues.

Numerical Asymptotic Solutions Of Differential Equations

NASA Technical Reports Server (NTRS)

Thurston, Gaylen A.

1992-01-01

Numerical algorithms derived and compared with classical analytical methods. In method, expansions replaced with integrals evaluated numerically. Resulting numerical solutions retain linear independence, main advantage of asymptotic solutions.

Cable and Line Inspection Mechanism

NASA Technical Reports Server (NTRS)

Ross, Terence J. (Inventor)

2003-01-01

An automated cable and line inspection mechanism visually scans the entire surface of a cable as the mechanism travels along the cable=s length. The mechanism includes a drive system, a video camera, a mirror assembly for providing the camera with a 360 degree view of the cable, and a laser micrometer for measuring the cable=s diameter. The drive system includes an electric motor and a plurality of drive wheels and tension wheels for engaging the cable or line to be inspected, and driving the mechanism along the cable. The mirror assembly includes mirrors that are positioned to project multiple images of the cable on the camera lens, each of which is of a different portion of the cable. A data transceiver and a video transmitter are preferably employed for transmission of video images, data and commands between the mechanism and a remote control station.

Cable and line inspection mechanism

NASA Technical Reports Server (NTRS)

Ross, Terence J. (Inventor)

2003-01-01

An automated cable and line inspection mechanism visually scans the entire surface of a cable as the mechanism travels along the cable=s length. The mechanism includes a drive system, a video camera, a mirror assembly for providing the camera with a 360 degree view of the cable, and a laser micrometer for measuring the cable=s diameter. The drive system includes an electric motor and a plurality of drive wheels and tension wheels for engaging the cable or line to be inspected, and driving the mechanism along the cable. The mirror assembly includes mirrors that are positioned to project multiple images of the cable on the camera lens, each of which is of a different portion of the cable. A data transceiver and a video transmitter are preferably employed for transmission of video images, data and commands between the mechanism and a remote control station.

Mechanisms of Cables 1 gene inactivation in human ovarian cancer development.

PubMed

Sakamoto, Hideo; Friel, Anne M; Wood, Antony W; Guo, Lankai; Ilic, Ana; Seiden, Michael V; Chung, Daniel C; Lynch, Maureen P; Serikawa, Takehiro; Munro, Elizabeth; Oliva, Esther; Orsulic, Sandra; Kirley, Sandra D; Foster, Rosemary; Zukerberg, Lawrence R; Rueda, Bo R

2008-02-01

Cables 1, a cyclin-dependent kinase binding protein, is primarily involved in cell cycle regulation. Loss of nuclear Cables 1 expression is observed in human colon, lung and endometrial cancers. We previously reported that loss of nuclear Cables 1 expression was also observed with high frequency in a limited sample set of human ovarian carcinomas, although the mechanisms underlying loss of nuclear Cables 1 expression remained unknown. Our present objective was to examine Cables 1 expression in ovarian cancer in greater detail, and determine the predominant mechanisms of Cables 1 loss. We assessed potential genetic and epigenetic modifications of the Cables 1 locus through analyses of mutation, polymorphisms, loss of heterozygosity and DNA methylation. We observed a marked loss of nuclear Cables 1 expression in serous and endometrioid ovarian carcinomas that correlated with decreased Cables 1 mRNA levels. Although we detected no Cables 1 mutations, there was evidence of LOH at the Cables 1 locus and epigenetic modification of the Cables 1 promoter region in a subset of ovarian carcinomas and established cancer cell lines. From a functional perspective, over-expression of Cables 1 induced apoptosis, whereas, knockdown of Cables 1 negated this effect. Together these findings suggest that multiple mechanisms underlie the loss of Cables 1 expression in ovarian cancer cells, supporting the hypothesis that Cables 1 is a tumor suppressor in human ovarian cancer.

Newton's laws of motion in the form of a Riccati equation.

PubMed

Nowakowski, Marek; Rosu, Haret C

2002-04-01

We discuss two applications of a Riccati equation to Newton's laws of motion. The first one is the motion of a particle under the influence of a power law central potential V(r)=kr(epsilon). For zero total energy we show that the equation of motion can be cast in the Riccati form. We briefly show here an analogy to barotropic Friedmann-Robertson-Lemaitre cosmology where the expansion of the universe can be also shown to obey a Riccati equation. A second application in classical mechanics, where again the Riccati equation appears naturally, are problems involving quadratic friction. We use methods reminiscent to nonrelativistic supersymmetry to generalize and solve such problems.

Center manifolds for a class of degenerate evolution equations and existence of small-amplitude kinetic shocks

NASA Astrophysics Data System (ADS)

Pogan, Alin; Zumbrun, Kevin

2018-06-01

We construct center manifolds for a class of degenerate evolution equations including the steady Boltzmann equation and related kinetic models, establishing in the process existence and behavior of small-amplitude kinetic shock and boundary layers. Notably, for Boltzmann's equation, we show that elements of the center manifold decay in velocity at near-Maxwellian rate, in accord with the formal Chapman-Enskog picture of near-equilibrium flow as evolution along the manifold of Maxwellian states, or Grad moment approximation via Hermite polynomials in velocity. Our analysis is from a classical dynamical systems point of view, with a number of interesting modifications to accommodate ill-posedness of the underlying evolution equation.

Introduction to Physical Intelligence

NASA Technical Reports Server (NTRS)

Zak, Michail

2011-01-01

A slight deviation from Newtonian dynamics can lead to new effects associated with the concept of physical intelligence. Non-Newtonian effects such as deviation from classical thermodynamic as well as quantum-like properties have been analyzed. A self-supervised (intelligent) particle that can escape from Brownian motion autonomously is introduced. Such a capability is due to a coupling of the particle governing equation with its own Liouville equation via an appropriate feedback. As a result, the governing equation is self-stabilized, and random oscillations are suppressed, while the Liouville equation takes the form of the Fokker-Planck equation with negative diffusion. Non- Newtonian properties of such a dynamical system as well as thermodynamical implications have been evaluated.

The 2006 Pingtung Earthquake Doublet Triggered Seafloor Liquefaction: Revisiting the Evidence with Ultra-High-Resolution Seafloor Mapping

NASA Astrophysics Data System (ADS)

Su, C. C.; Chen, T. T.; Paull, C. K.; Gwiazda, R.; Chen, Y. H.; Lundsten, E. M.; Caress, D. W.; Hsu, H. H.; Liu, C. S.

2017-12-01

Since Heezen and Ewing's (1952) classic work on the 1929 Grand Banks earthquake, the damage of submarine cables have provided critical information on the nature of seafloor mass movements or sediment density flows. However, the understanding of the local conditions that lead to particular seafloor failures earthquakes trigger is still unclear. The Decemeber 26, 2006 Pingtung earthquake doublet which occurred offshore of Fangliao Township, southwestern Taiwan damaged 14 submarine cables between Gaoping slope to the northern terminus of the Manila Trench. Local fisherman reported disturbed waters at the head of the Fangliao submarine canyon, which lead to conjectures that eruptions of mud volcanoes which are common off the southwestern Taiwan. Geophysical survey were conducted to evaluate this area which revealed a series of faults, liquefied strata, pockmarks and acoustically transparent sediments with doming structures which may relate to the submarine groundwater discharge. Moreover, shipboard multi-beam bathymetric survey which was conducted at the east of Fangliao submarine canyon head shows over 10 km2 area with maximum depth around 40 m of seafloor subsidence after Pingtung earthquake. The north end of the subsidence is connected to the Fangliao submarine canyon where the first cable failed after Pingtung earthquake. The evidences suggests the earthquake triggered widespeard liquefaction and generated debris flows within Fangliao submarine canyon. In May 2017, an IONTU-MBARI Joint Survey Cruise (OR1-1163) was conducted on using MBARI Mapping AUV and miniROV to revisit the area where the cable damaged after Pingtung earthquake. From newly collected ultra-high-resolution (1-m lateral resolution) bathymetry data, the stair-stepped morphology is observed at the edge of canyon. The comet-shaped depressions are located along the main headwall of the seafloor failure. The new detailed bathymetry reveal details which suggest Fangliao submarine canyon head is preconditioned to failure. Submarine groundwater discharge from the Pingtung Plain and the southern tip of the Central Mountains is inferred to generate elevated pore pressures leaving the area susceptible to liquefaction and failure when triggered by earthquakes.

Panel summary report

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

Gutjahr, A.L.; Kincaid, C.T.; Mercer, J.W.

1987-04-01

The objective of this report is to summarize the various modeling approaches that were used to simulate solute transport in a variably saturated emission. In particular, the technical strengths and weaknesses of each approach are discussed, and conclusions and recommendations for future studies are made. Five models are considered: (1) one-dimensional analytical and semianalytical solutions of the classical deterministic convection-dispersion equation (van Genuchten, Parker, and Kool, this report ); (2) one-dimensional simulation using a continuous-time Markov process (Knighton and Wagenet, this report); (3) one-dimensional simulation using the time domain method and the frequency domain method (Duffy and Al-Hassan, this report);more » (4) one-dimensional numerical approach that combines a solution of the classical deterministic convection-dispersion equation with a chemical equilibrium speciation model (Cederberg, this report); and (5) three-dimensional numerical solution of the classical deterministic convection-dispersion equation (Huyakorn, Jones, Parker, Wadsworth, and White, this report). As part of the discussion, the input data and modeling results are summarized. The models were used in a data analysis mode, as opposed to a predictive mode. Thus, the following discussion will concentrate on the data analysis aspects of model use. Also, all the approaches were similar in that they were based on a convection-dispersion model of solute transport. Each discussion addresses the modeling approaches in the order listed above.« less

Early history of extended irreversible thermodynamics (1953-1983): An exploration beyond local equilibrium and classical transport theory

NASA Astrophysics Data System (ADS)

Lebon, G.; Jou, D.

2015-06-01

This paper gives a historical account of the early years (1953-1983) of extended irreversible thermodynamics (EIT). The salient features of this formalism are to upgrade the thermodynamic fluxes of mass, momentum, energy, and others, to the status of independent variables, and to explore the consistency between generalized transport equations and a generalized version of the second law of thermodynamics. This requires going beyond classical irreversible thermodynamics by redefining entropy and entropy flux. EIT provides deeper foundations, closer relations with microscopic formalisms, a wider spectrum of applications, and a more exciting conceptual appeal to non-equilibrium thermodynamics. We first recall the historical contributions by Maxwell, Cattaneo, and Grad on generalized transport equations. A thermodynamic theory wide enough to cope with such transport equations was independently proposed between 1953 and 1983 by several authors, each emphasizing different kinds of problems. In 1983, the first international meeting on this theory took place in Bellaterra (Barcelona). It provided the opportunity for the various authors to meet together for the first time and to discuss the common points and the specific differences of their previous formulations. From then on, a large amount of applications and theoretical confirmations have emerged. From the historical point of view, the emergence of EIT has been an opportunity to revisit the foundations and to open new avenues in thermodynamics, one of the most classical and well consolidated physical theories.

Development of inspection robots for bridge cables.

PubMed

Yun, Hae-Bum; Kim, Se-Hoon; Wu, Liuliu; Lee, Jong-Jae

2013-01-01

This paper presents the bridge cable inspection robot developed in Korea. Two types of the cable inspection robots were developed for cable-suspension bridges and cable-stayed bridge. The design of the robot system and performance of the NDT techniques associated with the cable inspection robot are discussed. A review on recent advances in emerging robot-based inspection technologies for bridge cables and current bridge cable inspection methods is also presented.

Linear and angular coherence momenta in the classical second-order coherence theory of vector electromagnetic fields.

PubMed

Wang, Wei; Takeda, Mitsuo

2006-09-01

A new concept of vector and tensor densities is introduced into the general coherence theory of vector electromagnetic fields that is based on energy and energy-flow coherence tensors. Related coherence conservation laws are presented in the form of continuity equations that provide new insights into the propagation of second-order correlation tensors associated with stationary random classical electromagnetic fields.

Calculations, and comparison with an ideal minimum, of trimmed drag for conventional and canard configurations having various levels of static stability

NASA Technical Reports Server (NTRS)

Mclaughlin, M. D.

1977-01-01

Classical drag equations were used to calculate total and induced drag and ratios of stabilizer lift to wing lift for a variety of conventional and canard configurations. The Flight efficiencies of such configurations that are trimmed in pitch and have various values of static margin are evaluated. Classical calculation methods are compared with more modern lifting surface theory.

Quantum cosmology of a Bianchi III LRS geometry coupled to a source free electromagnetic field

NASA Astrophysics Data System (ADS)

Karagiorgos, A.; Pailas, T.; Dimakis, N.; Terzis, Petros A.; Christodoulakis, T.

2018-03-01

We consider a Bianchi type III axisymmetric geometry in the presence of an electromagnetic field. A first result at the classical level is that the symmetry of the geometry need not be applied on the electromagnetic tensor Fμν the algebraic restrictions, implied by the Einstein field equations to the stress energy tensor Tμν, suffice to reduce the general Fμν to the appropriate form. The classical solution thus found contains a time dependent electric and a constant magnetic charge. The solution is also reachable from the corresponding mini-superspace action, which is strikingly similar to the Reissner-Nordstr{öm one. This points to a connection between the black hole geometry and the cosmological solution here found, which is the analog of the known correlation between the Schwarzschild and the Kantowski-Sachs metrics. The configuration space is drastically modified by the presence of the magnetic charge from a 3D flat to a 3D pp wave geometry. We map the emerging linear and quadratic classical integrals of motion, to quantum observables. Along with the Wheeler-DeWitt equation these observables provide unique, up to constants, wave functions. The employment of a Bohmian interpretation of these quantum states results in deterministic (semi-classical) geometries most of which are singularity free.

Classical and quantum simulations of warm dense carbon

NASA Astrophysics Data System (ADS)

Whitley, Heather; Sanchez, David; Hamel, Sebastien; Correa, Alfredo; Benedict, Lorin

We have applied classical and DFT-based molecular dynamics (MD) simulations to study the equation of state of carbon in the warm dense matter regime (ρ = 3.7 g/cc, 0.86 eV

Environmental Impact of a Submarine Cable: Case Study of the Acoustic Thermometry of Ocean Climate (ATOC)/ Pioneer Seamount Cable

NASA Astrophysics Data System (ADS)

Kogan, I.; Paull, C. K.; Kuhnz, L.; von Thun, S.; Burton, E.; Greene, H. G.; Barry, J. P.

2003-12-01

To better understand the potential impacts of the presence of cables on the seabed, a topic of interest for which little data is published or publicly available, a study of the environmental impacts of the ATOC/Pioneer Seamount cable was conducted. The 95 km long, submarine, coaxial cable extends between Pioneer Seamount and the Pillar Point Air Force Station in Half Moon Bay, California. Approximately two thirds of the cable lies within the Monterey Bay National Marine Sanctuary. The cable is permitted to NOAA- Oceanic and Atmospheric Research for transmitting data from a hydrophone array on Pioneer Seamount to shore. The cable was installed unburied on the seafloor in 1995. The cable path crosses the continental shelf, descends to a maximum depth of 1,933 m, and climbs back upslope to 998 m depth near the crest of Pioneer Seamount. A total of 42 hours of video and 152 push cores were collected in 10 stations along cable and control transects using the ROVs Ventana and Tiburon equipped with cable-tracking tools. The condition of the cable, its effect on the seafloor, and distribution of benthic megafauna and infauna were determined. Video data indicated the nature of interaction between the cable and the seafloor. Rocky nearshore areas, where wave energies are greatest, showed the clearest evidence of impact. Here, evidence of abrasion included frayed and unraveling portions of the cable's armor and vertical grooves in the rock apparently cut by the cable. The greatest incision and armor damage occurred on ledges between spans in irregular rock outcrop areas. Unlike the nearshore rocky region, neither the rocks nor the cable appeared damaged along outcrops on Pioneer Seamount. Multiple loops of slack cable added during a 1997 cable repair operation were found lying flat on the seafloor. Several sharp kinks in the cable were seen at 240 m water depths in an area subjected to intense trawling activity. Most of the cable has become buried with time in sediment substrates on the continental shelf whereas much of the cable remains exposed in sediments at deeper depths. The cable is exposed in rocky environments of the nearshore region and on all of Pioneer Seamount. The main biological features associated with the cable were organisms utilizing the cable as substrate and occasionally as shelter. Considerable care was taken to count megafauna in video transects and macrofauna from the top 5 cm of push cores. Few differences were found between cable and control sites at the 95% confidence level. Anemones Metridium farcimen and Stomphia sp. colonized the cable and were more abundant in cable transects at most soft sediment sites. Coarse extrapolation of the transect data suggest that more than 5,000 M. farcimen may live on the continental shelf portion of the cable. Several other species of anemones living on the cable are common along deeper sections of the cable route. Where the cable was buried, the presence of linear rows of sea anemones proved to be a reliable indicator of the cable's position. Flatfish and rockfish apparently congregate near the cable and were as much as 1 order of magnitude more abundant near the cable at some sites.

30 CFR 75.827 - Guarding of trailing cables.

Code of Federal Regulations, 2012 CFR

2012-07-01

... grounded metal. (b) Suspended cables and cable crossovers. When equipment must cross any portion of the cable, the cable must be either: (1) Suspended from the mine roof; or (2) Protected by a cable crossover...

30 CFR 75.827 - Guarding of trailing cables.

Code of Federal Regulations, 2014 CFR

2014-07-01

... grounded metal. (b) Suspended cables and cable crossovers. When equipment must cross any portion of the cable, the cable must be either: (1) Suspended from the mine roof; or (2) Protected by a cable crossover...

30 CFR 75.827 - Guarding of trailing cables.

Code of Federal Regulations, 2011 CFR

2011-07-01

... grounded metal. (b) Suspended cables and cable crossovers. When equipment must cross any portion of the cable, the cable must be either: (1) Suspended from the mine roof; or (2) Protected by a cable crossover...

30 CFR 75.827 - Guarding of trailing cables.

Code of Federal Regulations, 2013 CFR

2013-07-01

... grounded metal. (b) Suspended cables and cable crossovers. When equipment must cross any portion of the cable, the cable must be either: (1) Suspended from the mine roof; or (2) Protected by a cable crossover...

47 CFR 76.802 - Disposition of cable home wiring.

Code of Federal Regulations, 2013 CFR

2013-10-01

... 47 Telecommunication 4 2013-10-01 2013-10-01 false Disposition of cable home wiring. 76.802... MULTICHANNEL VIDEO AND CABLE TELEVISION SERVICE Cable Inside Wiring § 76.802 Disposition of cable home wiring... cable operator shall not remove the cable home wiring unless it gives the subscriber the opportunity to...

47 CFR 76.802 - Disposition of cable home wiring.

Code of Federal Regulations, 2014 CFR

2014-10-01

... 47 Telecommunication 4 2014-10-01 2014-10-01 false Disposition of cable home wiring. 76.802... MULTICHANNEL VIDEO AND CABLE TELEVISION SERVICE Cable Inside Wiring § 76.802 Disposition of cable home wiring... cable operator shall not remove the cable home wiring unless it gives the subscriber the opportunity to...

47 CFR 76.802 - Disposition of cable home wiring.

Code of Federal Regulations, 2011 CFR

2011-10-01

... 47 Telecommunication 4 2011-10-01 2011-10-01 false Disposition of cable home wiring. 76.802... MULTICHANNEL VIDEO AND CABLE TELEVISION SERVICE Cable Inside Wiring § 76.802 Disposition of cable home wiring... cable operator shall not remove the cable home wiring unless it gives the subscriber the opportunity to...

47 CFR 76.802 - Disposition of cable home wiring.

Code of Federal Regulations, 2012 CFR

2012-10-01

... 47 Telecommunication 4 2012-10-01 2012-10-01 false Disposition of cable home wiring. 76.802... MULTICHANNEL VIDEO AND CABLE TELEVISION SERVICE Cable Inside Wiring § 76.802 Disposition of cable home wiring... cable operator shall not remove the cable home wiring unless it gives the subscriber the opportunity to...

47 CFR 27.1202 - Cable/BRS cross-ownership.

Code of Federal Regulations, 2014 CFR

2014-10-01

... portion of the franchise area actually served by the cable operator's cable system and the cable operator... franchise area actually served by the cable operator's cable system the cable operator will use the BRS... that no portion of the GSA of the BRS station is within the portion of the franchise area actually...

47 CFR 27.1202 - Cable/BRS cross-ownership.

Code of Federal Regulations, 2011 CFR

2011-10-01

... portion of the franchise area actually served by the cable operator's cable system and the cable operator... franchise area actually served by the cable operator's cable system the cable operator will use the BRS... that no portion of the GSA of the BRS station is within the portion of the franchise area actually...

47 CFR 27.1202 - Cable/BRS cross-ownership.

Code of Federal Regulations, 2012 CFR

2012-10-01

... portion of the franchise area actually served by the cable operator's cable system and the cable operator... franchise area actually served by the cable operator's cable system the cable operator will use the BRS... that no portion of the GSA of the BRS station is within the portion of the franchise area actually...

47 CFR 27.1202 - Cable/BRS cross-ownership.

Code of Federal Regulations, 2013 CFR

2013-10-01

... portion of the franchise area actually served by the cable operator's cable system and the cable operator... franchise area actually served by the cable operator's cable system the cable operator will use the BRS... that no portion of the GSA of the BRS station is within the portion of the franchise area actually...

Experimental Measurements and Comparison of Cable Performance for Mine Hunting Applications

NASA Astrophysics Data System (ADS)

Mangum, Katherine

2005-11-01

The Naval Surface Warfare Center (NSWCCD) conducted testing of multiple faired synthetic cables in the High Speed Basin in April, 2005. The objective of the test was to determine the hydrodynamic characteristics of bare cables, ribbon faired cables, and cables with extruded plastic ``strakes.'' Faired cables are used to gain on-station time and improve performance of the MH-60 Helicopter when towing mine hunting vehicles. Drag and strum were compared for all cases. Strum was quantified by computing standard deviations of lateral cable acceleration amplitudes. Drag coefficients were calculated using cable tension and angle readings. While the straked cables strummed less than the bare synthetic cable, they did not reduce strum levels as well as ribbon fairing at steep cable angles for speeds of 10, 15, 20 and 25 knots. The drag coefficient of the straked cables was calculated to be higher than that of a bare cable, although further testing is needed to determine an exact number.

Structural design and static analysis of a double-ring deployable truss for mesh antennas

NASA Astrophysics Data System (ADS)

Xu, Yan; Guan, Fuling; Chen, Jianjun; Zheng, Yao

2012-12-01

This paper addresses the structural design, the deployment control design, the static analysis and the model testing of a new double-ring deployable truss that is intended for large mesh antennas. This deployable truss is a multi-DOF (degree-of-freedom), over-constrained mechanism. Two kinds of deployable basic elements were introduced, as well as a process to synthesise the structure of the deployable truss. The geometric equations were formulated to determine the length of each strut, including the effects of the joint size. A DOF evaluation showed that the mechanism requires two active cables and requires deployment control. An open-loop control system was designed to control the rotational velocities of two motors. The structural stiffness of the truss was assessed by static analysis that considered the effects of the constraint condition and the pre-stress of the passive cables. A 4.2-metre demonstration model of an antenna was designed and fabricated. The geometry and the deployment behaviour of the double-ring truss were validated by the experiments using this model.

Development of Inspection Robots for Bridge Cables

PubMed Central

Kim, Se-Hoon; Lee, Jong-Jae

2013-01-01

This paper presents the bridge cable inspection robot developed in Korea. Two types of the cable inspection robots were developed for cable-suspension bridges and cable-stayed bridge. The design of the robot system and performance of the NDT techniques associated with the cable inspection robot are discussed. A review on recent advances in emerging robot-based inspection technologies for bridge cables and current bridge cable inspection methods is also presented. PMID:24459453

Gravitational self-interactions of a degenerate quantum scalar field

NASA Astrophysics Data System (ADS)

Chakrabarty, Sankha S.; Enomoto, Seishi; Han, Yaqi; Sikivie, Pierre; Todarello, Elisa M.

2018-02-01

We develop a formalism to help calculate in quantum field theory the departures from the description of a system by classical field equations. We apply the formalism to a homogeneous condensate with attractive contact interactions and to a homogeneous self-gravitating condensate in critical expansion. In their classical descriptions, such condensates persist forever. We show that in their quantum description, parametric resonance causes quanta to jump in pairs out of the condensate into all modes with wave vector less than some critical value. We calculate, in each case, the time scale over which the homogeneous condensate is depleted and after which a classical description is invalid. We argue that the duration of classicality of inhomogeneous condensates is shorter than that of homogeneous condensates.

47 CFR 36.153 - Assignment of Cable and Wire Facilities (C&WF) to categories.

Code of Federal Regulations, 2011 CFR

2011-10-01

... 47 Telecommunication 2 2011-10-01 2011-10-01 false Assignment of Cable and Wire Facilities (C&WF... Telecommunications Property Cable and Wire Facilities § 36.153 Assignment of Cable and Wire Facilities (C&WF) to... cable and intrabuilding network cable. Where an entire cable or aerial wire is assignable to one...

47 CFR 36.153 - Assignment of Cable and Wire Facilities (C&WF) to categories.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 47 Telecommunication 2 2010-10-01 2010-10-01 false Assignment of Cable and Wire Facilities (C&WF... Telecommunications Property Cable and Wire Facilities § 36.153 Assignment of Cable and Wire Facilities (C&WF) to... cable and intrabuilding network cable. Where an entire cable or aerial wire is assignable to one...

Damping Estimation from Free Decay Responses of Cables with MR Dampers.

PubMed

Weber, Felix; Distl, Hans

2015-01-01

This paper discusses the damping measurements on cables with real-time controlled MR dampers that were performed on a laboratory scale single strand cable and on cables of the Sutong Bridge, China. The control approach aims at producing amplitude and frequency independent cable damping which is confirmed by the tests. The experimentally obtained cable damping in comparison to the theoretical value due to optimal linear viscous damping reveals that support conditions of the cable anchors, force tracking errors in the actual MR damper force, energy spillover to higher modes, and excitation and sensor cables hanging on the stay cable must be taken into consideration for the interpretation of the identified cable damping values.

Damping Estimation from Free Decay Responses of Cables with MR Dampers

PubMed Central

Weber, Felix; Distl, Hans

2015-01-01

This paper discusses the damping measurements on cables with real-time controlled MR dampers that were performed on a laboratory scale single strand cable and on cables of the Sutong Bridge, China. The control approach aims at producing amplitude and frequency independent cable damping which is confirmed by the tests. The experimentally obtained cable damping in comparison to the theoretical value due to optimal linear viscous damping reveals that support conditions of the cable anchors, force tracking errors in the actual MR damper force, energy spillover to higher modes, and excitation and sensor cables hanging on the stay cable must be taken into consideration for the interpretation of the identified cable damping values. PMID:26167537

Fractional bosonic strings

NASA Astrophysics Data System (ADS)

Diaz, Victor Alfonzo; Giusti, Andrea

2018-03-01

The aim of this paper is to present a simple generalization of bosonic string theory in the framework of the theory of fractional variational problems. Specifically, we present a fractional extension of the Polyakov action, for which we compute the general form of the equations of motion and discuss the connection between the new fractional action and a generalization the Nambu-Goto action. Consequently, we analyze the symmetries of the modified Polyakov action and try to fix the gauge, following the classical procedures. Then we solve the equations of motion in a simplified setting. Finally, we present a Hamiltonian description of the classical fractional bosonic string and introduce the fractional light-cone gauge. It is important to remark that, throughout the whole paper, we thoroughly discuss how to recover the known results as an "integer" limit of the presented model.

Physical interpretation and application of principles of ultrasonic nondestructive evaluation of high-performance materials

NASA Technical Reports Server (NTRS)

Miller, James G.

1990-01-01

An ultrasonic measurement system employed in the experimental interrogation of the anisotropic properties (through the measurement of the elastic stiffness constants) of the uniaxial graphite-epoxy composites is presented. The continuing effort for the development of improved visualization techniques for physical parameters is discussed. The background is set for the understanding and visualization of the relationship between the phase and energy/group velocity for propagation in high-performance anisotropic materials by investigating the general requirements imposed by the classical wave equation. The consequences are considered when the physical parameters of the anisotropic material are inserted into the classical wave equation by a linear elastic model. The relationship is described between the phase velocity and the energy/group velocity three dimensional surfaces through graphical techniques.

Lagrangian dynamics for classical, Brownian, and quantum mechanical particles

NASA Astrophysics Data System (ADS)

Pavon, Michele

1996-07-01

In the framework of Nelson's stochastic mechanics [E. Nelson, Dynamical Theories of Brownian Motion (Princeton University, Princeton, 1967); F. Guerra, Phys. Rep. 77, 263 (1981); E. Nelson, Quantum Fluctuations (Princeton University, Princeton, 1985)] we seek to develop the particle counterpart of the hydrodynamic results of M. Pavon [J. Math. Phys. 36, 6774 (1995); Phys. Lett. A 209, 143 (1995)]. In particular, a first form of Hamilton's principle is established. We show that this variational principle leads to the correct equations of motion for the classical particle, the Brownian particle in thermodynamical equilibrium, and the quantum particle. In the latter case, the critical process q satisfies a stochastic Newton law. We then introduce the momentum process p, and show that the pair (q,p) satisfies canonical-like equations.

Development of iterative techniques for the solution of unsteady compressible viscous flows

NASA Technical Reports Server (NTRS)

Sankar, Lakshmi N.; Hixon, Duane

1992-01-01

The development of efficient iterative solution methods for the numerical solution of two- and three-dimensional compressible Navier-Stokes equations is discussed. Iterative time marching methods have several advantages over classical multi-step explicit time marching schemes, and non-iterative implicit time marching schemes. Iterative schemes have better stability characteristics than non-iterative explicit and implicit schemes. In this work, another approach based on the classical conjugate gradient method, known as the Generalized Minimum Residual (GMRES) algorithm is investigated. The GMRES algorithm has been used in the past by a number of researchers for solving steady viscous and inviscid flow problems. Here, we investigate the suitability of this algorithm for solving the system of non-linear equations that arise in unsteady Navier-Stokes solvers at each time step.

From integrability to conformal symmetry: Bosonic superconformal Toda theories

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

Bo-Yu Hou; Liu Chao

In this paper the authors study the conformal integrable models obtained from conformal reductions of WZNW theory associated with second order constraints. These models are called bosonic superconformal Toda models due to their conformal spectra and their resemblance to the usual Toda theories. From the reduction procedure they get the equations of motion and the linearized Lax equations in a generic Z gradation of the underlying Lie algebra. Then, in the special case of principal gradation, they derive the classical r matrix, fundamental Poisson relation, exchange algebra of chiral operators and find out the classical vertex operators. The result showsmore » that their model is very similar to the ordinary Toda theories in that one can obtain various conformal properties of the model from its integrability.« less

Thermodynamics of an ideal generalized gas: I. Thermodynamic laws.

PubMed

Lavenda, B H

2005-11-01

The equations of state for an ideal relativistic, or generalized, gas, like an ideal quantum gas, are expressed in terms of power laws of the temperature. In contrast to an ideal classical gas, the internal energy is a function of volume at constant temperature, implying that the ideal generalized gas will show either attractive or repulsive interactions. This is a necessary condition in order that the third law be obeyed and for matter to have an electromagnetic origin. The transition from an ideal generalized to a classical gas occurs when the two independent solutions of the subsidiary equation to Lagrange's equation coalesce. The equation of state relating the pressure to the internal energy encompasses the full range of cosmological scenarios, from the radiation to the matter dominated universes and finally to the vacuum energy, enabling the coefficient of proportionality, analogous to the Grüeisen ratio, to be interpreted in terms of the degrees of freedom related to the temperature exponents of the internal energy and the absolute temperature expressed in terms of a power of the empirical temperature. The limit where these exponents merge is shown to be the ideal classical gas limit. A corollary to Carnot's theorem is proved, asserting that the ratio of the work done over a cycle to the heat absorbed to increase the temperature at constant volume is the same for all bodies at the same volume. As power means, the energy and entropy are incomparable, and a new adiabatic potential is introduced by showing that the volume raised to a characteristic exponent is also the integrating factor for the quantity of heat so that the second law can be based on the property that power means are monotonically increasing functions of their order. The vanishing of the chemical potential in extensive systems implies that energy cannot be transported without matter and is equivalent to the condition that Clapeyron's equation be satisfied.

Comparison study of cable geometries and superconducting tape layouts for high-temperature superconductor cables

NASA Astrophysics Data System (ADS)

Ta, Wurui; Shao, Tianchong; Gao, Yuanwen

2018-04-01

High-temperature superconductor (HTS) rare-earth-barium-copper-oxide (REBCO) tapes are very promising for use in high-current cables. The cable geometry and the layout of the superconducting tapes are directly related to the performance of the HTS cable. In this paper, we use numerical methods to perform a comparison study of multiple-stage twisted stacked-tape cable (TSTC) conductors to find better cable structures that can both improve the critical current and minimize the alternating current (AC) losses of the cable. The sub-cable geometry is designed to have a stair-step shape. Three superconducting tape layouts are chosen and their transport performance and AC losses are evaluated. The magnetic field and current density profiles of the cables are obtained. The results show that arrangement of the superconducting tapes from the interior towards the exterior of the cable based on their critical current values in descending order can enhance the cable's transport capacity while significantly reducing the AC losses. These results imply that cable transport capacity improvements can be achieved by arranging the superconducting tapes in a manner consistent with the electromagnetic field distribution. Through comparison of the critical currents and AC losses of four types of HTS cables, we determine the best structural choice among these cables.

Smart Kirigami open honeycombs in shape changing actuation and dynamics

NASA Astrophysics Data System (ADS)

Neville, R. M.; Scarpa, F.; Leng, J.

2017-04-01

Kirigami is the ancient Japanese art of cutting and folding paper, widespread in Asia since the 17th century. Kirigami offers a broader set of geometries and topologies than classical fold/valleys Origami, because of the presence of cuts. Moreover, Kirigami can be readily applied to a large set of composite and smart 2D materials, and can be used to up-scaled productions with modular molding. We describe the manufacturing and testing of a topology of Kirigami cellular structures defined as Open Honeycombs. Open Honeycombs (OHs) can assume fully closed shape and be alike classical hexagonal centresymmetric honeycombs, or can vary their morphology by tuning the opening angle and rotational stiffness of the folds. We show the performance of experimental PEEK OHs with cable actuation and morphing shape characteristics, and the analogous morphing behavior of styrene SMPs under combined mechanical and thermal loading. We also show the dynamic (modal analysis) behavior of OHs configurations parameterized against their geometry characteristics, and the controllable modal density characteristics that one could obtain by tuning the topology and folding properties.

Crystal River 3 Cable Materials for Thermal and Gamma Radiation Aging

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

Fifield, Leonard S.; Correa, Miguel; Zwoster, Andy

The Expanded Materials Degradation Assessment Volume 5: Aging of Cables and Cable Systems (EMDA) summarizes the state of knowledge of materials, constructions, operating environments, and aging behavior of low voltage and medium cables in nuclear power plants (NPPs) and identifies potential knowledge gaps with regard to cable operation beyond 60 years. The greatest area of uncertainty relates to how well the accelerated aging used in the original equipment qualification (EQ) processes predicts the performance of cable materials in extended operation. General opinion and utility experience have indicated that actual operating environments of in-plant cables are not as severe, however, asmore » the operating and design basis environments used in the qualification process. Better understanding of the long term aging behavior of cable insulation materials in service conditions and the analysis of actual cable operating environments are the objectives of ongoing research to support subsequent license renewal activities in particular and long term cable aging management in general. A key component of the effort to better understand cable material aging behavior is the availability of representative samples of cables that have been installed in operating light water reactors and have experienced long term service. Unique access to long term service cables, including relatively rich information on cable identity and history, occurred in 2016 through the assistance of the Electric Power Research Institute (EPRI). EPRI facilitated DOE receipt of harvested cables from the decommissioned Crystal River Unit 3 (CR3) pressurized water reactor representing six of the nine most common low voltage cable manufacturers (EPRI 103841R1): Rockbestos, Anaconda Wire and Cable Company (Anaconda), Boston Insulated Wire (BIW), Brand-Rex, Kerite and Okonite. Cable samples received had been installed in the operating plant for durations ranging from 10 years to 36 years. These cables provide the opportunity to assess actual in-plant material aging and compare it to the expectations for service aging implied in original equipment qualification. The received samples are from cables manufactured as early as 1971 and as late as 1998. Of the original manufacturers, BIW, Anaconda and Kerite no longer supply low-voltage cables to the nuclear industry. Okonite, Rockbestos, and Brand-Rex do still supply nuclear-grade low-voltage cables, but most cable insulation formulations have changed over the years. Thus the availability of the CR3 samples representative of cables installed in existing U.S. NPPs also presents the opportunity for additional aging studies on the most relevant insulation and jacketing materials. This report describes the cables received from CR3 through EPRI assistance, some of the specific knowledge gaps that study of these cable materials can be used to address, and experimental plans for addressing those gaps using these materials. Harvested cables from CR3 and other NPPs that have experienced long term service, new old stock cables (manufactured before 2000, but never put in service), and relevant modern nuclear cables and materials from cable manufacturers are enabling research to address identified knowledge gaps and better understand long term aging behavior for cable materials currently installed in NPPs. This research, combined with refined understanding of actual service environments and conditions, will both support subsequent licensing activities and more efficient plant cable aging management.« less

Decoherence, discord, and the quantum master equation for cosmological perturbations

NASA Astrophysics Data System (ADS)

Hollowood, Timothy J.; McDonald, Jamie I.

2017-05-01

We examine environmental decoherence of cosmological perturbations in order to study the quantum-to-classical transition and the impact of noise on entanglement during inflation. Given an explicit interaction between the system and environment, we derive a quantum master equation for the reduced density matrix of perturbations, drawing parallels with quantum Brownian motion, where we see the emergence of fluctuation and dissipation terms. Although the master equation is not in Lindblad form, we see how typical solutions exhibit positivity on super-horizon scales, leading to a physically meaningful density matrix. This allows us to write down a Langevin equation with stochastic noise for the classical trajectories which emerge from the quantum system on super-horizon scales. In particular, we find that environmental decoherence increases in strength as modes exit the horizon, with the growth driven essentially by white noise coming from local contributions to environmental correlations. Finally, we use our master equation to quantify the strength of quantum correlations as captured by discord. We show that environmental interactions have a tendency to decrease the size of the discord and that these effects are determined by the relative strength of the expansion rate and interaction rate of the environment. We interpret this in terms of the competing effects of particle creation versus environmental fluctuations, which tend to increase and decrease the discord respectively.

Cable load sensing device

DOEpatents

Beus, Michael J.; McCoy, William G.

1998-01-01

Apparatus for sensing the magnitude of a load on a cable as the cable is employed to support the load includes a beam structure clamped to the cable so that a length of the cable lies along the beam structure. A spacer associated with the beam structure forces a slight curvature in a portion of the length of cable under a cable "no-load" condition so that the portion of the length of cable is spaced from the beam structure to define a cable curved portion. A strain gauge circuit including strain gauges is secured to the beam structure by welding. As the cable is employed to support a load the load causes the cable curved portion to exert a force normal to the cable through the spacer and on the beam structure to deform the beam structure as the cable curved portion attempts to straighten under the load. As this deformation takes place, the resistance of the strain gauges is set to a value proportional to the magnitude of the normal strain on the beam structure during such deformation. The magnitude of the normal strain is manipulated in a control device to generate a value equal to the magnitude or weight of the load supported by the cable.

Quantum Dynamics in the HMF Model

NASA Astrophysics Data System (ADS)

Plestid, Ryan; O'Dell, Duncan

2017-04-01

The Hamiltonian Mean Field (HMF) model represents a paradigm in the study of long-range interactions but has never been realized in a lab. Recently Shutz and Morigi (PRL 113) have come close but ultimately fallen short. Their proposal relied on cavity-induced interactions between atoms. If a design using cold atoms is to be successful, an understanding of quantum effects is essential. I will outline the natural quantum generalization of the HMF assuming a BEC by using a generalized Gross-Pitaevskii equation (gGPE). I will show how quantum effects modify features which are well understood in the classical model. More specifically, by working in the semi-classical regime (strong interparticle interactions) we can identify the universal features predicted by catastrophe theory dressed with quantum interference effects. The stationary states of gGPE can be solved exactly and are found to be described by self-consistent Mathieu functions. Finally, I will discuss the connection between the classical description of the dynamics in terms of the Vlassov equation, and the gGPE. We would like to thank the Government of Ontario's OGS program, NSERC, and the Perimeter Institute of Theoretical Physics.

Improvement of Quench Factor Analysis in Phase and Hardness Prediction of a Quenched Steel

NASA Astrophysics Data System (ADS)

Kianezhad, M.; Sajjadi, S. A.

2013-05-01

The accurate prediction of alloys' properties introduced by heat treatment has been considered by many researchers. The advantages of such predictions are reduction of test trails and materials' consumption as well as time and energy saving. One of the most important methods to predict hardness in quenched steel parts is Quench Factor Analysis (QFA). Classical QFA is based on the Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation. In this study, a modified form of the QFA based on the work by Rometsch et al. is compared with the classical QFA, and they are applied to prediction of hardness of steels. For this purpose, samples of CK60 steel were utilized as raw material. They were austenitized at 1103 K (830 °C). After quenching in different environments, they were cut and their hardness was determined. In addition, the hardness values of the samples were fitted using the classical and modified equations for the quench factor analysis and the results were compared. Results showed a significant improvement in fitted values of the hardness and proved the higher efficiency of the new method.

Cubic Equations and the Ideal Trisection of the Arbitrary Angle

ERIC Educational Resources Information Center

Farnsworth, Marion B.

2006-01-01

In the year 1837 mathematical proof was set forth authoritatively stating that it is impossible to trisect an arbitrary angle with a compass and an unmarked straightedge in the classical sense. The famous proof depends on an incompatible cubic equation having the cosine of an angle of 60 and the cube of the cosine of one-third of an angle of 60 as…

On Insensitivity of the Chi-Square Model Test to Nonlinear Misspecification in Structural Equation Models

ERIC Educational Resources Information Center

Mooijaart, Ab; Satorra, Albert

2009-01-01

In this paper, we show that for some structural equation models (SEM), the classical chi-square goodness-of-fit test is unable to detect the presence of nonlinear terms in the model. As an example, we consider a regression model with latent variables and interactions terms. Not only the model test has zero power against that type of…

On One Possible Generalization of the Regression Theorem

NASA Astrophysics Data System (ADS)

Bogolubov, N. N.; Soldatov, A. V.

2018-03-01

A general approach to derivation of formally exact closed time-local or time-nonlocal evolution equations for non-equilibrium multi-time correlations functions made of observables of an open quantum system interacting simultaneously with external time-dependent classical fields and dissipative environment is discussed. The approach allows for the subsequent treatment of these equations within a perturbative scheme assuming that the system-environment interaction is weak.

Some Boussinesq Equations with Saturation

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

Christou, M. A.

2010-11-25

We investigate numerically some Boussinesq type equations with square or cubic and saturated nonlinearity. We examine the propagation, interaction and overtake interaction of soliton solutions. Moreover, we examine the effect of the saturation term on the solution and compare it with the classical case of the square or cubic nonlinearity without saturation. We calculate numerically the phase shift experienced by the solitons upon collision and conclude the impact of saturation.

Classical-Quantum Correspondence by Means of Probability Densities

NASA Technical Reports Server (NTRS)

Vegas, Gabino Torres; Morales-Guzman, J. D.

1996-01-01

Within the frame of the recently introduced phase space representation of non relativistic quantum mechanics, we propose a Lagrangian from which the phase space Schrodinger equation can be derived. From that Lagrangian, the associated conservation equations, according to Noether's theorem, are obtained. This shows that one can analyze quantum systems completely in phase space as it is done in coordinate space, without additional complications.

The interaction of Dirac particles with non-abelian gauge fields and gravity - bound states

NASA Astrophysics Data System (ADS)

Finster, Felix; Smoller, Joel; Yau, Shing-Tung

2000-09-01

We consider a spherically symmetric, static system of a Dirac particle interacting with classical gravity and an SU(2) Yang-Mills field. The corresponding Einstein-Dirac-Yang-Mills equations are derived. Using numerical methods, we find different types of soliton-like solutions of these equations and discuss their properties. Some of these solutions are stable even for arbitrarily weak gravitational coupling.

Does loop quantum cosmology replace the big rip singularity by a non-singular bounce?

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

Haro, Jaume de, E-mail: jaime.haro@upc.edu

It is stated that holonomy corrections in loop quantum cosmology introduce a modification in Friedmann's equation which prevent the big rip singularity. Recently in [1] it has been proved that this modified Friedmann equation is obtained in an inconsistent way, what means that the results deduced from it, in particular the big rip singularity avoidance, are not justified. The problem is that holonomy corrections modify the gravitational part of the Hamiltonian of the system leading, after Legendre's transformation, to a non covariant Lagrangian which is in contradiction with one of the main principles of General Relativity. A more consistent waymore » to deal with the big rip singularity avoidance is to disregard modification in the gravitational part of the Hamiltonian, and only consider inverse volume effects [2]. In this case we will see that, not like the big bang singularity, the big rip singularity survives in loop quantum cosmology. Another way to deal with the big rip avoidance is to take into account geometric quantum effects given by the the Wheeler-De Witt equation. In that case, even though the wave packets spread, the expectation values satisfy the same equations as their classical analogues. Then, following the viewpoint adopted in loop quantum cosmology, one can conclude that the big rip singularity survives when one takes into account these quantum effects. However, the spreading of the wave packets prevents the recover of the semiclassical time, and thus, one might conclude that the classical evolution of the universe come to and end before the big rip is reached. This is not conclusive because. as we will see, it always exists other external times that allows us to define the classical and quantum evolution of the universe up to the big rip singularity.« less

A gradual update method for simulating the steady-state solution of stiff differential equations in metabolic circuits.

PubMed

Shiraishi, Emi; Maeda, Kazuhiro; Kurata, Hiroyuki

2009-02-01

Numerical simulation of differential equation systems plays a major role in the understanding of how metabolic network models generate particular cellular functions. On the other hand, the classical and technical problems for stiff differential equations still remain to be solved, while many elegant algorithms have been presented. To relax the stiffness problem, we propose new practical methods: the gradual update of differential-algebraic equations based on gradual application of the steady-state approximation to stiff differential equations, and the gradual update of the initial values in differential-algebraic equations. These empirical methods show a high efficiency for simulating the steady-state solutions for the stiff differential equations that existing solvers alone cannot solve. They are effective in extending the applicability of dynamic simulation to biochemical network models.

Braided tubular superelastic cables provide improved spinal stability compared to multifilament sublaminar cables.

PubMed

Tremblay, Jaëlle; Mac-Thiong, Jean-Marc; Brailovski, Vladimir; Petit, Yvan

2015-09-01

This study investigates the use of braided tubular superelastic cables, previously used for sternum closure following sternotomy, as sublaminar fixation method. It compares the biomechanical performance of spinal instrumentation fixation systems with regular sublaminar cables and proprietary superelastic cables. A hybrid experimental protocol was applied to six porcine L1-L4 spinal segments to compare multifilament sublaminar cables (Atlas, Medtronic Sofamor Danek, Memphis, TN) with proprietary superelastic cables. First, intact total range of motion was determined for all specimens using pure moment loading. Second, pure moments were imposed to the instrumented specimens until these intact total ranges of motion were reproduced. Compared to the intact specimens, the use of superelastic cables resulted in stiffer instrumented specimens than the use of multifilament cables for all the loading modes except axial torsion. Consequently, the superelastic cables limited the instrumented segments mobility more than the multifilament cables. Spinal instrumentation fixation systems using superelastic cables could be a good alternative to conventional sublaminar cables as it maintains a constant stabilization of the spine during loading. © IMechE 2015.

Lie symmetry analysis and reduction for exact solution of (2+1)-dimensional Bogoyavlensky-Konopelchenko equation by geometric approach

NASA Astrophysics Data System (ADS)

Ray, S. Saha

2018-04-01

In this paper, the symmetry analysis and similarity reduction of the (2+1)-dimensional Bogoyavlensky-Konopelchenko (B-K) equation are investigated by means of the geometric approach of an invariance group, which is equivalent to the classical Lie symmetry method. Using the extended Harrison and Estabrook’s differential forms approach, the infinitesimal generators for (2+1)-dimensional B-K equation are obtained. Firstly, the vector field associated with the Lie group of transformation is derived. Then the symmetry reduction and the corresponding explicit exact solution of (2+1)-dimensional B-K equation is obtained.

On the theory of Brownian motion with the Alder-Wainwright effect

NASA Astrophysics Data System (ADS)

Okabe, Yasunori

1986-12-01

The Stokes-Boussinesq-Langevin equation, which describes the time evolution of Brownian motion with the Alder-Wainwright effect, can be treated in the framework of the theory of KMO-Langevin equations which describe the time evolution of a real, stationary Gaussian process with T-positivity (reflection positivity) originating in axiomatic quantum field theory. After proving the fluctuation-dissipation theorems for KMO-Langevin equations, we obtain an explicit formula for the deviation from the classical Einstein relation that occurs in the Stokes-Boussinesq-Langevin equation with a white noise as its random force. We are interested in whether or not it can be measured experimentally.

Diffusion equations and the time evolution of foreign exchange rates

NASA Astrophysics Data System (ADS)

Figueiredo, Annibal; de Castro, Marcio T.; da Fonseca, Regina C. B.; Gleria, Iram

2013-10-01

We investigate which type of diffusion equation is most appropriate to describe the time evolution of foreign exchange rates. We modify the geometric diffusion model assuming a non-exponential time evolution and the stochastic term is the sum of a Wiener noise and a jump process. We find the resulting diffusion equation to obey the Kramers-Moyal equation. Analytical solutions are obtained using the characteristic function formalism and compared with empirical data. The analysis focus on the first four central moments considering the returns of foreign exchange rate. It is shown that the proposed model offers a good improvement over the classical geometric diffusion model.

System for stabilizing cable phase delay utilizing a coaxial cable under pressure

NASA Technical Reports Server (NTRS)

Clements, P. A. (Inventor)

1974-01-01

Stabilizing the phase delay of signals passing through a pressurizable coaxial cable is disclosed. Signals from an appropriate source at a selected frequency, e.g., 100 MHz, are sent through the controlled cable from a first cable end to a second cable end which, electrically, is open or heavily mismatched at 100 MHz, thereby reflecting 100 MHz signals back to the first cable end. Thereat, the phase difference between the reflected-back signals and the signals from the source is detected by a phase detector. The output of the latter is used to control the flow of gas to or from the cable, thereby controlling the cable pressure, which in turn affects the cable phase delay.

Fire related hazards of cables: The Canadian position development of fire resistant inside wiring cable

NASA Astrophysics Data System (ADS)

Hartley, M. D.; Jaques, R. E.

1986-11-01

The Canadian Electrical Code and the National Building Code in Canada recognize only two designations in regards to fire resistance of cables; cables for use in combustible (residential) buildings and cables for use in non-combustible buildings. The Test standard for cables for non-combustible buildings resembles IEEE-383. However, it is more severe; particularly for small nonarmoured cables such as Inside Wiring Cable. This forthcoming requirement has necessitated material and product development. Although an Inside Wiring cable modification of both insulation and jacket was undertaken, the large volume fraction of combustible material in the jacket vis a vis the insulation made it the area of greatest impact. The paper outlines the development and its effect on cable performance.

Fractional Klein-Gordon equation composed of Jumarie fractional derivative and its interpretation by a smoothness parameter

NASA Astrophysics Data System (ADS)

Ghosh, Uttam; Banerjee, Joydip; Sarkar, Susmita; Das, Shantanu

2018-06-01

Klein-Gordon equation is one of the basic steps towards relativistic quantum mechanics. In this paper, we have formulated fractional Klein-Gordon equation via Jumarie fractional derivative and found two types of solutions. Zero-mass solution satisfies photon criteria and non-zero mass satisfies general theory of relativity. Further, we have developed rest mass condition which leads us to the concept of hidden wave. Classical Klein-Gordon equation fails to explain a chargeless system as well as a single-particle system. Using the fractional Klein-Gordon equation, we can overcome the problem. The fractional Klein-Gordon equation also leads to the smoothness parameter which is the measurement of the bumpiness of space. Here, by using this smoothness parameter, we have defined and interpreted the various cases.

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

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

Brantley, P S

2006-09-27

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

Modal resonant dynamics of cables with a flexible support: A modulated diffraction problem

NASA Astrophysics Data System (ADS)

Guo, Tieding; Kang, Houjun; Wang, Lianhua; Liu, Qijian; Zhao, Yueyu

2018-06-01

Modal resonant dynamics of cables with a flexible support is defined as a modulated (wave) diffraction problem, and investigated by asymptotic expansions of the cable-support coupled system. The support-cable mass ratio, which is usually very large, turns out to be the key parameter for characterizing cable-support dynamic interactions. By treating the mass ratio's inverse as a small perturbation parameter and scaling the cable tension properly, both cable's modal resonant dynamics and the flexible support dynamics are asymptotically reduced by using multiple scale expansions, leading finally to a reduced cable-support coupled model (i.e., on a slow time scale). After numerical validations of the reduced coupled model, cable-support coupled responses and the flexible support induced coupling effects on the cable, are both fully investigated, based upon the reduced model. More explicitly, the dynamic effects on the cable's nonlinear frequency and force responses, caused by the support-cable mass ratio, the resonant detuning parameter and the support damping, are carefully evaluated.

105. VIEW NORTH FROM SLC3W CABLE TUNNEL INTO CABLE VAULT ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

105. VIEW NORTH FROM SLC-3W CABLE TUNNEL INTO CABLE VAULT AND SLC-3E CABLE TUNNEL. NOTE WOODEN PLANKING ON FLOOR OF TUNNEL AND CABLE TRAYS LINING TUNNEL WALLS. STAIRS ON EAST WALL OF CABLE VAULT LEAD INTO LANDLINE INSTRUMENTATION ROOM. - Vandenberg Air Force Base, Space Launch Complex 3, Launch Operations Building, Napa & Alden Roads, Lompoc, Santa Barbara County, CA

Frequency domain reflectometry NDE for aging cables in nuclear power plants

NASA Astrophysics Data System (ADS)

Glass, S. W.; Jones, A. M.; Fifield, L. S.; Hartman, T. S.

2017-02-01

Degradation of the cable jacket, electrical insulation, and other cable components of installed cables within nuclear power plants (NPPs) is known to occur as a function of age, temperature, radiation, and other environmental factors. Although system tests verify cable function under normal loads, demonstration of some cable's ability to perform under exceptional loads associated with design-basis events is essential to assuring plant integrity. The cable's ability to perform safely over the initial 40-year planned and licensed life has generally been demonstrated and there have been very few age-related cable failures. With greater than 1000 km of power, control, instrumentation, and other cables typically found in an NPP, replacing all the cables would be a severe cost burden. Justification for life extension to 60 and 80 years requires a cable aging management program that includes condition monitoring to justify cable performance under normal operation as well as accident conditions. A variety of tests are available to assess various aspects of electrical and mechanical cable performance, but none are suitable for all cable configurations nor does any single test confirm all features of interest. One particularly promising test that is beginning to be used more and more by utilities is frequency domain reflectometry (FDR). FDR is a nondestructive electrical inspection technique used to detect and localize faults in power and communication system conductors along the length of a cable from a single connection point. FDR detects discontinuities in the electrical impedance that arise due to cable splices or similar changes along the path of the conductor pair. In addition, FDR has the potential to provide sensitivity to insulation degradation by detecting small changes in impedance between the cable conductors being examined. The technique is also sensitive to cable bends, the particular lay of the cable in tray, proximity to other cable, and other factors that bear consideration when interpreting the test results. This paper examines various influences on the FDR approach and compares results of three different instruments to assess accelerated aging damage among several NPP representative cables.

The Cables Gene on Chromosome 18q Is Silenced by Promoter Hypermethylation and Allelic Loss in Human Colorectal Cancer

PubMed Central

Park, Do Youn; Sakamoto, Hideo; Kirley, Sandra D.; Ogino, Shuji; Kawasaki, Takako; Kwon, Eunjeong; Mino-Kenudson, Mari; Lauwers, Gregory Y.; Chung, Daniel C.; Rueda, Bo R.; Zukerberg, Lawrence R.

2007-01-01

Cables is a cyclin-dependent kinase-binding nuclear protein that maps to chromosome 18q11-12. Here, we assessed Cables expression in 160 colorectal cancers (CRCs), its role in colon cancer cell growth, and the potential mechanisms of Cables inactivation. Expression levels, promoter methylation, and mutational status of Cables were investigated in colon cancer cell lines and primary colon tumors. Chromosome 18q loss of heterozygosity (LOH) was evaluated with multiple polymorphic markers. Cables inhibited cellular proliferation and colony formation in colon cancer cell lines. Cables expression was reduced in 65% of primary CRCs. No mutations were detected in 10 exons of Cables in 20 primary colon tumors. Cables promoter was methylated in cell lines with decreased Cables expression and vice versa. 5-Aza-2′-deoxycytidine resulted in increased Cables expression in methylated cell lines. There was a significant correlation between promoter methylation and Cables gene expression in primary colon tumors. Sixty-five percent of primary colon tumors demonstrated chromosome 18q LOH. LOH involving the Cables region was observed in 35% of cases, including those in which more distal portions of chromosome 18q were retained, and Cables expression was decreased in all such cases. Loss of Cables expression in 65% of CRCs suggests that it is a common event in colonic carcinogenesis, with promoter methylation and LOH appearing to be important mechanisms of Cables gene inactivation. PMID:17982127

Non-dispersive conservative regularisation of nonlinear shallow water (and isentropic Euler equations)

NASA Astrophysics Data System (ADS)

Clamond, Didier; Dutykh, Denys

2018-02-01

A new regularisation of the shallow water (and isentropic Euler) equations is proposed. The regularised equations are non-dissipative, non-dispersive and posses a variational structure; thus, the mass, the momentum and the energy are conserved. Hence, for instance, regularised hydraulic jumps are smooth and non-oscillatory. Another particularly interesting feature of this regularisation is that smoothed 'shocks' propagates at exactly the same speed as the original discontinuous ones. The performance of the new model is illustrated numerically on some dam-break test cases, which are classical in the hyperbolic realm.

Sqeezing generated by a nonlinear master equation and by amplifying-dissipative Hamiltonians

NASA Technical Reports Server (NTRS)

Dodonov, V. V.; Marchiolli, M. A.; Mizrahi, Solomon S.; Moussa, M. H. Y.

1994-01-01

In the first part of this contribution we show that the master equation derived from the generalized version of the nonlinear Doebner-Goldin equation leads to the squeezing of one of the quadratures. In the second part we consider two familiar Hamiltonians, the Bateman- Caldirola-Kanai and the optical parametric oscillator; going back to their classical Lagrangian form we introduce a stochastic force and a dissipative factor. From this new Lagrangian we obtain a modified Hamiltonian that treats adequately the simultaneous amplification and dissipation phenomena, presenting squeezing, too.

Direct simulation Monte Carlo method for the Uehling-Uhlenbeck-Boltzmann equation.

PubMed

Garcia, Alejandro L; Wagner, Wolfgang

2003-11-01

In this paper we describe a direct simulation Monte Carlo algorithm for the Uehling-Uhlenbeck-Boltzmann equation in terms of Markov processes. This provides a unifying framework for both the classical Boltzmann case as well as the Fermi-Dirac and Bose-Einstein cases. We establish the foundation of the algorithm by demonstrating its link to the kinetic equation. By numerical experiments we study its sensitivity to the number of simulation particles and to the discretization of the velocity space, when approximating the steady-state distribution.

Towards an exact relativistic theory of Earth's geoid undulation

NASA Astrophysics Data System (ADS)

Kopeikin, Sergei M.; Mazurova, Elena M.; Karpik, Alexander P.

2015-08-01

The present paper extends the Newtonian concept of the geoid in classic geodesy towards the realm of general relativity by utilizing the covariant geometric methods of the perturbation theory of curved manifolds. It yields a covariant definition of the anomalous (disturbing) gravity potential and formulates differential equation for it in the form of a covariant Laplace equation. The paper also derives the Bruns equation for calculation of geoid's height with full account for relativistic effects beyond the Newtonian approximation. A brief discussion of the relativistic Bruns formula is provided.

A New Scheme of Integrability for (bi)Hamiltonian PDE

NASA Astrophysics Data System (ADS)

De Sole, Alberto; Kac, Victor G.; Valeri, Daniele

2016-10-01

We develop a new method for constructing integrable Hamiltonian hierarchies of Lax type equations, which combines the fractional powers technique of Gelfand and Dickey, and the classical Hamiltonian reduction technique of Drinfeld and Sokolov. The method is based on the notion of an Adler type matrix pseudodifferential operator and the notion of a generalized quasideterminant. We also introduce the notion of a dispersionless Adler type series, which is applied to the study of dispersionless Hamiltonian equations. Non-commutative Hamiltonian equations are discussed in this framework as well.

Fedosov differentials and Catalan numbers

NASA Astrophysics Data System (ADS)

Löffler, Johannes

2010-06-01

The aim of the paper is to establish a non-recursive formula for the general solution of Fedosov's 'quadratic' fixed-point equation (Fedosov 1994 J. Diff. Geom. 40 213-38). Fedosov's geometrical fixed-point equation for a differential is rewritten in a form similar to the functional equation for the generating function of Catalan numbers. This allows us to guess the solution. An adapted example for Kaehler manifolds of constant sectional curvature is considered in detail. Also for every connection on a manifold a familiar classical differential will be introduced. Dedicated to the memory of Nikolai Neumaier.

The effective resistance between twisted superconducting filaments in tapes

NASA Astrophysics Data System (ADS)

Takács, S.; Iwakuma, M.; Funaki, K.

2001-05-01

We consider two mechanisms, which influence the effective resistance between crossing strands on flat cables or filaments in twisted tapes. The one-layer classical Rutherford-type cable and the tapes with twisted BSCCO filaments in silver matrix are taken as analogous cases. The amount of the matrix between strands or filaments increases the effective conductance compared with the direct current paths (determined by the touching area of the filaments). The increase factor is about two and can easily be suppressed by other effects, like the contact resistance between the superconductor and the matrix. The second mechanism is due to the existence of induced voltage between any points of crossing filaments. This leads to an additional effective conductance, proportional to the square of the total number of filaments. Both effects are not very important for isotropic superconductors, but due to the strong anisotropy of critical parameters they can dominate for high temperature superconductors. The first one may partially compensate the influence of the usually weaker critical current density perpendicular to the tape. The contribution due to the second effect can explain the higher resistivity of the matrix in BSCCO tapes compared with pure silver. It seems that to obtain low AC coupling losses in BSCCO tapes, structures with small filament number are required.

Application of singular value decomposition to structural dynamics systems with constraints

NASA Technical Reports Server (NTRS)

Juang, J.-N.; Pinson, L. D.

1985-01-01

Singular value decomposition is used to construct a coordinate transformation for a linear dynamic system subject to linear, homogeneous constraint equations. The method is compared with two commonly used methods, namely classical Gaussian elimination and Walton-Steeves approach. Although the classical method requires fewer numerical operations, the singular value decomposition method is more accurate and convenient in eliminating the dependent coordinates. Numerical examples are presented to demonstrate the application of the method.

Investigation of cables for ionization chambers.

PubMed

Spokas, J J; Meeker, R D

1980-01-01

Seven coaxial cables which are in use for carrying currents generated in ionization chambers have been critically studied with reference to their suitability to this application. Included in this study are four low-noise triaxial cables and three low-noise two-conductor cables. For each cable the following characteristics were considered: inherent noise currents, currents produced by cable movements, polarization currents, the degree of electrostatic shielding of the central signal-carrying conductor, and radiation-induced cable currents. The study indicated that of the seven cables, two low-noise triaxial cables, both employing solid Teflon dielectric surrounding the central conductor, appear to offer the best overall performance for use with ionization chambers.

An Internal Coaxial Cable Electrical Connector For Use In Downhole Tools

DOEpatents

Hall, David R.; Hall, Jr., H. Tracy; Pixton, David S.; Dahlgren, Scott; Fox, Joe; Sneddon, Cameron; Briscoe, Michael

2005-11-29

A coaxial cable electrical connector more specifically an internal coaxial cable connector placed within a coaxial cable and its constituent components. A coaxial cable connector is in electrical communcation with an inductive transformer and a coaxial cable. The connector is in electrical communication with the outer housing of the inductive transfonner. A generally coaxial center conductor, a portion of which could be the coil in the inductive transformer, passes through the connector, is electrically insulated from the connector, and is in electrical communication with the conductive care of the coaxial cable. A plurality of bulbous pliant tabs on the coaxial cable connector mechanically engage the inside diameter of the coaxial cable thus grounding the transformer to the coaxial cable. The coaxial cable and inductive transformer are disposed within downhole tools to transmit electrical signals between downhole tools within a drill string.

High power cable with internal water cooling 400 kV

NASA Astrophysics Data System (ADS)

Rasquin, W.; Harjes, B.

1982-08-01

Due to the concentration of electricity production in large power plants, the need of higher power transmissions, and the protection of environment, developement of a 400 kV water cooled cable in the power range of 1 to 5 GVA was undertaken. The fabrication and testing of equipment, engineering of cable components, fabrication of a test cable, development of cable terminal laboratory, testing of test cable, field testing of test cable, fabrication of industrial cable laboratory, testing of industrial cable, field testing of industrial cable, and system analysis for optimization were prepared. The field testing was impossible to realize. However, it is proved that a cable consisting of an internal stainless steel water cooled tube, covered by stranded copper profiles, insulated with heavy high quality paper, and protected by an aluminum cover can be produced, withstand tests accordingly to IEC/VDE recommendations, and is able to fulfill all exploitation conditions.

30 CFR 7.403 - Application requirements.

Code of Federal Regulations, 2013 CFR

2013-07-01

... APPROVAL OF MINING PRODUCTS TESTING BY APPLICANT OR THIRD PARTY Electric Cables, Signaling Cables, and Cable Splice Kits § 7.403 Application requirements. (a) Electric cables and signaling cables. A single... product: (1) Product information: (i) Cable type (for example, G or G-GC). (ii) Construction (for example...

30 CFR 7.403 - Application requirements.

Code of Federal Regulations, 2012 CFR

2012-07-01

... APPROVAL OF MINING PRODUCTS TESTING BY APPLICANT OR THIRD PARTY Electric Cables, Signaling Cables, and Cable Splice Kits § 7.403 Application requirements. (a) Electric cables and signaling cables. A single... product: (1) Product information: (i) Cable type (for example, G or G-GC). (ii) Construction (for example...

30 CFR 7.403 - Application requirements.

Code of Federal Regulations, 2014 CFR

2014-07-01

... APPROVAL OF MINING PRODUCTS TESTING BY APPLICANT OR THIRD PARTY Electric Cables, Signaling Cables, and Cable Splice Kits § 7.403 Application requirements. (a) Electric cables and signaling cables. A single... product: (1) Product information: (i) Cable type (for example, G or G-GC). (ii) Construction (for example...

Effect of oxygen concentration on fire growth of various types of cable bending in horizontal and vertical orientations

NASA Astrophysics Data System (ADS)

Pangaribuan, Adrianus; Dhiputra, I. M. K.; Nugroho, Yulianto S.

2017-03-01

Electrical cable is a whole of the material including metal (cooper) conductor and its insulation, when an electrical cable is flowed by electric current, based on its own capacity, the temperature of cable conductor increases gradually. If the current flows above the cable carrying capacity, then an extreme temperature rises are expected. When temperature increase, the electric current flow inside cable conductor will decrease gradually related to the resistance and could occur repeatedly in a period. Since electrical faults on electrical cable system are often suspected as the cause of fires, thus this research aims to investigate measures of preventing the fire to start by means of controlling oxygen concentration in a cable compartment. The experimental work was conducted in laboratory by using electrical power cable of 1.5 mm2 size. Two transparent chambers were applied for studying the effect of vertical and horizontal orientations on the cable temperature rise, under various oxygen concentration of the gas streams. In the present work, the electrical was maintained at a constant level during a typical test run. Parametric studies reported in the paper include the use of a bare and insulated cables as well as the bending shape of the cable lines of a straight cable, coiled cable and randomly bent cable which were loaded with the same electric load and oxygen concentration in the gas supply.

The Over-Selling of Fiber Optics? Cable Planning for Educational Technology.

ERIC Educational Resources Information Center

Kovacs, Robert E.

1993-01-01

Describes fiber optic cables and coaxial cables and considers when each would be appropriate for educational technology. Single mode versus multimode fiber optics are explained, advantages and disadvantages of each type of cable are discussed, and guidelines for choosing fiber optic cables and coaxial cables are offered. (LRW)

Helical grip for the cable cars of San Francisco

NASA Technical Reports Server (NTRS)

Peyran, R. J.

1979-01-01

A helical cable car grip to minimize high maintenance costs of San Francisco's cable car operation is presented. The grip establishes a rolling contact between the cable and grip to reduce sliding friction and associated cable wear. The design, development, and testing of the helical cable car grip are described.

47 CFR 76.1001 - Unfair practices generally.

Code of Federal Regulations, 2012 CFR

2012-10-01

... control with a cable operator or cable operators, satellite cable programming vendor or vendors in which a... under common control with, such terrestrial cable programming vendor shall be deemed responsible for... programming vendor is wholly owned by, controlled by, or under common control with a cable operator or cable...

14 CFR 25.689 - Cable systems.

Code of Federal Regulations, 2013 CFR

2013-01-01

... STANDARDS: TRANSPORT CATEGORY AIRPLANES Design and Construction Control Systems § 25.689 Cable systems. (a) Each cable, cable fitting, turnbuckle, splice, and pulley must be approved. In addition— (1) No cable... 14 Aeronautics and Space 1 2013-01-01 2013-01-01 false Cable systems. 25.689 Section 25.689...

47 CFR 76.1001 - Unfair practices generally.

Code of Federal Regulations, 2014 CFR

2014-10-01

... control with a cable operator or cable operators, satellite cable programming vendor or vendors in which a... under common control with, such terrestrial cable programming vendor shall be deemed responsible for... programming vendor is wholly owned by, controlled by, or under common control with a cable operator or cable...

47 CFR 76.1001 - Unfair practices generally.

Code of Federal Regulations, 2013 CFR

2013-10-01

... control with a cable operator or cable operators, satellite cable programming vendor or vendors in which a... under common control with, such terrestrial cable programming vendor shall be deemed responsible for... programming vendor is wholly owned by, controlled by, or under common control with a cable operator or cable...

30 CFR 57.12014 - Handling energized power cables.

Code of Federal Regulations, 2013 CFR

2013-07-01

... 30 Mineral Resources 1 2013-07-01 2013-07-01 false Handling energized power cables. 57.12014... Electricity Surface and Underground § 57.12014 Handling energized power cables. Power cables energized to.... This does not prohibit pulling or dragging of cable by the equipment it powers when the cable is...

30 CFR 57.12014 - Handling energized power cables.

Code of Federal Regulations, 2014 CFR

2014-07-01

... 30 Mineral Resources 1 2014-07-01 2014-07-01 false Handling energized power cables. 57.12014... Electricity Surface and Underground § 57.12014 Handling energized power cables. Power cables energized to.... This does not prohibit pulling or dragging of cable by the equipment it powers when the cable is...

30 CFR 57.12014 - Handling energized power cables.

Code of Federal Regulations, 2012 CFR

2012-07-01

... 30 Mineral Resources 1 2012-07-01 2012-07-01 false Handling energized power cables. 57.12014... Electricity Surface and Underground § 57.12014 Handling energized power cables. Power cables energized to.... This does not prohibit pulling or dragging of cable by the equipment it powers when the cable is...

30 CFR 57.12014 - Handling energized power cables.

Code of Federal Regulations, 2011 CFR

2011-07-01

... 30 Mineral Resources 1 2011-07-01 2011-07-01 false Handling energized power cables. 57.12014... Electricity Surface and Underground § 57.12014 Handling energized power cables. Power cables energized to.... This does not prohibit pulling or dragging of cable by the equipment it powers when the cable is...

30 CFR 57.12014 - Handling energized power cables.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 30 Mineral Resources 1 2010-07-01 2010-07-01 false Handling energized power cables. 57.12014... Electricity Surface and Underground § 57.12014 Handling energized power cables. Power cables energized to.... This does not prohibit pulling or dragging of cable by the equipment it powers when the cable is...

14 CFR 29.685 - Control system details.

Code of Federal Regulations, 2010 CFR

2010-01-01

... must be means to prevent the slapping of cables or tubes against other parts. (d) Cable systems must be designed as follows: (1) Cables, cable fittings, turnbuckles, splices, and pulleys must be of an acceptable kind. (2) The design of cable systems must prevent any hazardous change in cable tension throughout the...

14 CFR 27.685 - Control system details.

Code of Federal Regulations, 2010 CFR

2010-01-01

... must be means to prevent the slapping of cables or tubes against other parts. (d) Cable systems must be designed as follows: (1) Cables, cable fittings, turnbuckles, splices, and pulleys must be of an acceptable kind. (2) The design of the cable systems must prevent any hazardous change in cable tension throughout...

The contrasting roles of Planck's constant in classical and quantum theories

NASA Astrophysics Data System (ADS)

Boyer, Timothy H.

2018-04-01

We trace the historical appearance of Planck's constant in physics, and we note that initially the constant did not appear in connection with quanta. Furthermore, we emphasize that Planck's constant can appear in both classical and quantum theories. In both theories, Planck's constant sets the scale of atomic phenomena. However, the roles played in the foundations of the theories are sharply different. In quantum theory, Planck's constant is crucial to the structure of the theory. On the other hand, in classical electrodynamics, Planck's constant is optional, since it appears only as the scale factor for the (homogeneous) source-free contribution to the general solution of Maxwell's equations. Since classical electrodynamics can be solved while taking the homogenous source-free contribution in the solution as zero or non-zero, there are naturally two different theories of classical electrodynamics, one in which Planck's constant is taken as zero and one where it is taken as non-zero. The textbooks of classical electromagnetism present only the version in which Planck's constant is taken to vanish.

Effective dynamics of a classical point charge

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

Polonyi, Janos, E-mail: polonyi@iphc.cnrs.fr

2014-03-15

The effective Lagrangian of a point charge is derived by eliminating the electromagnetic field within the framework of the classical closed time path formalism. The short distance singularity of the electromagnetic field is regulated by an UV cutoff. The Abraham–Lorentz force is recovered and its similarity to quantum anomalies is underlined. The full cutoff-dependent linearized equation of motion is obtained, no runaway trajectories are found but the effective dynamics shows acausality if the cutoff is beyond the classical charge radius. The strength of the radiation reaction force displays a pole in its cutoff-dependence in a manner reminiscent of the Landau-polemore » of perturbative QED. Similarity between the dynamical breakdown of the time reversal invariance and dynamical symmetry breaking is pointed out. -- Highlights: •Extension of the classical action principle for dissipative systems. •New derivation of the Abraham–Lorentz force for a point charge. •Absence of a runaway solution of the Abraham–Lorentz force. •Acausality in classical electrodynamics. •Renormalization of classical electrodynamics of point charges.« less

Actin cable dynamics in budding yeast

PubMed Central

Yang, Hyeong-Cheol; Pon, Liza A.

2002-01-01

Actin cables, bundles of actin filaments that align along the long axis of budding yeast, are crucial for establishment of cell polarity. We fused green fluorescent protein (GFP) to actin binding protein 140 (Abp140p) and visualized actin cable dynamics in living yeast. We detected two populations of actin cables: (i) bud-associated cables, which extend from the bud along the mother-bud axis, and (ii) randomly oriented cables, which are relatively short. Time-lapse imaging of Abp140p–GFP revealed an apparent increase in the length of bud-associated actin cables. Analysis of movement of Abp140p–GFP fiduciary marks on bud-associated cables and fluorescence loss in photobleaching experiments revealed that this apparent elongation occurs by assembly of new material at the end of the cable within the bud and movement of the opposite end of the cable toward the tip of the mother cell distal to the bud. The rate of extension of the tip of an elongating actin cable is 0.29 ± 0.08 μm/s. Latrunculin A (Lat-A) treatment completely blocked this process. We also observed movement of randomly oriented cables around the cortex of cells at a rate of 0.59 ± 0.14 μm/s. Mild treatment with Lat-A did not affect the velocity of movement of randomly oriented cables. However, Lat-A treatment did increase the number of randomly oriented, motile cables per cell. Our observations suggest that establishment of bud-associated actin cables during the cell cycle is accomplished not by realignment of existing cables but by assembly of new cables within the bud or bud neck, followed by elongation. PMID:11805329

Investigation of the strength of shielded and unshielded underwater electrical cables

NASA Astrophysics Data System (ADS)

Glowe, D. E.; Arnett, S. L.

1981-09-01

The mechanical properties of shielded and unshielded submarine cables (MIL-C-915/8E) were investigated to determine the effect of shielding on cable life, performance, and reliability. Ten cables (five shielded and five unshielded) were selected for laboratory evaluation. A mission profile was developed to establish the mechanical stress limits that cables must endure in service and a test sequence designed to measure tensile strength, flexural abrasion endurance, crush resistance, creep under static tension, and performance in a hull-stuffing tube. The results of this program showed that: (1) DSS-2 cable does not have adequate tensile strength and should have a strength member added. DSS-3 and larger cables have adequate tensile strength with or without the shield; (2) Unshielded DSS-3 type cable does not perform satisfactorily in hull-stuffing tubes; (3) Shielding is not required to meet mission profile specifications for cable crush or flexural abrasion resistance; (4) Construction parameters other than shielding can significantly affect mechanical performance of cable; (5) Unshielded cable construction can result in increased reliability since it permits a thicker single-jacket construction; and (6) Unshielded cable construction can reduce the cost of cable by 8 to 20 percent.