Dissipative Forces and Quantum Mechanics
ERIC Educational Resources Information Center
Eck, John S.; Thompson, W. J.
1977-01-01
Shows how to include the dissipative forces of classical mechanics in quantum mechanics by the use of non-Hermetian Hamiltonians. The Ehrenfest theorem for such Hamiltonians is derived, and simple examples which show the classical correspondences are given. (MLH)
Asymptotic boundary conditions for dissipative waves: General theory
NASA Technical Reports Server (NTRS)
Hagstrom, Thomas
1990-01-01
An outstanding issue in the computational analysis of time dependent problems is the imposition of appropriate radiation boundary conditions at artificial boundaries. Accurate conditions are developed which are based on the asymptotic analysis of wave propagation over long ranges. Employing the method of steepest descents, dominant wave groups are identified and simple approximations to the dispersion relation are considered in order to derive local boundary operators. The existence of a small number of dominant wave groups may be expected for systems with dissipation. Estimates of the error as a function of domain size are derived under general hypotheses, leading to convergence results. Some practical aspects of the numerical construction of the asymptotic boundary operators are also discussed.
Asymptotic analysis of dissipative waves with applications to their numerical simulation
NASA Technical Reports Server (NTRS)
Hagstrom, Thomas
1990-01-01
Various problems involving the interplay of asymptotics and numerics in the analysis of wave propagation in dissipative systems are studied. A general approach to the asymptotic analysis of linear, dissipative waves is developed. It was applied to the derivation of asymptotic boundary conditions for numerical solutions on unbounded domains. Applications include the Navier-Stokes equations. Multidimensional traveling wave solutions to reaction-diffusion equations are also considered. A preliminary numerical investigation of a thermo-diffusive model of flame propagation in a channel with heat loss at the walls is presented.
NASA Astrophysics Data System (ADS)
Frank, T. D.; Patanarapeelert, K.; Beek, P. J.
2008-05-01
We derive a fundamental relationship between the mean and the variability of isometric force. The relationship arises from an optimal collection of active motor units such that the force variability assumes a minimum (optimal isometric force). The relationship is shown to be independent of the explicit motor unit properties and of the dynamical features of isometric force production. A constant coefficient of variation in the asymptotic regime and a nonequilibrium fluctuation-dissipation theorem for optimal isometric force are predicted.
Energy transfer and dissipation in forced isotropic turbulence
NASA Astrophysics Data System (ADS)
Linkmann, Moritz; McComb, W. David; Berera, Arjun; Yoffe, Samuel
2014-11-01
A model for the Reynolds number dependence of the dimensionless dissipation rate Cɛ is derived from the dimensionless Kármán-Howarth equation, resulting in Cɛ =Cɛ , ∞ + C /RL , where RL is the integral scale Reynolds number. The coefficients C and Cɛ , ∞ arise from asymptotic expansions of the dimensionless second- and third-order structure functions. The model equation is fitted to data from direct numerical simulations (DNS) of forced isotropic turbulence for integral scale Reynolds numbers up to RL = 5875 (Rλ = 435), which results in an asymptote for Cɛ in the infinite Reynolds number limit Cɛ , ∞ = 0 . 47 +/- 0 . 01 . Since the coefficients in the model equation are scale-dependent while the dimensionless dissipation rate is not, we modelled the scale dependences of the coefficients by an ad hoc profile function such that they cancel out, leaving the model equation scale-independent, as it must be. The profile function was compared to DNS data to very good agreement, provided we restrict the comparison to scales small enough to be well resolved in our simulations. This work has made use of the resources provided by the UK supercomputing service HECToR, made available through the Edinburgh Compute and Data Facility (ECDF). A.B. is supported by STFC, S.R.Y. and M.F.L. are funded by EPSRC.
NASA Technical Reports Server (NTRS)
Haslach, Henry W., Jr.; Freed, Alan D.; Walker, Kevin P.
1994-01-01
Nonlinear asymptotic integrators are applied to one-dimensional, nonlinear, autonomous, dissipative, ordinary differential equations. These integrators, including a one-step explicit, a one-step implicit, and a one- and two-step midpoint algorithm, are designed to follow the asymptotic behavior of a system approaching a steady state. The methods require that the differential equation be written in a particular asymptotic form. This is always possible for a one-dimensional equation with a globally asymptotic steady state. In this case, conditions are obtained to guarantee that the implicit algorithms are well defined. Further conditions are determined for the implicit methods to be contractive. These methods are all first order accurate, while under certain conditions the midpoint algorithms may also become second order accurate. The stability of each method is investigated and an estimate of the local error is provided.
NASA Astrophysics Data System (ADS)
Lenarčič, Zala; Prosen, Tomaž
2015-03-01
A boundary-driven quantum master equation for a general inhomogeneous (nonintegrable) anisotropic Heisenberg spin-1 /2 chain, or an equivalent nearest neighbor interacting spinless fermion chain, is considered in the presence of a strong external field f . We present an exact closed form expression for large f asymptotics of the current in the presence of a pure incoherent source and sink dissipation at the boundaries. In application, we demonstrate an arbitrary large current rectification in the presence of the interaction.
Ubiquitous mechanisms of energy dissipation in noncontact atomic force microscopy.
Ghasemi, S Alireza; Goedecker, Stefan; Baratoff, Alexis; Lenosky, Thomas; Meyer, Ernst; Hug, Hans J
2008-06-13
Atomistic simulations considering larger tip structures than hitherto assumed reveal novel dissipation mechanisms in noncontact atomic force microscopy. The potential energy surfaces of realistic silicon tips exhibit many energetically close local minima that correspond to different structures. Most of them easily deform, thus causing dissipation arising from hysteresis in force versus distance characteristics. Furthermore, saddle points which connect local minima can suddenly switch to connect different minima. Configurations driven into metastability by the tip motion can thus suddenly access lower energy structures when thermal activation becomes allowed within the time required to detect the resulting average dissipation.
Dynamo action in dissipative, forced, rotating MHD turbulence
NASA Astrophysics Data System (ADS)
Shebalin, John V.
2016-06-01
Magnetohydrodynamic (MHD) turbulence is an inherent feature of large-scale, energetic astrophysical and geophysical magnetofluids. In general, these are rotating and are energized through buoyancy and shear, while viscosity and resistivity provide a means of dissipation of kinetic and magnetic energy. Studies of unforced, rotating, ideal (i.e., non-dissipative) MHD turbulence have produced interesting results, but it is important to determine how these results are affected by dissipation and forcing. Here, we extend our previous work and examine dissipative, forced, and rotating MHD turbulence. Incompressibility is assumed, and finite Fourier series represent turbulent velocity and magnetic field on a 643 grid. Forcing occurs at an intermediate wave number by a method that keeps total energy relatively constant and allows for injection of kinetic and magnetic helicity. We find that 3-D energy spectra are asymmetric when forcing is present. We also find that dynamo action occurs when forcing has either kinetic or magnetic helicity, with magnetic helicity injection being more important. In forced, dissipative MHD turbulence, the dynamo manifests itself as a large-scale coherent structure that is similar to that seen in the ideal case. These results imply that MHD turbulence, per se, may play a fundamental role in the creation and maintenance of large-scale (i.e., dipolar) stellar and planetary magnetic fields.
Collision of viscoelastic bodies: Rigorous derivation of dissipative force.
Goldobin, Denis S; Susloparov, Eugeniy A; Pimenova, Anastasiya V; Brilliantov, Nikolai V
2015-06-01
We report a new theory of dissipative forces acting between colliding viscoelastic bodies. The impact velocity is assumed not to be large to neglect plastic deformations in the material and propagation of sound waves. We consider the general case of bodies of an arbitrary convex shape and of different materials. We develop a mathematically rigorous perturbation scheme to solve the continuum mechanics equations that deal with both displacement and displacement rate fields and accounts for the dissipation in the bulk of the material. The perturbative solution of these equations allows to go beyond the previously used quasi-static approximation and obtain the dissipative force. The derived force does not suffer from the inconsistencies of the quasi-static approximation, like the violation of the third Newton's law for the case of different materials, and depends on particle deformation and deformation rate.
Asymptotic stability for force reflecting teleoperators with time delay
Anderson, R.J. ); Spong, M.W. )
1992-04-01
A bilateral system consists of a local master manipulator and a remotely located slave manipulator. Velocity commands are sent forward from the master to the slave, and force information is reflected back from the slave to the master. Often, there is a transmission delay when communicating between the two subsystems, which causes instability in the force-reflecting teleoperator. Recently, a solution for this problem was found, based on mimicking the behavior of a lossless transmission line. Although the resulting control law was shown to stabilize an actual single-DOF teleoperator system, and although the control law is intuitively stable because of its passivity properties, stability for the system has not yet been proven. In this article the authors extend these results to a nonlinear n-DOF system and prove its stability. Nonlinear, multidimensional networks are used to characterize the nonlinear equations for the master and slave manipulators, the time-delayed communication systems, the human operator, and the environment. Tellegen's theorem and the Lyapunov theory are then applied to prove that the master and slave subsystems have asymptotically stable velocities. In addition, they show how gain scaling can be used without disturbing the stability of the system.
Forcing of oceanic mean flows by dissipating internal tides
NASA Astrophysics Data System (ADS)
Grisouard, Nicolas; Buhler, Oliver
2012-11-01
We present a theoretical study of the effective mean force exerted on an oceanic mean flow due to the presence of small-amplitude internal waves that are forced by a barotropic tide flowing over a topography and are also subject to dissipation. Although the details of our computation are quite different, we recover the main action-at-a-distance result familiar from atmospheric wave-mean interaction theory, namely that the effective mean force that is felt by the mean flow is located in regions of wave dissipation, and not necessarily near the topographic wave source. Specifically, using a perturbation series in small wave amplitude, we compute the three-dimensional leading-order wave field using a Green's function approach, derive an explicit expression for the leading-order effective mean force at the next order within the framework of generalized Lagrangian-mean theory, discuss in detail the range of situations in which a strong, secularly growing mean-flow response can be expected, and finally compute the effective mean force numerically in a number of illustrative examples with simple topographies. Financial support under the United States National Science Foundation grants NSF/OCE 1024180 and NSF/DMS 1009213 is gratefully acknowledged.
NASA Astrophysics Data System (ADS)
Butuzov, V. F.
2016-08-01
Asymptotic formulae for the solution of the initial-boundary value problem for a singularly perturbed partially dissipative system of reaction-diffusion type are constructed and justified. The system consists of a parabolic and an ordinary differential equation in the case when the corresponding degenerate equation has a root of multiplicity two. The behaviour of the boundary layer functions and the algorithm for constructing them are significantly distinct from the case of a simple (multiplicity-one) root of the degenerate equation. Bibliography: 8 titles.
A stochastic boundary forcing for dissipative particle dynamics
NASA Astrophysics Data System (ADS)
Altenhoff, Adrian M.; Walther, Jens H.; Koumoutsakos, Petros
2007-07-01
The method of dissipative particle dynamics (DPD) is an effective, coarse grained model of the hydrodynamics of complex fluids. DPD simulations of wall-bounded flows are however often associated with spurious fluctuations of the fluid properties near the wall. We present a novel stochastic boundary forcing for DPD simulations of wall-bounded flows, based on the identification of fluctuations in simulations of the corresponding homogeneous system at equilibrium. The present method is shown to enforce accurately the no-slip boundary condition, while minimizing spurious fluctuations of material properties, in a number of benchmark problems.
Forte, Giuseppe; Cecconi, Fabio; Vulpiani, Angelo
2014-12-01
We study the asymptotic and preasymptotic diffusive properties of Brownian particles in channels whose section varies periodically in space. The effective diffusion coefficient D(eff) is numerically determined by the asymptotic behavior of the root mean square displacement in different geometries, considering even cases of steep variations of the channel boundaries. Moreover, we compared the numerical results to the predictions from the various corrections proposed in the literature to the well known Fick-Jacobs approximation. Building an effective one-dimensional equation for the longitudinal diffusion, we obtain an approximation for the effective diffusion coefficient. Such a result goes beyond a perturbation approach, and it is in good agreement with the actual values obtained by the numerical simulations. We discuss also the preasymptotic diffusion which is observed up to a crossover time whose value, in the presence of strong spatial variation of the channel cross section, can be very large. In addition, we show how the Einstein's relation between the mean drift induced by a small external field and the mean square displacement of the unperturbed system is valid in both asymptotic and preasymptotic regimes.
NASA Astrophysics Data System (ADS)
Forte, Giuseppe; Cecconi, Fabio; Vulpiani, Angelo
2014-12-01
We study the asymptotic and preasymptotic diffusive properties of Brownian particles in channels whose section varies periodically in space. The effective diffusion coefficient Deff is numerically determined by the asymptotic behavior of the root mean square displacement in different geometries, considering even cases of steep variations of the channel boundaries. Moreover, we compared the numerical results to the predictions from the various corrections proposed in the literature to the well known Fick-Jacobs approximation. Building an effective one-dimensional equation for the longitudinal diffusion, we obtain an approximation for the effective diffusion coefficient. Such a result goes beyond a perturbation approach, and it is in good agreement with the actual values obtained by the numerical simulations. We discuss also the preasymptotic diffusion which is observed up to a crossover time whose value, in the presence of strong spatial variation of the channel cross section, can be very large. In addition, we show how the Einstein's relation between the mean drift induced by a small external field and the mean square displacement of the unperturbed system is valid in both asymptotic and preasymptotic regimes.
NASA Astrophysics Data System (ADS)
Paulo, Álvaro San; García, Ricardo
2001-11-01
Amplitude-modulation (tapping mode) atomic force microscopy is a technique for high resolution imaging of a wide variety of surfaces in air and liquid environments. Here by using the virial theorem and energy conservation principles we have derived analytical relationships between the oscillation amplitude, phase shift, and average tip-surface forces. We find that the average value of the interaction force and oscillation and the average power dissipated by the tip-surface interaction are the quantities that control the amplitude reduction. The agreement obtained between analytical and numerical results supports the analytical method.
NASA Astrophysics Data System (ADS)
Filipovic, N.; Haber, S.; Kojic, M.; Tsuda, A.
2008-02-01
Traditional DPD methods address dissipative and random forces exerted along the line connecting neighbouring particles. Espanol (1998 Phys. Rev. E 57 2930-48) suggested adding dissipative and random force components in a direction perpendicular to this line. This paper focuses on the advantages and disadvantages of such an addition as compared with the traditional DPD method. Our benchmark system comprises fluid initially at rest occupying the space between two concentric cylinders rotating with various angular velocities. The effect of the lateral force components on the time evolution of the simulated velocity profile was also compared with that of the known analytical solution. The results show that (i) the solution accuracy at steady state has improved and the error has been reduced by at least 30% (in one case by 75%), (ii) the DPD time to reach steady state has been halved, (iii) the CPU time has increased by only 30%, and (iv) no significant differences exist in density and temperature distributions.
Magnetic energy dissipation in force-free jets
NASA Technical Reports Server (NTRS)
Choudhuri, Arnab Rai; Konigl, Arieh
1986-01-01
It is shown that a magnetic pressure-dominated, supersonic jet which expands or contracts in response to variations in the confining external pressure can dissipate magnetic energy through field-line reconnection as it relaxes to a minimum-energy configuration. In order for a continuous dissipation to occur, the effective reconnection time must be a fraction of the expansion time. The dissipation rate for the axisymmetric minimum-energy field configuration is analytically derived. The results indicate that the field relaxation process could be a viable mechanism for powering the synchrotron emission in extragalactic jets if the reconnection time is substantially shorter than the nominal resistive tearing time in the jet.
NASA Technical Reports Server (NTRS)
Sturrock, P. A.; Antiochos, S. K.; Klinchuk, J. A.; Roumeliotis, G.
1994-01-01
It is known from computer calculations that if a force-free magnetic field configuration is stressed progressively by footpoint displacements, the configuration expands and approaches the open configuration with the same surface flux distribution and the energy of the field increases progressively. For configurations of translationalsymmetry, it has been found empirically that the energy tends asymptotically to a certain functional form. It is here shown that analysis of a simple model of the asymptotic form of force-free fields of translational symmetry leads to and therefore justifies this functional form. According to this model, the field evolves in a well-behaved manner with no indication of instability or loss of equilibrium.
Accurate formula for dissipative interaction in frequency modulation atomic force microscopy
Suzuki, Kazuhiro; Matsushige, Kazumi; Yamada, Hirofumi; Kobayashi, Kei; Labuda, Aleksander
2014-12-08
Much interest has recently focused on the viscosity of nano-confined liquids. Frequency modulation atomic force microscopy (FM-AFM) is a powerful technique that can detect variations in the conservative and dissipative forces between a nanometer-scale tip and a sample surface. We now present an accurate formula to convert the dissipation power of the cantilever measured during the experiment to damping of the tip-sample system. We demonstrated the conversion of the dissipation power versus tip-sample separation curve measured using a colloidal probe cantilever on a mica surface in water to the damping curve, which showed a good agreement with the theoretical curve. Moreover, we obtained the damping curve from the dissipation power curve measured on the hydration layers on the mica surface using a nanometer-scale tip, demonstrating that the formula allows us to quantitatively measure the viscosity of a nano-confined liquid using FM-AFM.
Asymptotic analysis of force-free magnetic fields of cylindrical symmetry
NASA Technical Reports Server (NTRS)
Sturrock, P. A.; Antiochos, S. K.; Roumeliotis, G.
1995-01-01
It is known from computer calculations that if a force-free magnetic-field configuration is stressed progressively by footpoint displacements, the configuration expands and approaches the open configuration with the same surface flux distribution, and, in the process, the energy of the field increases progressively. Analysis of a simple model of force-free fields of cylindrical symmetry leads to simple asymptotic expressions for the extent and energy of such a configuration. The analysis is carried through for both spherical and planar source surfaces. According to this model, the field evolves in a well-behaved manner with no indication of instability or loss of equilibrium.
Metal Dissipation and Inefficient Recycling Intensify Climate Forcing.
Ciacci, Luca; Harper, E M; Nassar, N T; Reck, Barbara K; Graedel, T E
2016-10-07
In the metals industry, recycling is commonly included among the most viable options for climate change mitigation, because using secondary (recycled) instead of primary sources in metal production carries both the potential for significant energy savings and for greenhouse gas emissions reduction. Secondary metal production is, however, limited by the relative quantity of scrap available at end-of-life for two reasons: long product lifespans during use delay the availability of the material for reuse and recycling; and end-of-life recycling rates are low, a result of inefficient collection, separation, and processing. For a few metals, additional losses exist in the form of in-use dissipation. The sum of these lost material flows forms the theoretical maximum potential for future efficiency improvements. Based on a dynamic material flow analysis, we have evaluated these factors from an energy perspective for 50 metals and calculated the corresponding greenhouse gas emissions associated with the supply of lost material from primary sources that would otherwise be used to satisfy demand. A use-by-use examination demonstrates the potential emission gains associated with major application sectors. The results show that minimizing in-use dissipation and constraints to metal recycling have the potential to reduce greenhouse gas emissions from the metal industry by about 13-23%, corresponding to 1% of global anthropogenic greenhouse gas emissions.
Dissipative, forced turbulence in two-dimensional magnetohydrodynamics
NASA Technical Reports Server (NTRS)
Fyfe, D.; Montgomery, D.; Joyce, G.
1976-01-01
The equations of motion for turbulent two-dimensional magnetohydrodynamic flows are solved in the presence of finite viscosity and resistivity, for the case in which external forces (mechanical and/or magnetic) act on the fluid. The goal is to verify the existence of a magnetohydrodynamic dynamo effect which is represented mathematically by a substantial back-transfer of mean square vector potential to the longest allowed Fourier wavelengths. External forces consisting of a random part plus a fraction of the value at the previous time step are employed, after the manner of Lilly for the Navier-Stokes case. The regime explored is that for which the mechanical and magnetic Reynolds numbers are in the region of 100 to 1000. The conclusions are that mechanical forcing terms alone cannot lead to dynamo action, but that dynamo action can result from either magnetic forcing terms or from both mechanical and magnetic forcing terms simultaneously.
Computational model for noncontact atomic force microscopy: energy dissipation of cantilever.
Senda, Yasuhiro; Blomqvist, Janne; Nieminen, Risto M
2016-09-21
We propose a computational model for noncontact atomic force microscopy (AFM) in which the atomic force between the cantilever tip and the surface is calculated using a molecular dynamics method, and the macroscopic motion of the cantilever is modeled by an oscillating spring. The movement of atoms in the tip and surface is connected with the oscillating spring using a recently developed coupling method. In this computational model, the oscillation energy is dissipated, as observed in AFM experiments. We attribute this dissipation to the hysteresis and nonconservative properties of the interatomic force that acts between the atoms in the tip and sample surface. The dissipation rate strongly depends on the parameters used in the computational model.
NASA Astrophysics Data System (ADS)
Grannan, Alex; Favier, Benjamin; Bills, Bruce; Lemasquerier, Daphne; Le Bars, Michael; Aurnou, Jonathan
2016-10-01
The turbulent fluid motions generated in the liquid metal cores and oceans of planetary bodies can have profound effects on energy dissipation and magnetic field generation. An important driver of such fluid motions is mechanical forcing from precession, libration, and tidal forcing. On Earth, the dissipation of energy through tidal forcing occurs primarily in the oceans and may be due, in part, to nonlinear tidally forced resonances. However, the role that such nonlinear resonances play are not generally considered for other planetary bodies also possessing oceans and liquid metal cores.Recent laboratory experimental and numerical studies of Grannan et al. 2014 and Favier et al. 2015 have shown that nonlinear fluid resonances generated by sufficiently strong librational forcing can drive turbulent flows in ellipsoidal containers that mimic gravitational deformations. In Grannan et al. 2016, similar results were found for strong tidal forcing. Thus, a generalized scaling law for the turbulent r.m.s. velocity is derived, U~ɛβE-α, where ɛ is the dimensionless amplitude of the tidal or librational forcing, β is the dimensionless tidal deformation of the body, E is the dimensionless Ekman number characterizing the ratio of viscous to Coriolis forces, and α is a varying exponent.Using planetary values for tidal and librational forcing parameters, the turbulent dissipation is estimated for multiple bodies. For the subsurface oceans of Europa and Enceladus, the amount of nonlinear dissipation is comparable to the dissipation generated from linear resonances of the fluid layer and from upper bounding estimates of the tidal dissipation in the solid icy shell. In addition, our estimates of this turbulent dissipation provide bounds for the stratification in these subsurface oceans. Finally we find that dissipation from these nonlinear resonances in the liquid metal cores of the the early and present Earth, Io, and several exoplanets may help drive the dynamos in these
NASA Astrophysics Data System (ADS)
Yasumura, Kevin Youl
In 1986 the atomic force microscope (AFM) was invented by Binnig, Quate, and Gerber. Cantilever based force microscopy has been used in a wide range of fields including the study of biological samples, data storage media, and microelectronics. These AFM-based imaging techniques typically measure forces in the piconewton (10-12 N) range. Recent developments in microcantilever fabrication and optical fiber displacement sensors have allowed for the construction of force microscope systems that are capable of measuring forces in the attonewton (10-18 N) range. Applications such as magnetic resonance force microscopy (MRFM) require the cantilevers used to have subattonewton force resolution in order to eventually detect single nuclear spins. It is believed that improvements in cantilever and experimental design will allow for improved force resolution. A fundamental limit to the detection of small forces is thermomechanical noise. The thermal noise force limit, via the fluctuation dissipation theorem, is directly related to the amount of mechanical energy dissipation in the cantilever-based force sensor. Work has therefore been focused on developing an understanding of which mechanisms are limiting the force resolution of these microcantilever oscillators. Arrays of silicon nitride, single-crystal silicon, and polysilicon cantilevers have been fabricated and studied. By measuring the dependence of Q on cantilever material, geometry, and surface treatments, significant insight into the dissipation mechanisms has been obtained. For submicron thick cantilevers, Q is found to decrease with decreasing cantilever thickness, indicative of surface loss mechanisms. For single-crystal silicon cantilevers, significant increase in room temperature Q is obtained after 700 C heat treatment in either N 2 or forming gas. Thermoelastic dissipation is not a factor for submicron thick cantilevers, but is shown to be significant for silicon nitride cantilevers as thin as 2.3 um. At low
Kiracofe, Daniel; Raman, Arvind
2011-12-02
The use of a piezoelectric element (acoustic excitation) to vibrate the base of microcantilevers is a popular method for dynamic atomic force microscopy. In air or vacuum, the base motion is so small (relative to tip motion) that it can be neglected. However, in liquid environments the base motion can be large and cannot be neglected. Yet it cannot be directly observed in most AFMs. Therefore, in liquids, quantitative force and energy dissipation spectroscopy with acoustic AFM relies on theoretical formulae and models to estimate the magnitude of the base motion. However, such formulae can be inaccurate due to several effects. For example, a significant component of the piezo excitation does not mechanically excite the cantilever but rather transmits acoustic waves through the surrounding liquid, which in turn indirectly excites the cantilever. Moreover, resonances of the piezo, chip and holder can obscure the true cantilever dynamics even in well-designed liquid cells. Although some groups have tried to overcome these limitations (either by theory modification or better design of piezos and liquid cells), it is generally accepted that acoustic excitation is unsuitable for quantitative force and dissipation spectroscopy in liquids. In this paper the authors present a careful study of the base motion and excitation forces and propose a method by which quantitative analysis is in fact possible, thus opening this popular method for quantitative force and dissipation spectroscopy using dynamic AFM in liquids. This method is validated by experiments in water on mica using a scanning laser Doppler vibrometer, which can measure the actual base motion. Finally, the method is demonstrated by using small-amplitude dynamic AFM to extract the force gradients and dissipation on solvation shells of octamethylcyclotetrasiloxane (OMCTS) molecules on mica.
Effects of gas interparticle interaction on dissipative wake-mediated forces
NASA Astrophysics Data System (ADS)
Kliushnychenko, O. V.; Lukyanets, S. P.
2017-01-01
We examine how the short-range repulsive interaction in a gas of Brownian particles affects behavior of the nonequilibrium depletion forces between obstacles embedded into the gas flow. It is shown that for an ensemble of small and widely separated obstacles the dissipative wake-mediated interaction belongs to the type of induced dipole-dipole interaction governed by an anisotropic screened Coulomb-like potential. For closely located obstacles, formation of a common density perturbation "coat" around them leads to enhancement of dissipative interaction, manifested by characteristic peaks in its dependence on both the bath fraction and the external driving field. Moreover, additional screening of the gas flow due to nonlinear blockade effect gives rise to generation of a pronounced step-like profile of gas density distribution around the obstacles. This can lead to additional enhancement of dissipative interaction between obstacles. The possibility of the dissipative pairing effect and dissipative interaction switching provoked by wake inversion is briefly discussed. All the results are obtained within the classical lattice-gas model.
Ledezma, G.A.; Campo, A.
1999-04-01
The utilization of internal longitudinal finned tubes has received unparallel attention in the heat transfer literature over the years as a result of its imminent application in high performance compact heat exchangers to enhance the heat transfer between laminar streams of viscous fluids and tube walls. Here, the central goal of this paper is to report a simple approximate way for the prediction of the two asymptotes for the local Nusselt number in laminar forced convection flows inside internal longitudinal finned tubes. The computational attributes of the Method Of Lines (MOL) are propitious for the determination of asymptotic temperature solutions and corresponding heat transfer rates (one for Z {r_arrow} 0 and the other for z {r_arrow} {infinity}). The two local Nusselt number sub-distributions, namely Nu{sub z{r_arrow}0} and Nu{sub z{r_arrow}{infinity}}, blend themselves into an approximate Nusselt number distribution that covers the entire z-domain in a natural way.
Can Dissipative Properties of Single Molecules Be Extracted from a Force Spectroscopy Experiment?
Benedetti, Fabrizio; Gazizova, Yulia; Kulik, Andrzej J; Marszalek, Piotr E; Klinov, Dmitry V; Dietler, Giovanni; Sekatskii, Sergey K
2016-09-20
We performed dynamic force spectroscopy of single dextran and titin I27 molecules using small-amplitude and low-frequency (40-240 Hz) dithering of an atomic force microscope tip excited by a sine wave voltage fed onto the tip-carrying piezo. We show that for such low-frequency dithering experiments, recorded phase information can be unambiguously interpreted within the framework of a transparent theoretical model that starts from a well-known partial differential equation to describe the dithering of an atomic force microscope cantilever and a single molecule attached to its end system, uses an appropriate set of initial and boundary conditions, and does not exploit any implicit suggestions. We conclude that the observed phase (dissipation) signal is due completely to the dissipation related to the dithering of the cantilever itself (i.e., to the change of boundary conditions in the course of stretching). For both cases, only the upper bound of the dissipation of a single molecule has been established as not exceeding 3⋅10(-7)kg/s. We compare our results with previously reported measurements of the viscoelastic properties of single molecules, and we emphasize that extreme caution must be taken in distinguishing between the dissipation related to the stretched molecule and the dissipation that originates from the viscous damping of the dithered cantilever. We also present the results of an amplitude channel data analysis, which reveal that the typical values of the spring constant of a I27 molecule at the moment of module unfolding are equal to 4±1.5mN/m, and the typical values of the spring constant of dextran at the moment of chair-boat transition are equal to 30-50mN/m.
Thermal dissipation force modeling with preliminary results for Pioneer 10/11
NASA Astrophysics Data System (ADS)
Rievers, Benny; Bremer, Stefanie; List, Meike; Lämmerzahl, Claus; Dittus, Hansjörg
2010-02-01
The dissipation of thermal energy can produce disturbance forces on spacecraft surfaces if the energy is not dissipated in a symmetric pattern. This force can be computed as the quotient of the radiated power and the speed of light for a plate surface element. Depending on mission and spacecraft design the resulting surface forces have to be included into the disturbance budget. At ZARM (Center of Applied Space Technology and Microgravity) a raytracing algorithm was developed that allows the computation of the resulting force for complex spacecraft geometries. The method is based on the modeling of the spacecraft geometry in finite elements (FEs). Using an FE-solver the surface temperatures of the satellite can be derived with geometry and material parameters using heat sources/sinks as constraints. The outgoing radiation force is computed including reflectivity and absorption between all elements of the model. As an example for the method a test case model of the radio isotope thermal generators (RTGs) of Pioneer 11 is processed with this force computing method. The results show that detailed thermal modeling for the whole craft is necessary as the simplified test case results in a force that is non-negligible with respect to the pioneer anomaly.
Thermal Noise Reduction of Mechanical Oscillators by Actively Controlled External Dissipative Forces
NASA Technical Reports Server (NTRS)
Liang, Shoudan; Medich, David; Czajkowsky, Daniel M.; Sheng, Sitong; Yuan, Jian-Yang; Shao, Zhifeng
1999-01-01
We show that the thermal fluctuations of very soft mechanical oscillators, such as the cantilever in an atomic force microscope (AFM), can be reduced without changing the stiffness of the spring or having to lower the environment temperature. We derive a theoretical relationship between the thermal fluctuations of an oscillator and an actively external-dissipative force. This relationship is verified by experiments with an AFM cantilever where the external active force is coupled through a magnetic field. With simple instrumentation, we have reduced the thermal noise amplitude of the cantilever by a factor of 3.4, achieving an apparent temperature of 25 K with the environment at 295K. This active noise reduction approach can significantly improve the accuracy of static position or static force measurements in a number of practical applications.
The effect of dissipation on the torque and force experienced by nanoparticles in an AC field
NASA Astrophysics Data System (ADS)
Claro, F.; Fuchs, R.; Robles, P.; Rojas, R.
2015-09-01
We discuss the force and torque acting on spherical particles in an ensemble in the presence of a uniform AC electric field. We show that for a torque causing particle rotation to appear the particle must be absorptive. Our proof includes all electromagnetic excitations, which in the case of two or more particles gives rise to one or more resonances in the spectrum of force and torque depending on interparticle distance. Several peaks are found in the force and torque between two spheres at small interparticle distances, which coalesce to just one as the separation grows beyond three particle radii. We also show that in the presence of dissipation the force on each particle is nonconservative and may not be derived from the classical interaction potential energy as has been done in the past.
NASA Astrophysics Data System (ADS)
Huang, Sumei; Agarwal, G. S.
2017-02-01
We theoretically investigate optical detection of a weak classical force acting on a free particle in a dissipative coupling optomechanical system with a degenerate parametric amplifier (PA). We show that the PA allows one to achieve the force sensitivity far better than the standard quantum limit (SQL) over a broad range of the detection frequencies. The improvement depends on the parametric gain and the driving power. Moreover, we discuss the effects of the mechanical damping and the thermal noise on the force sensitivity. We find that the robustness of the force sensitivity is much better than the SQL against the mechanical damping and the thermal noise is achievable in the presence of the PA with a high parametric gain. For the temperature T =1 K, the improvement in sensitivity is better by a factor of about 7 when the driving power is set at a value corresponding to the SQL with no PA.
NASA Technical Reports Server (NTRS)
Hickey, M. P.
1988-01-01
This paper examines the effect of inclusion of Coriolis force and eddy dissipation in the gravity wave dynamics theory of Walterscheid et al. (1987). It was found that the values of the ratio 'eta' (where eta is a complex quantity describing the ralationship between the intensity oscillation about the time-averaged intensity, and the temperature oscillation about the time-averaged temperature) strongly depend on the wave period and the horizontal wavelength; thus, if comparisons are to be made between observations and theory, horizontal wavelengths will need to be measured in conjunction with the OH nightglow measurements. For the waves with horizontal wavelengths up to 1000 km, the eddy dissipation was found to dominate over the Coriolis force in the gravity wave dynamics and also in the associated values of eta. However, for waves with horizontal wavelengths of 10,000 km or more, the Coriolis force cannot be neglected; it has to be taken into account along with the eddy dissipation.
Mori-Zwanzig theory for dissipative forces in coarse-grained dynamics in the Markov limit
NASA Astrophysics Data System (ADS)
Izvekov, Sergei
2017-01-01
We derive alternative Markov approximations for the projected (stochastic) force and memory function in the coarse-grained (CG) generalized Langevin equation, which describes the time evolution of the center-of-mass coordinates of clusters of particles in the microscopic ensemble. This is done with the aid of the Mori-Zwanzig projection operator method based on the recently introduced projection operator [S. Izvekov, J. Chem. Phys. 138, 134106 (2013), 10.1063/1.4795091]. The derivation exploits the "generalized additive fluctuating force" representation to which the projected force reduces in the adopted projection operator formalism. For the projected force, we present a first-order time expansion which correctly extends the static fluctuating force ansatz with the terms necessary to maintain the required orthogonality of the projected dynamics in the Markov limit to the space of CG phase variables. The approximant of the memory function correctly accounts for the momentum dependence in the lowest (second) order and indicates that such a dependence may be important in the CG dynamics approaching the Markov limit. In the case of CG dynamics with a weak dependence of the memory effects on the particle momenta, the expression for the memory function presented in this work is applicable to non-Markov systems. The approximations are formulated in a propagator-free form allowing their efficient evaluation from the microscopic data sampled by standard molecular dynamics simulations. A numerical application is presented for a molecular liquid (nitromethane). With our formalism we do not observe the "plateau-value problem" if the friction tensors for dissipative particle dynamics (DPD) are computed using the Green-Kubo relation. Our formalism provides a consistent bottom-up route for hierarchical parametrization of DPD models from atomistic simulations.
NASA Astrophysics Data System (ADS)
Yaghoubi, S.; Shirani, E.; Pishevar, A. R.; Afshar, Y.
2015-04-01
To simulate liquid fluid flows with high Schmidt numbers (Sc), one needs to use a modified version of the Dissipative Particle Dynamics (DPD) method. Recently the modifications made by others for the weight function of dissipative forces, enables DPD simulations for Sc, up to 10. In this paper, we introduce a different dissipative force weight function for DPD simulations that allows achieving a solution with higher values of Sc and improving the dynamic characteristics of the simulating fluid. Moreover, by reducing the energy of DPD particles, even higher values of Sc can be achieved. Finally, using the new proposed weight function and kBT =0.2 , the Sc values can reach up to 200.
Forced cubic Schrödinger equation with Robin boundary data: large-time asymptotics.
Kaikina, Elena I
2013-11-08
We consider the initial-boundary-value problem for the cubic nonlinear Schrödinger equation, formulated on a half-line with inhomogeneous Robin boundary data. We study traditionally important problems of the theory of nonlinear partial differential equations, such as the global-in-time existence of solutions to the initial-boundary-value problem and the asymptotic behaviour of solutions for large time.
Kisiel, M; Pellegrini, F; Santoro, G E; Samadashvili, M; Pawlak, R; Benassi, A; Gysin, U; Buzio, R; Gerbi, A; Meyer, E; Tosatti, E
2015-07-24
The critical fluctuations at second order structural transitions in a bulk crystal may affect the dissipation of mechanical probes even if completely external to the crystal surface. Here, we show that noncontact force microscope dissipation bears clear evidence of the antiferrodistortive phase transition of SrTiO_{3}, known for a long time to exhibit a unique, extremely narrow neutron scattering "central peak." The noncontact geometry suggests a central peak linear response coupling connected with strain. The detailed temperature dependence reveals for the first time the intrinsic central peak width of order 80 kHz, 2 orders of magnitude below the established neutron upper bound.
Goicochea, Armando Gama; Alarcón, Francisco
2011-01-07
The thermodynamic properties of a simple fluid confined by effective wall forces are calculated using Monte Carlo simulations in the grand canonical ensemble. The solvation force produced by polymer brushes of two different lengths is obtained also. For the particular type of model interactions used, known as the dissipative particle dynamics method, we find that it is possible to obtain an exact, simple expression for the effective force induced by a planar wall composed of identical particles that interact with those in the fluid. We show that despite the short range of all forces in the model, the solvation force can be finite at relatively large distances and therefore does not depend only on the range of the interparticle or solvent-surface forces. As for the polymer brushes, we find that the shape of the solvation force profiles is in fair agreement with scaling and self-consistent field theories. The applications and possible extensions of this work are discussed.
NASA Astrophysics Data System (ADS)
Cyranka, Jacek; Zgliczyński, Piotr
2016-10-01
We describe a topological method to study the dynamics of dissipative PDEs on a torus with rapidly oscillating forcing terms. We show that a dissipative PDE, which is invariant with respect to the Galilean transformations, with a large average initial velocity can be reduced to a problem with rapidly oscillating forcing terms. We apply the technique to the viscous Burgers' equation, and the incompressible 2D Navier-Stokes equations with a time-dependent forcing. We prove that for a large initial average speed the equation admits a bounded eternal solution, which attracts all other solutions forward in time. For the incompressible 3D Navier-Stokes equations we establish the existence of a locally attracting solution.
NASA Astrophysics Data System (ADS)
Brancati, Renato; Strano, Salvatore; Timpone, Francesco
2011-10-01
When in use, a tire dissipates energy according to various mechanisms: rolling resistance, viscosity, hysteresis, friction energy, etc. This dissipation of energy contributes to influencing tire temperature, contact conditions and the resulting friction coefficient. This research project deals with viscoelastic and hysteretic mechanisms, and presents an explicit expression of the energy dissipated by tire-road interactions caused by these mechanisms. It is based on the Dahl model with regard to the hysteretic force together with a spring and a frequency variable damping coefficient with regard to the viscoelastic one. The energy expression found in this way can be used in tire thermal models to determine one of the heat flows needed to estimate the contact temperature and to find out the actual friction coefficient to be used in real time tire-road interaction models. Experimental tests were carried out, for longitudinal interaction only, in order to evaluate the effectiveness of the proposed expression by identifying the parameters and validating the results.
Two-photon exchange force in scalar quantum electrodynamics: The asymptotic story
NASA Astrophysics Data System (ADS)
Sucher, J.
1994-04-01
The dependence of the potential V2γ arising from two-photon exchange between charged spinless systems on the one-photon exchange potential V1γ is examined. It is found that, unlike the case when at least one of the two systems is neutral, the form of V1γ can play a key role in determining the large-r behavior of V2γ. It is shown that if V1γ is defined in a way inspired by the use of the Coulomb gauge rather than the Feynman gauge, V2γ falls off as r-3, rather than as r-2. This result, which removes an apparent cognitive dissonance with the related work of Spruch, does not mean that the effective potential is inherently gauge dependent. Instead it highlights the fact that in this case the concept of the asymptotic behavior of V2γ is not as sharp as one might have thought. The relation of this result to an analogous one expected to hold for spinor QED and to the nonrelativistic form of the orbit-orbit interaction is also discussed.
Diaz, Alfredo J.; Eslami, Babak; López-Guerra, Enrique A.; Solares, Santiago D.
2014-09-14
This paper explores the effect of the amplitude ratio of the higher to the fundamental eigenmode in bimodal atomic force microscopy (AFM) on the phase contrast and the dissipated power contrast of the higher eigenmode. We explore the optimization of the amplitude ratio in order to maximize the type of contrast that is most relevant to the particular study. Specifically, we show that the trends in the contrast range behave differently for different quantities, especially the dissipated power and the phase, with the former being more meaningful than the latter (a similar analysis can be carried out using the virial, for which we also provide a brief example). Our work is based on numerical simulations using two different conservative-dissipative tip-sample models, including the standard linear solid and the combination of a dissipation coefficient with a conservative model, as well as experimental images of thin film Nafion{sup ®} proton exchange polymers. We focus on the original bimodal AFM method, where the higher eigenmode is driven with constant amplitude and frequency (i.e., in “open loop”).
ERIC Educational Resources Information Center
Dobbs, David E.
2010-01-01
This note develops and implements the theory of polynomial asymptotes to (graphs of) rational functions, as a generalization of the classical topics of horizontal asymptotes and oblique/slant asymptotes. Applications are given to hyperbolic asymptotes. Prerequisites include the division algorithm for polynomials with coefficients in the field of…
NASA Astrophysics Data System (ADS)
Cho, Yeunwoo
2014-11-01
The shedding phenomena of 3-D viscous gravity-capillary solitary waves generated by a moving air-forcing on the surface of deep water are investigated. Near the resonance where the forcing speed is close to 23 cm/s, two kinds of shedding modes are possible; Anti-symmetric and symmetric modes. A relevant theoretical model equation is numerically solved for the identification of shedding of solitary waves, and is analytically studied in terms of their linear stability to transverse perturbations. Furthermore, by tracing trajectories of shed solitary waves, the decay rate of a 3-D solitary wave due to viscous dissipation is estimated. This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (NRF-2014R1A1A1002441).
NASA Astrophysics Data System (ADS)
Yazdani, Alireza; Deng, Mingge; Caswell, Bruce; Karniadakis, George Em
2016-01-01
We demonstrate how the quality of simulations by Dissipative Particle Dynamics (DPD) of flows in complex geometries is greatly enhanced when driven by body forces suitably tailored to the geometry. In practice, the body force fields are most conveniently chosen to be the pressure gradient of the corresponding Navier-Stokes (N-S) flow. In the first of three examples, the driving-force required to yield a stagnation-point flow is derived from the pressure field of the potential flow for a lattice of counter-rotating line vortices. Such a lattice contains periodic squares bounded by streamlines with four vortices within them. Hence, the DPD simulation can be performed with periodic boundary conditions to demonstrate the value of a non-uniform driving-force without the need to model real boundaries. The second example is an irregular geometry consisting of a 2D rectangular cavity on one side of an otherwise uniform channel. The Navier-Stokes pressure field for the same geometry is obtained numerically, and its interpolated gradient is then employed as the driving-force for the DPD simulation. Finally, we present a third example, where the proposed method is applied to a complex 3D geometry of an asymmetric constriction. It is shown that in each case the DPD simulations closely reproduce the Navier-Stokes solutions. Convergence rates are found to be much superior to alternative methods; in addition, the range of convergence with respect to Reynolds number and Mach number is greatly extended.
Wang, Chao; Kittle, Joshua D; Qian, Chen; Roman, Maren; Esker, Alan R
2013-08-12
Chitinases are widely distributed in nature and have wide-ranging pharmaceutical and biotechnological applications. This work highlights a real-time and label-free method to assay Chitinase activity via a quartz crystal microbalance with dissipation monitoring (QCM-D) and atomic force microscopy (AFM). The chitin substrate was prepared by spincoating a trimethylsilyl chitin solution onto a silica substrate, followed by regeneration to amorphous chitin (RChi). The QCM-D and AFM results clearly showed that the hydrolysis rate of RChi films increased as Chitinase (from Streptomyces griseus) concentrations increased, and the optimal temperature and pH for Chitinase activity were around 37 °C and 6-8, respectively. The Chitinase showed greater activity on chitin substrates, having a high degree of acetylation, than on chitosan substrates, having a low degree of acetylation.
Engl, Christoph; Beek, Alex Ter; Bekker, Martijn; de Mattos, Joost Teixeira; Jovanovic, Goran; Buck, Martin
2011-05-01
Phage shock proteins (Psp) and their homologues are found in species from the three domains of life: Bacteria, Archaea and Eukarya (e.g. higher plants). In enterobacteria, the Psp response helps to maintain the proton motive force (PMF) of the cell when the inner membrane integrity is impaired. The presumed ability of ArcB to sense redox changes in the cellular quinone pool and the strong decrease of psp induction in ΔubiG or ΔarcAB backgrounds suggest a link between the Psp response and the quinone pool. The authors now provide evidence indicating that the physiological signal for inducing psp by secretin-induced stress is neither the quinone redox state nor a drop in PMF. Neither the loss of the H(+)-gradient nor the dissipation of the electrical potential alone is sufficient to induce the Psp response. A set of electron transport mutants differing in their redox states due to the lack of a NADH dehydrogenase and a quinol oxidase, but retaining a normal PMF displayed low levels of psp induction inversely related to oxidised ubiquinone levels under microaerobic growth and independent of PMF. In contrast, cells displaying higher secretin induced psp expression showed increased levels of ubiquinone. Taken together, this study suggests that not a single but likely multiple signals are needed to be integrated to induce the Psp response.
Wang, Chao; Qian, Chen; Roman, Maren; Glasser, Wolfgang G; Esker, Alan R
2013-11-11
This work highlights a real-time and label-free method to monitor the dehydrogenative polymerization of monolignols initiated by horseradish peroxidase (HRP) physically immobilized on surfaces using a quartz crystal microbalance with dissipation monitoring (QCM-D). The dehydrogenative polymer (DHP) films are expected to provide good model substrates for studying ligninolytic enzymes. The HRP was adsorbed onto gold or silica surfaces or onto and within porous desulfated nanocrystalline cellulose films from an aqueous solution. Surface-immobilized HRP retained its activity and selectivity for monolignols as coniferyl and p-coumaryl alcohol underwent dehydrogenative polymerization in the presence of hydrogen peroxide, whereas sinapyl alcohol polymerization required the addition of a nucleophile. The morphologies of the DHP layers on the surfaces were investigated via atomic force microscopy (AFM). Data from QCM-D and AFM showed that the surface-immobilized HRP-initiated dehydrogenative polymerization of monolignols was greatly affected by the support surface, monolignol concentration, hydrogen peroxide concentration, and temperature.
NASA Technical Reports Server (NTRS)
Thompson, P. M.; Stein, G.
1980-01-01
The behavior of the closed loop eigenstructure of a linear system with output feedback is analyzed as a single parameter multiplying the feedback gain is varied. An algorithm is presented that computes the asymptotically infinite eigenstructure, and it is shown how a system with high gain feedback decouples into single input single ouput systems. Then a synthesis algorithm is presented which uses full state feedback to achieve a desired asymptotic eigenstructure.
NASA Technical Reports Server (NTRS)
Thompson, P. M.; Stein, G.
1980-01-01
The behavior of the closed loop eigenstructure of a linear system with output feedback is analyzed as a single parameter multiplying the feedback gain is varied. An algorithm is presented that computes the asymptotically infinite eigenstructure, and it is shown how a system with high gain, feedback decouples into single input, single output systems. Then a synthesis algorithm is presented which uses full state feedback to achieve a desired asymptotic eigenstructure.
NASA Astrophysics Data System (ADS)
Berry, M. V.
2005-01-01
By applying the technique of uniform asymptotic approximation to the oscillatory integrals representing tsunami wave profiles, the form of the travelling wave far from the source is calculated for arbitrary initial disturbances. The approximations reproduce the entire profiles very accurately, from the front to the tail, and their numerical computation is much faster than that of the oscillatory integrals. For one-dimensional propagation, the uniform asymptotics involve Airy functions and their derivatives; for two-dimensional propagation, the uniform asymptotics involve products of these functions. Separate analyses are required when the initial disturbance is specified as surface elevation or surface velocity as functions of position, and when these functions are even or odd. 'There was an awful rainbow once in heaven' (John Keats, 1820)
Dissipative Solitons that Cannot be Trapped
Pardo, Rosa; Perez-Garcia, Victor M.
2006-12-22
We show that dissipative solitons in systems with high-order nonlinear dissipation cannot survive in the presence of trapping potentials of the rigid wall or asymptotically increasing type. Solitons in such systems can survive in the presence of a weak potential but only with energies out of the interval of existence of linear quantum mechanical stationary states.
NASA Astrophysics Data System (ADS)
Aschwanden, Markus J.
2016-06-01
In this work we provide an updated description of the Vertical-Current Approximation Nonlinear Force-Free Field (VCA-NLFFF) code, which is designed to measure the evolution of the potential, non-potential, free energies, and the dissipated magnetic energies during solar flares. This code provides a complementary and alternative method to existing traditional NLFFF codes. The chief advantages of the VCA-NLFFF code over traditional NLFFF codes are the circumvention of the unrealistic assumption of a force-free photosphere in the magnetic field extrapolation method, the capability to minimize the misalignment angles between observed coronal loops (or chromospheric fibril structures) and theoretical model field lines, as well as computational speed. In performance tests of the VCA-NLFFF code, by comparing with the NLFFF code of Wiegelmann, we find agreement in the potential, non-potential, and free energy within a factor of ≲ 1.3, but the Wiegelmann code yields in the average a factor of 2 lower flare energies. The VCA-NLFFF code is found to detect decreases in flare energies in most X, M, and C-class flares. The successful detection of energy decreases during a variety of flares with the VCA-NLFFF code indicates that current-driven twisting and untwisting of the magnetic field is an adequate model to quantify the storage of magnetic energies in active regions and their dissipation during flares. The VCA-NLFFF code is also publicly available in the Solar SoftWare.
Tidal waves within the thermosphere. [emphasizing wave dissipation and diffusion
NASA Technical Reports Server (NTRS)
Volland, H.; Mayr, H. G.
1974-01-01
The eigenfunctions of the atmosphere (the Hough functions within the lower atmosphere below about 100 km) change their structure and their propagation characteristics within the thermosphere due to dissipation effects such as heat conduction, viscosity, and ion drag. Wave dissipation can be parameterized to a first-order approximation by a complex frequency, the imaginary term of which simulates an effective ion drag force. It is shown how the equivalent depth, the attenuation, and the vertical wavelength of the predominant symmetric diurnal tidal modes change with height as functions of effective ion drag. The boundary conditions of tidal waves are discussed, and asymptotic solutions for the wave parameters like pressure, density, temperature, and wind generated by a heat input proportional to the mean pressure are given. Finally, diffusion effects upon the minor constituents within the thermosphere are described.
NASA Astrophysics Data System (ADS)
Vysotskii, V. I.; Vysotskyy, M. V.
2014-04-01
The features of the formation of correlated coherent states of a particle in a parabolic potential well at its monotonic deformation (expansion or compression) in finite limits have been considered in the presence of dissipation and a stochastic force. It has been shown that, in both deformation regimes, a correlated coherent state is rapidly formed with a large correlation coefficient | r| → 1, which corresponds at a low energy of the particle to a very significant (by a factor of 1050-10100 or larger) increase in the transparency of the potential barrier at its interaction with atoms (nuclei) forming the "walls" of the potential well or other atoms located in the same well. The efficiency of the formation of correlated coherent states, as well as | r|, increases with an increase in the deformation interval and with a decrease in the deformation time. The presence of the stochastic force acting on the particle can significantly reduce the maximum | r| value and result in the fast relaxation of correlated coherent states with | r| → 0. The effect of dissipation in real systems is weaker than the action of the stochastic force. It has been shown that the formation of correlated coherent states at the fast expansion of the well can underlie the mechanism of nuclear reactions at a low energy, e.g., in microcracks developing in the bulk of metal hydrides loaded with hydrogen or deuterium, as well as in a low-pressure plasma in a variable magnetic field in which the motion of ions is similar to a harmonic oscillator with a variable frequency.
An asymptotic model of the F layer
NASA Astrophysics Data System (ADS)
Oliver, W. L.
2012-01-01
A model of the F layer of the ionosphere is presented that consists of a bottomside asymptote that ignores transport and a topside asymptote that ignores chemistry. The asymptotes connect at the balance height dividing the chemistry and transport regimes. A combination of these two asymptotes produces a good approximation to the true F layer. Analogously, a model of F layer response to an applied vertical drift is presented that consists of two asymptotic responses, one that ignores transport and one that ignores chemistry. The combination of these asymptotic responses produces a good approximation to the response of the true F layer. This latter response is identical to the “servo” response of Rishbeth et al. (1978), derived from the continuity equation. The asymptotic approach bypasses the continuity equation in favor of “force balance” arguments and so replaces a differential equation with simpler algebraic equations. This new approach provides a convenient and intuitive mean for first-order estimates of the change in F layer peak height and density in terms of changes in neutral density, composition, temperature, winds, and electric fields. It is applicable at midlatitudes and at magnetically quiet times at high latitudes. Forensic inverse relations are possible but are not unique. The validity of the asymptotic relations is shown through numerical simulation.
NASA Astrophysics Data System (ADS)
Shargel, Benjamin Hertz; Chou, Tom
2009-10-01
Asymptotic fluctuation theorems are statements of a Gallavotti-Cohen symmetry in the rate function of either the time-averaged entropy production or heat dissipation of a process. Such theorems have been proved for various general classes of continuous-time deterministic and stochastic processes, but always under the assumption that the forces driving the system are time independent, and often relying on the existence of a limiting ergodic distribution. In this paper we extend the asymptotic fluctuation theorem for the first time to inhomogeneous continuous-time processes without a stationary distribution, considering specifically a finite state Markov chain driven by periodic transition rates. We find that for both entropy production and heat dissipation, the usual Gallavotti-Cohen symmetry of the rate function is generalized to an analogous relation between the rate functions of the original process and its corresponding backward process, in which the trajectory and the driving protocol have been time-reversed. The effect is that spontaneous positive fluctuations in the long time average of each quantity in the forward process are exponentially more likely than spontaneous negative fluctuations in the backward process, and vice-versa, revealing that the distributions of fluctuations in universes in which time moves forward and backward are related. As an additional result, the asymptotic time-averaged entropy production is obtained as the integral of a periodic entropy production rate that generalizes the constant rate pertaining to homogeneous dynamics.
Dissipative structures and related methods
Langhorst, Benjamin R; Chu, Henry S
2013-11-05
Dissipative structures include at least one panel and a cell structure disposed adjacent to the at least one panel having interconnected cells. A deformable material, which may comprise at least one hydrogel, is disposed within at least one interconnected cell proximate to the at least one panel. Dissipative structures may also include a cell structure having interconnected cells formed by wall elements. The wall elements may include a mesh formed by overlapping fibers having apertures formed therebetween. The apertures may form passageways between the interconnected cells. Methods of dissipating a force include disposing at least one hydrogel in a cell structure proximate to at least one panel, applying a force to the at least one panel, and forcing at least a portion of the at least one hydrogel through apertures formed in the cell structure.
NASA Technical Reports Server (NTRS)
Gokoglu, S. A.; Rosner, D. E.
1984-01-01
A cooled object (heat exchanger tube or turbine blade) is considered to be immersed in a hot fluid stream containing trace amounts of suspended vapors and/or small particles. Numerical prediction calculations were done for self-similar laminar boundary layers and law-of-the-wall turbulent boundary layers. Correlations are presented for the effect of thermophoresis in the absence of transpiration cooling and viscous dissipation; the effect of real suction and blowing in the absence of thermophoresis; the effect of viscous dissipation on thermophoresis in the absence of transpiration cooling; and the combined effect of viscous dissipation and transpiration cooling on thermophoresis. The final correlation, St/St-sub-zero, is insensitive to particle properties, Euler number, and local mainstream temperature.
Quantum dissipative Higgs model
Amooghorban, Ehsan Mahdifar, Ali
2015-09-15
By using a continuum of oscillators as a reservoir, we present a classical and a quantum-mechanical treatment for the Higgs model in the presence of dissipation. In this base, a fully canonical approach is used to quantize the damped particle on a spherical surface under the action of a conservative central force, the conjugate momentum is defined and the Hamiltonian is derived. The equations of motion for the canonical variables and in turn the Langevin equation are obtained. It is shown that the dynamics of the dissipative Higgs model is not only determined by a projected susceptibility tensor that obeys the Kramers–Kronig relations and a noise operator but also the curvature of the spherical space. Due to the gnomonic projection from the spherical space to the tangent plane, the projected susceptibility displays anisotropic character in the tangent plane. To illuminate the effect of dissipation on the Higgs model, the transition rate between energy levels of the particle on the sphere is calculated. It is seen that appreciable probabilities for transition are possible only if the transition and reservoir’s oscillators frequencies to be nearly on resonance.
Dissipation effects in mechanics and thermodynamics
NASA Astrophysics Data System (ADS)
Güémez, J.; Fiolhais, M.
2016-07-01
With the discussion of three examples, we aim at clarifying the concept of energy transfer associated with dissipation in mechanics and in thermodynamics. The dissipation effects due to dissipative forces, such as the friction force between solids or the drag force in motions in fluids, lead to an internal energy increase of the system and/or to heat transfer to the surroundings. This heat flow is consistent with the second law, which states that the entropy of the universe should increase when those forces are present because of the irreversibility always associated with their actions. As far as mechanics is concerned, the effects of the dissipative forces are included in Newton’s equations as impulses and pseudo-works.
Large Time Asymptotics for Partially Dissipative Hyperbolic Systems
NASA Astrophysics Data System (ADS)
Beauchard, Karine; Zuazua, Enrique
2011-01-01
This work is concerned with ( n-component) hyperbolic systems of balance laws in m space dimensions. First, we consider linear systems with constant coefficients and analyze the possible behavior of solutions as t → ∞. Using the Fourier transform, we examine the role that control theoretical tools, such as the classical Kalman rank condition, play. We build Lyapunov functionals allowing us to establish explicit decay rates depending on the frequency variable. In this way we extend the previous analysis by Shizuta and Kawashima under the so-called algebraic condition (SK). In particular, we show the existence of systems exhibiting more complex behavior than the one that the (SK) condition allows. We also discuss links between this analysis and previous literature in the context of damped wave equations, hypoellipticity and hypocoercivity. To conclude, we analyze the existence of global solutions around constant equilibria for nonlinear systems of balance laws. Our analysis of the linear case allows proving existence results in situations that the previously existing theory does not cover.
Dissipative Boltzmann-Robertson-Walker cosmologies
Hiscock, W.A.; Salmonson, J. )
1991-05-15
The equations governing a flat Robertson-Walker cosmological model containing a dissipative Boltzmann gas are integrated numerically. The bulk viscous stress is modeled using the Eckart and Israel-Stewart theories of dissipative relativistic fluids; the resulting cosmologies are compared and contrasted. The Eckart models are shown to always differ in a significant quantitative way from the Israel-Stewart models. It thus appears inappropriate to use the pathological (nonhyperbolic) Eckart theory for cosmological applications. For large bulk viscosities, both cosmological models approach asymptotic nonequilibrium states; in the Eckart model the total pressure is negative, while in the Israel-Stewart model the total pressure is asymptotically zero. The Eckart model also expands more rapidly than the Israel-Stewart models. These results suggest that bulk-viscous'' inflation may be an artifact of using a pathological fluid theory such as the Eckart theory.
Apertet, Y; Ouerdane, H; Goupil, C; Lecoeur, Ph
2013-08-01
We present an in-depth analysis of the sometimes understated role of the principle of energy conservation in linear irreversible thermodynamics. Our case study is that of a thermoelectric generator (TEG), which is a heat engine of choice in irreversible thermodynamics, owing to the coupling between the electrical and heat fluxes. We show why Onsager's reciprocal relations must be considered locally and how internal dissipative processes emerge from the extension of these relations to a global scale: The linear behavior of a heat engine at the local scale is associated with a dissipation process that must partake in the global energy balance. We discuss the consequences of internal dissipations on the so-called efficiency at maximum power, in the light of our comparative analyses of exoreversibility and endoreversibility on the one hand and of two classes of heat engines, autonomous and periodically driven, on the other hand. Finally, basing our analysis on energy conservation, we also discuss recent works which claim the possibility to overcome the traditional boundaries on efficiency imposed by finite-time thermodynamics in thermoelectric systems with broken time-reversal symmetry; this we do by introducing a "thermal" thermopower and an "electrical" thermopower which permits an analysis of the thermoelectric response of the TEG considering a possible dissymmetry between the electrical/thermal and the thermal/electrical couplings.
Material Systems for Blast-Energy Dissipation
James Schondel; Henry S. Chu
2010-10-01
Lightweight panels have been designed to protect buildings and vehicles from blast pressures by activating energy dissipation mechanisms under the influence of blast loading. Panels were fabricated which featured a variety of granular materials and hydraulic dissipative deformation mechanisms and the test articles were subjected to full-scale blast loading. The force time-histories transmitted by each technology were measured by a novel method that utilized inexpensive custom-designed force sensors. The array of tests revealed that granular materials can effectively dissipate blast energy if they are employed in a way that they easily crush and rearrange. Similarly, hydraulic dissipation can effectively dissipate energy if the panel features a high fraction of porosity and the panel encasement features low compressive stiffness.
Asymptotic analysis of numerical wave propagation in finite difference equations
NASA Technical Reports Server (NTRS)
Giles, M.; Thompkins, W. T., Jr.
1983-01-01
An asymptotic technique is developed for analyzing the propagation and dissipation of wave-like solutions to finite difference equations. It is shown that for each fixed complex frequency there are usually several wave solutions with different wavenumbers and the slowly varying amplitude of each satisfies an asymptotic amplitude equation which includes the effects of smoothly varying coefficients in the finite difference equations. The local group velocity appears in this equation as the velocity of convection of the amplitude. Asymptotic boundary conditions coupling the amplitudes of the different wave solutions are also derived. A wavepacket theory is developed which predicts the motion, and interaction at boundaries, of wavepackets, wave-like disturbances of finite length. Comparison with numerical experiments demonstrates the success and limitations of the theory. Finally an asymptotic global stability analysis is developed.
Asymptotics of a horizontal liquid bridge
NASA Astrophysics Data System (ADS)
Haynes, M.; O'Brien, S. B. G.; Benilov, E. S.
2016-04-01
This paper uses asymptotic techniques to find the shape of a two dimensional liquid bridge suspended between two vertical walls. We model the equilibrium bridge shape using the Laplace-Young equation. We use the Bond number as a small parameter to deduce an asymptotic solution which is then compared with numerical solutions. The perturbation approach demonstrates that equilibrium is only possible if the contact angle lies within a hysteresis interval and the analysis relates the width of this interval to the Bond number. This result is verified by comparison with a global force balance. In addition, we examine the quasi-static evolution of such a two dimensional bridge.
ERIC Educational Resources Information Center
Gamble, Reed
1989-01-01
Discusses pupil misconceptions concerning forces. Summarizes some of Assessment of Performance Unit's findings on meaning of (1) force, (2) force and motion in one dimension and two dimensions, and (3) Newton's second law. (YP)
Energy shaping and dissipation: Underwater vehicle stabilization using internal rotors
NASA Astrophysics Data System (ADS)
Woolsey, Craig Arthur
This dissertation concerns nonlinear feedback stabilization of mechanical systems using energy-based methods. Nonlinear techniques are appealing because they can yield large regions of attraction for feedback-stabilized equilibria. Energy-based methods are particularly attractive for mechanical systems because these methods preserve a physical view of a system's dynamics and because they yield Lyapunov functions. For conservative systems, proof of stability typically requires the existence of a Lyapunov function. For systems with damping, Lyapunov functions can be used to design feedback dissipation to ensure or enhance asymptotic stability and to obtain more global conclusions. Both as a case study of a particular control methodology and as a practical contribution in the area of underwater vehicle control, we consider stabilization of an underwater vehicle using internal rotors as actuators. The methodology used to develop stabilizing control laws consists of three steps. The first step involves shaping the kinetic energy of the conservative dynamics. For the underwater vehicle, the control term in this step may be interpreted as modifying the system inertia. In the second step, feedback dissipation is designed based on a Lyapunov function developed in the first step. In the third step, it is verified that the effect of external damping due to viscous forces does not destroy the stability results. This method is applied first to a vehicle whose centers of gravity and buoyancy coincide and then to a vehicle with noncoincident centers of gravity and buoyancy. The method of controlled Lagrangians, developed in recent years, is a generalization of the idea of kinetic energy shaping. The method applies to underactuated mechanical systems (systems with more degrees of freedom than independent actuators). Motivated by the results of the investigation into the effect of external damping on an underwater vehicle with internal rotors, we study the effect of damping on more
Asymptotic expansions in nonlinear rotordynamics
NASA Technical Reports Server (NTRS)
Day, William B.
1987-01-01
This paper is an examination of special nonlinearities of the Jeffcott equations in rotordynamics. The immediate application of this analysis is directed toward understanding the excessive vibrations recorded in the LOX pump of the SSME during hot-firing ground testing. Deadband, side force, and rubbing are three possible sources of inducing nonlinearity in the Jeffcott equations. The present analysis initially reduces these problems to the same mathematical description. A special frequency, named the nonlinear natural frequency, is defined and used to develop the solutions of the nonlinear Jeffcott equations as singular asymptotic expansions. This nonlinear natural frequency, which is the ratio of the cross-stiffness and the damping, plays a major role in determining response frequencies.
NASA Astrophysics Data System (ADS)
Linkmann, Moritz; Berera, Arjun; Goldstraw, Erin E.
2017-01-01
This paper examines the behavior of the dimensionless dissipation rate Cɛ for stationary and nonstationary magnetohydrodynamic (MHD) turbulence in the presence of external forces. By combining with previous studies for freely decaying MHD turbulence, we obtain here both the most general model equation for Cɛ applicable to homogeneous MHD turbulence and a comprehensive numerical study of the Reynolds number dependence of the dimensionless total energy dissipation rate at unity magnetic Prandtl number. We carry out a series of medium to high resolution direct numerical simulations of mechanically forced stationary MHD turbulence in order to verify the predictions of the model equation for the stationary case. Furthermore, questions of nonuniversality are discussed in terms of the effect of external forces as well as the level of cross- and magnetic helicity. The measured values of the asymptote Cɛ ,∞ lie between 0.193 ≤Cɛ ,∞≤0.268 for free decay, where the value depends on the initial level of cross- and magnetic helicities. In the stationary case we measure Cɛ ,∞=0.223 .
Linkmann, Moritz; Berera, Arjun; Goldstraw, Erin E
2017-01-01
This paper examines the behavior of the dimensionless dissipation rate C_{ɛ} for stationary and nonstationary magnetohydrodynamic (MHD) turbulence in the presence of external forces. By combining with previous studies for freely decaying MHD turbulence, we obtain here both the most general model equation for C_{ɛ} applicable to homogeneous MHD turbulence and a comprehensive numerical study of the Reynolds number dependence of the dimensionless total energy dissipation rate at unity magnetic Prandtl number. We carry out a series of medium to high resolution direct numerical simulations of mechanically forced stationary MHD turbulence in order to verify the predictions of the model equation for the stationary case. Furthermore, questions of nonuniversality are discussed in terms of the effect of external forces as well as the level of cross- and magnetic helicity. The measured values of the asymptote C_{ɛ,∞} lie between 0.193≤C_{ɛ,∞}≤0.268 for free decay, where the value depends on the initial level of cross- and magnetic helicities. In the stationary case we measure C_{ɛ,∞}=0.223.
Quons in a quantum dissipative system
NASA Astrophysics Data System (ADS)
Lee, Taejin
2016-03-01
String theory proves to be an imperative tool to explore the critical behavior of the quantum dissipative system. We discuss the quantum particles moving in two dimensions, in the presence of a uniform magnetic field, subject to a periodic potential and a dissipative force, which are described by the dissipative Wannier-Azbel-Hofstadter (DWAH) model. Using string theory formulation of the model, we find that the elementary excitations of the system at the generic points of the off-critical regions, in the zero temperature limit are quons, which satisfy q-deformed statistics.
Asymptotically hyperbolic connections
NASA Astrophysics Data System (ADS)
Fine, Joel; Herfray, Yannick; Krasnov, Kirill; Scarinci, Carlos
2016-09-01
General relativity in four-dimensions can be equivalently described as a dynamical theory of {SO}(3)˜ {SU}(2)-connections rather than metrics. We introduce the notion of asymptotically hyperbolic connections, and work out an analogue of the Fefferman-Graham expansion in the language of connections. As in the metric setup, one can solve the arising ‘evolution’ equations order by order in the expansion in powers of the radial coordinate. The solution in the connection setting is arguably simpler, and very straightforward algebraic manipulations allow one to see how the unconstrained by Einstein equations ‘stress-energy tensor’ appears at third order in the expansion. Another interesting feature of the connection formulation is that the ‘counter terms’ required in the computation of the renormalised volume all combine into the Chern-Simons functional of the restriction of the connection to the boundary. As the Chern-Simons invariant is only defined modulo large gauge transformations, the requirement that the path integral over asymptotically hyperbolic connections is well-defined requires the cosmological constant to be quantised. Finally, in the connection setting one can deform the 4D Einstein condition in an interesting way, and we show that asymptotically hyperbolic connection expansion is universal and valid for any of the deformed theories.
Kolmogorov turbulence by matched asymptotic expansions
NASA Astrophysics Data System (ADS)
Lundgren, Thomas S.
2003-04-01
The Kolmogorov [Dokl. Akad. Nauk. SSSR 30, 299 (1941), hereafter K41] inertial range theory is derived from first principles by analysis of the Navier-Stokes equation using the method of matched asymptotic expansions without assuming isotropy or homogeneity and the Kolmogorov (K62) [J. Fluid Mech. 13, 82 (1962)] refined theory is analyzed. This paper is an extension of Lundgren [Phys. Fluids 14, 638 (2002)], in which the second- and third-order structure functions were determined from the isotropic Karman-Howarth [Proc. R. Soc. London, Ser. A 164, 192 (1938)] equation. The starting point for the present analysis is an equation for the difference in velocity between two points, one of which is a Lagrangian fluid point and the second, slaved to the first by a fixed separation r, is not Lagrangian. The velocity difference, so defined, satisfies the Navier-Stokes equation with spatial variable r. The analysis is carried out in two parts. In the first part the physical hypothesis is made that the mean dissipation is independent of viscosity as viscosity tends to zero, as assumed in K41. This means that the mean dissipation is finite as Reynolds number tends to infinity and leads to the K41 inertial range results. In the second part this dissipation assumption is relaxed in an attempt to duplicate the K62 theory. While the K62 structure is obtained, there are restrictions, resulting from the analysis which shows that there can be no inertial range intermittency as Reynolds number tends to infinity, and therefore the mean dissipation has to be finite as Reynolds number tends to infinity, as assumed in part one. Reynolds number-dependent corrections to the K41 results are obtained in the form of compensating functions of r/λ, which tend to zero slowly like Rλ-2/3 as Rλ→∞.
Alfven wave absorption in dissipative plasma
NASA Astrophysics Data System (ADS)
Gavrikov, M. B.; Taiurskii, A. A.
2017-01-01
We consider nonlinear absorption of Alfven waves due to dissipative effects in plasma and relaxation of temperatures of electrons and ions. This study is based on an exact solution of the equations of two-fluid electromagnetic hydrodynamics (EMHD) of plasma. It is shown that in order to study the decay of Alfven waves, it suffices to examine the behavior of their amplitudes whose evolution is described by a system of ordinary differential equations (ODEs) obtained in this paper. On finite time intervals, the system of equations on the amplitudes is studied numerically, while asymptotic integration (the Hartman-Grobman theorem) is used to examine its large-time behavior.
NASA Astrophysics Data System (ADS)
Ho, Pei-Ming
2017-04-01
Following earlier works on the KMY model of black-hole formation and evaporation, we construct the metric for a matter sphere in gravitational collapse, with the back-reaction of pre-Hawking radiation taken into consideration. The mass distribution and collapsing velocity of the matter sphere are allowed to have an arbitrary radial dependence. We find that a generic gravitational collapse asymptote to a universal configuration which resembles a black hole but without horizon. This approach clarifies several misunderstandings about black-hole formation and evaporation, and provides a new model for black-hole-like objects in the universe.
Asymptotically flat multiblack lenses
NASA Astrophysics Data System (ADS)
Tomizawa, Shinya; Okuda, Taika
2017-03-01
We present an asymptotically flat and stationary multiblack lens solution with biaxisymmetry of U (1 )×U (1 ) as a supersymmetric solution in the five-dimensional minimal ungauged supergravity. We show that the spatial cross section of each degenerate Killing horizon admits different lens space topologies of L (n ,1 )=S3/Zn as well as a sphere S3. Moreover, we show that, in contrast to the higher-dimensional Majumdar-Papapetrou multiblack hole and multi-Breckenridge-Myers-Peet-Vafa (BMPV) black hole spacetime, the metric is smooth on each horizon even if the horizon topology is spherical.
Asymptotic dynamics on a singular chemotaxis system modeling onset of tumor angiogenesis
NASA Astrophysics Data System (ADS)
Wang, Zhi-An; Xiang, Zhaoyin; Yu, Pei
2016-02-01
The asymptotic behavior of solutions to a singular chemotaxis system modeling the onset of tumor angiogenesis in two and three dimensional whole spaces is investigated in the paper. By a Cole-Hopf type transformation, the singular chemotaxis is converted into a non-singular hyperbolic system. Then we study the transformed system and establish the global existence, asymptotic decay rates and diffusion convergence rate of solutions by the method of energy estimates. The main novelty of our results is the finding of a hidden interactive dissipation structure in the system by which the energy dissipation is established.
Dissipation in Planetary Atmospheres
NASA Astrophysics Data System (ADS)
Schubert, Gerald; Mitchell, J.
2012-10-01
The net radiative entropy flux of a planet is negative because atmospheres absorb solar radiation at a higher temperature than the temperature at which they re-emit an equal amount of longwave radiation to space. If in the long term the entropy of an atmosphere is constant, the radiative entropy loss must be balanced by the entropy production associated with thermally direct heat transports and dissipation. Given estimates of the thermally direct sources of entropy production and the temperature at which dissipation occurs, this determines the rate of dissipation in an atmosphere. It is estimated that the entropy production due to dissipation in the atmospheres of Venus, Earth, Mars and Titan occurs at the rate, respectively, of about ≤23, 29, 2, and ≤4 mW m-2 K-1. If the dissipation in Earth’s atmosphere occurs between temperatures of 250 K and 288 K the dissipation rate must lie between 7.3 and 8.4 W m- 2, consistent with other recent estimates. The terrestrial heat engine operates with an efficiency of about 60% of the Carnot efficiency. Sources of dissipation in planetary atmospheres are highly uncertain, even for Earth. For Earth, frictional dissipation in rainfall is comparable to the turbulent dissipation of kinetic energy. Rainfall might also be a significant source of dissipation on Titan but it is not likely to be important for Mars or Venus. The breaking of upward propagating internal gravity waves generated by convection and flow over the surface topography is another source of dissipation and is possibly dominant on Venus.
NASA Astrophysics Data System (ADS)
Pfahl, V.; Phani, M. K.; Büchsenschütz-Göbeler, M.; Kumar, A.; Moshnyaga, V.; Arnold, W.; Samwer, K.
2017-01-01
We report on friction measurements on a La0.6Sr0.4MnO3 (LSMO) thin film using atomic force microscopy cantilever contact-resonances. There is a contribution to the damping of the cantilever oscillations, which is caused by micro-sliding of the cantilever tip on the surface of the thin film. This frictional part decreases with temperature parallel to the increase in the resistivity of the thin film. The LSMO is well-known for a ferromagnetic to paramagnetic phase transition that occurs without changes in the rhombohedral (R-3c) crystalline structure. The magnetic transition at the Curie temperature TC ˜ 360 K is accompanied by a metal-to-metal transition with a large increase in electrical resistivity. The behavior of the cantilever damping constant demonstrates that there is a direct coupling between mechanical friction and the mobility of the electrons in the LSMO film.
Thermodynamics of Asymptotically Conical Geometries.
Cvetič, Mirjam; Gibbons, Gary W; Saleem, Zain H
2015-06-12
We study the thermodynamical properties of a class of asymptotically conical geometries known as "subtracted geometries." We derive the mass and angular momentum from the regulated Komar integral and the Hawking-Horowitz prescription and show that they are equivalent. By deriving the asymptotic charges, we show that the Smarr formula and the first law of thermodynamics hold. We also propose an analog of Christodulou-Ruffini inequality. The analysis can be generalized to other asymptotically conical geometries.
Dissipative photonic lattice solitons.
Ultanir, Erdem A; Stegeman, George I; Christodoulides, Demetrios N
2004-04-15
We show that discrete dissipative optical lattice solitons are possible in waveguide array configurations that involve periodically patterned semiconductor optical amplifiers and saturable absorbers. The characteristics of these low-power soliton states are investigated, and their propagation constant eigenvalues are mapped on Floquet-Bloch band diagrams. The prospect of observing such low-power dissipative lattice solitons is discussed in detail.
Asymptotic symmetries on Killing horizons
NASA Astrophysics Data System (ADS)
Koga, Jun-Ichirou
2001-12-01
We investigate asymptotic symmetries regularly defined on spherically symmetric Killing horizons in Einstein theory with or without the cosmological constant. These asymptotic symmetries are described by asymptotic Killing vectors, along which the Lie derivatives of perturbed metrics vanish on a Killing horizon. We derive the general form of the asymptotic Killing vectors and find that the group of asymptotic symmetries consists of rigid O(3) rotations of a horizon two-sphere and supertranslations along the null direction on the horizon, which depend arbitrarily on the null coordinate as well as the angular coordinates. By introducing the notion of asymptotic Killing horizons, we also show that local properties of Killing horizons are preserved not only under diffeomorphisms but also under nontrivial transformations generated by the asymptotic symmetry group. Although the asymptotic symmetry group contains the Diff(S1) subgroup, which results from supertranslations dependent only on the null coordinate, it is shown that the Poisson brackets algebra of the conserved charges conjugate to asymptotic Killing vectors does not acquire nontrivial central charges. Finally, by considering extended symmetries, we discuss the fact that unnatural reduction of the symmetry group is necessary in order to obtain the Virasoro algebra with nontrivial central charges, which is not justified when we respect the spherical symmetry of Killing horizons.
Dynamics of dissipative gravitational collapse
Herrera, L.; Santos, N.O.
2004-10-15
The Misner and Sharp approach to the study of gravitational collapse is extended to the dissipative case in, both, the streaming out and the diffusion approximations. The role of different terms in the dynamical equation are analyzed in detail. The dynamical equation is then coupled to a causal transport equation in the context of Israel-Stewart theory. The decreasing of the inertial mass density of the fluid, by a factor which depends on its internal thermodynamics state, is reobtained, at any time scale. In accordance with the equivalence principle, the same decreasing factor is obtained for the gravitational force term. Prospective applications of this result to some astrophysical scenarios are discussed.
Asymptotically safe grand unification
NASA Astrophysics Data System (ADS)
Bajc, Borut; Sannino, Francesco
2016-12-01
Phenomenologically appealing supersymmetric grand unified theories have large gauge representations and thus are not asymptotically free. Their ultraviolet validity is limited by the appearance of a Landau pole well before the Planck scale. One could hope that these theories save themselves, before the inclusion of gravity, by generating an interacting ultraviolet fixed point, similar to the one recently discovered in non-supersymmetric gauge-Yukawa theories. Employing a-maximization, a-theorem, unitarity bounds, as well as positivity of other central charges we nonperturbatively rule out this possibility for a broad class of prime candidates of phenomenologically relevant supersymmetric grand unified theories. We also uncover candidates passing these tests, which have either exotic matter or contain one field decoupled from the superpotential. The latter class of theories contains a model with the minimal matter content required by phenomenology.
Kheirandish, F.; Amooshahi, M.
2008-11-18
Quantum field theory of a damped vibrating string as the simplest dissipative scalar field theory is investigated by introducing a minimal coupling method. The rate of energy flowing between the system and its environment is obtained.
Asymptotic behavior of the warm inflation scenario with viscous pressure
Mimoso, Jose P.; Nunes, Ana; Pavon, Diego
2006-01-15
We analyze the dynamics of models of warm inflation with general dissipative effects. We consider phenomenological terms both for the inflaton decay rate and for viscous effects within matter. We provide a classification of the asymptotic behavior of these models and show that the existence of a late-time scaling regime depends not only on an asymptotic behavior of the scalar field potential, but also on an appropriate asymptotic behavior of the inflaton decay rate. There are scaling solutions whenever the latter evolves to become proportional to the Hubble rate of expansion regardless of the steepness of the scalar field exponential potential. We show from thermodynamic arguments that the scaling regime is associated with a power-law dependence of the matter-radiation temperature on the scale factor, which allows a mild variation of the temperature of the matter/radiation fluid. We also show that the late-time contribution of the dissipative terms alleviates the depletion of matter, and increases the duration of inflation.
Asymptotic modal analysis and statistical energy analysis
NASA Technical Reports Server (NTRS)
Dowell, Earl H.
1988-01-01
Statistical Energy Analysis (SEA) is defined by considering the asymptotic limit of Classical Modal Analysis, an approach called Asymptotic Modal Analysis (AMA). The general approach is described for both structural and acoustical systems. The theoretical foundation is presented for structural systems, and experimental verification is presented for a structural plate responding to a random force. Work accomplished subsequent to the grant initiation focusses on the acoustic response of an interior cavity (i.e., an aircraft or spacecraft fuselage) with a portion of the wall vibrating in a large number of structural modes. First results were presented at the ASME Winter Annual Meeting in December, 1987, and accepted for publication in the Journal of Vibration, Acoustics, Stress and Reliability in Design. It is shown that asymptotically as the number of acoustic modes excited becomes large, the pressure level in the cavity becomes uniform except at the cavity boundaries. However, the mean square pressure at the cavity corner, edge and wall is, respectively, 8, 4, and 2 times the value in the cavity interior. Also it is shown that when the portion of the wall which is vibrating is near a cavity corner or edge, the response is significantly higher.
Singular asymptotic expansions in nonlinear rotordynamics
NASA Technical Reports Server (NTRS)
Day, W. B.
1984-01-01
During hot firing ground testing of the Space Shuttle's Main Engine, vibrations of the liquid oxygen pump occur at frequencies which cannot be explained by the linear Jeffcott model of the rotor. The model becomes nonlinear after accounting for deadband, side forces, and rubbing. Two phenomena present in the numerical solutions of the differential equations are unexpected periodic orbits of the rotor and tracking of the nonlinear frequency. A multiple scale asymptotic expansion of the differential equations is used to give an analytic explanation of these characteristics.
Singular asymptotic expansions in nonlinear rotordynamics
NASA Technical Reports Server (NTRS)
Day, W. B.
1985-01-01
During hot firing ground testing of the Space shuttle's Main Engine, vibrations of the liquid oxygen pump occur at frequencies which cannot be explained by the linear Jeffcott model of the rotor. The model becomes nonlinear after accounting for deadband, side forces, and rubbing. Two phenomena present in the numerical solutions of the differential equations are unexpected periodic orbits of the rotor and tracking of the nonlinear frequency. A multiple scale asymptotic expansion of the differential equations is used to give an analytic explanation of these characteristics.
Rayleigh-Lagrange formalism for classical dissipative systems.
Virga, Epifanio G
2015-01-01
It is often believed that the Rayleigh-Lagrange formalism for classical dissipative systems is unable to encompass forces described by nonlinear functions of the velocities. Here we show that this is indeed a misconception.
Asymptotic Parachute Performance Sensitivity
NASA Technical Reports Server (NTRS)
Way, David W.; Powell, Richard W.; Chen, Allen; Steltzner, Adam D.
2006-01-01
In 2010, the Mars Science Laboratory mission will pioneer the next generation of robotic Entry, Descent, and Landing systems by delivering the largest and most capable rover to date to the surface of Mars. In addition to landing more mass than any other mission to Mars, Mars Science Laboratory will also provide scientists with unprecedented access to regions of Mars that have been previously unreachable. By providing an Entry, Descent, and Landing system capable of landing at altitudes as high as 2 km above the reference gravitational equipotential surface, or areoid, as defined by the Mars Orbiting Laser Altimeter program, Mars Science Laboratory will demonstrate sufficient performance to land on 83% of the planet s surface. By contrast, the highest altitude landing to date on Mars has been the Mars Exploration Rover at 1.3 km below the areoid. The coupling of this improved altitude performance with latitude limits as large as 60 degrees off of the equator and a precise delivery to within 10 km of a surface target, will allow the science community to select the Mars Science Laboratory landing site from thousands of scientifically interesting possibilities. In meeting these requirements, Mars Science Laboratory is extending the limits of the Entry, Descent, and Landing technologies qualified by the Mars Viking, Mars Pathfinder, and Mars Exploration Rover missions. Specifically, the drag deceleration provided by a Viking-heritage 16.15 m supersonic Disk-Gap-Band parachute in the thin atmosphere of Mars is insufficient, at the altitudes and ballistic coefficients under consideration by the Mars Science Laboratory project, to maintain necessary altitude performance and timeline margin. This paper defines and discusses the asymptotic parachute performance observed in Monte Carlo simulation and performance analysis and its effect on the Mars Science Laboratory Entry, Descent, and Landing architecture.
Velmurugan, G; Rakkiyappan, R; Vembarasan, V; Cao, Jinde; Alsaedi, Ahmed
2017-02-01
As we know, the notion of dissipativity is an important dynamical property of neural networks. Thus, the analysis of dissipativity of neural networks with time delay is becoming more and more important in the research field. In this paper, the authors establish a class of fractional-order complex-valued neural networks (FCVNNs) with time delay, and intensively study the problem of dissipativity, as well as global asymptotic stability of the considered FCVNNs with time delay. Based on the fractional Halanay inequality and suitable Lyapunov functions, some new sufficient conditions are obtained that guarantee the dissipativity of FCVNNs with time delay. Moreover, some sufficient conditions are derived in order to ensure the global asymptotic stability of the addressed FCVNNs with time delay. Finally, two numerical simulations are posed to ensure that the attention of our main results are valuable.
Investigation of dissipative forces near macroscopic media
Becker, R.S.
1982-12-01
The interaction of classical charged particles with the fields they induce in macroscopic dielectric media is investigated. For 10- to 1000-eV electrons, the angular perturbation of the trajectory by the image potential for surface impact parameters of 50 to 100 A is shown to be of the order of 0.001 rads over a distance of 100 A. The energy loss incurred by low-energy particles due to collective excitations such as surface plasmons is shown to be observable with a transition probability of 0.01 to 0.001 (Becker, et al., 1981b). The dispersion of real surface plasmon modes in planar and cylindrical geometries is discussed and is derived for pinhole geometry described in terms of a single-sheeted hyperboloid of revolution. An experimental apparatus for the measurement of collective losses for medium-energy electrons translating close to a dielectric surface is described and discussed. Data showing such losses at electron energies of 500 to 900 eV in silver foils containing many small apertures are presented and shown to be in good agreement with classical stopping power calculations and quantum mechanical calculations carried out in the low-velocity limit. The data and calculations are compared and contrasted with earlier transmission and reflection measurements, and the course of further investigation is discussed.
Energy dissipation in substorms
NASA Technical Reports Server (NTRS)
Weiss, Loretta A.; Reiff, P. H.; Moses, J. J.; Heelis, R. A.; Moore, B. D.
1992-01-01
The energy dissipated by substorms manifested in several ways is discussed: the Joule dissipation in the ionosphere; the energization of the ring current by the injection of plasma sheet particles; auroral election and ion acceleration; plasmoid ejection; and plasma sheet ion heating during the recovery phase. For each of these energy dissipation mechanisms, a 'rule of thumb' formula is given, and a typical dissipation rate and total energy expenditure is estimated. The total energy dissipated as Joule heat (approximately) 2 x 10(exp 15) is found about twice the ring current injection term, and may be even larger if small scale effects are included. The energy expended in auroral electron precipitation, on the other hand, is smaller than the Joule heating by a factor of five. The energy expended in refilling and heating the plasma sheets is estimated to be approximately 5 x 10(exp 14)J, while the energy lost due to plasmoid ejection is between (approximately) (10 exp 13)(exp 14)J.
Asymptotic dynamics of monopole walls
NASA Astrophysics Data System (ADS)
Cross, R.
2015-08-01
We determine the asymptotic dynamics of the U(N) doubly periodic BPS monopole in Yang-Mills-Higgs theory, called a monopole wall, by exploring its Higgs curve using the Newton polytope and amoeba. In particular, we show that the monopole wall splits into subwalls when any of its moduli become large. The long-distance gauge and Higgs field interactions of these subwalls are Abelian, allowing us to derive an asymptotic metric for the monopole wall moduli space.
Fractional dissipative standard map.
Tarasov, Vasily E; Edelman, M
2010-06-01
Using kicked differential equations of motion with derivatives of noninteger orders, we obtain generalizations of the dissipative standard map. The main property of these generalized maps, which are called fractional maps, is long-term memory. The memory effect in the fractional maps means that their present state of evolution depends on all past states with special forms of weights. Already a small deviation of the order of derivative from the integer value corresponding to the regular dissipative standard map (small memory effects) leads to the qualitatively new behavior of the corresponding attractors. The fractional dissipative standard maps are used to demonstrate a new type of fractional attractors in the wide range of the fractional orders of derivatives.
Circulation and Dissipation on Hot Jupiters
NASA Astrophysics Data System (ADS)
Li, J.; Goodman, J.
2010-12-01
Many global circulation models predict supersonic zonal winds and large vertical shears in the atmospheres of short-period Jovian exoplanets. Using linear analysis and nonlinear local simulations, we investigate hydrodynamic dissipation mechanisms to balance the thermal acceleration of these winds. The adiabatic Richardson criterion remains a good guide to linear stability, although thermal diffusion allows some modes to violate it at very long wavelengths and very low growth rates. Nonlinearly, wind speeds saturate at Mach numbers ≈2 and Richardson numbers lsim1/4 for a broad range of plausible diffusivities and forcing strengths. Turbulence and vertical mixing, though accompanied by weak shocks, dominate the dissipation, which appears to be the outcome of a recurrent Kelvin-Helmholtz instability. An explicit shear viscosity, as well as thermal diffusivity, is added to ZEUS to capture dissipation outside of shocks. The wind speed is neither monotonic nor single valued for a range of shear viscosities larger than about 10-3 of the sound speed times the pressure scale height. Coarsening the numerical resolution can also increase the speed. Hence global simulations that are incapable of representing vertical turbulence and shocks, either because of reduced physics or because of limited resolution, may overestimate wind speeds. We recommend that such simulations include artificial dissipation terms to control the Mach and Richardson numbers and to capture mechanical dissipation as heat.
Polynomial Asymptotes of the Second Kind
ERIC Educational Resources Information Center
Dobbs, David E.
2011-01-01
This note uses the analytic notion of asymptotic functions to study when a function is asymptotic to a polynomial function. Along with associated existence and uniqueness results, this kind of asymptotic behaviour is related to the type of asymptote that was recently defined in a more geometric way. Applications are given to rational functions and…
Dissipative Work in Thermodynamics
ERIC Educational Resources Information Center
Anacleto, Joaquim; Pereira, Mario G.; Ferreira, J. M.
2011-01-01
This work explores the concept of dissipative work and shows that such a kind of work is an invariant non-negative quantity. This feature is then used to get a new insight into adiabatic irreversible processes; for instance, why the final temperature in any adiabatic irreversible process is always higher than that attained in a reversible process…
Asymptotic conditions and conserved quantities
Koul, R.K.
1990-01-01
Two problems have been investigated in this dissertation. The first one deals with the relationship between stationary space-times which are flat at null infinity and stationary space-times which are asymptotic flat at space-like infinity. It is shown that the stationary space-times which are asymptotically flat, in the Penrose sense, at null infinity, are asymptotically flat at space-like infinity in the Geroch sense and metric at space like infinity is at least C{sup 1}. In the converse it is shown that the stationary space-times which are asymptotically flat at space like infinity, in the Beig sense, are asymptotically flat at null infinity in the Penrose sense. The second problem addressed deals with the theories of arbitrary dimensions. The theories treated are the ones which have fiber bundle structure, outside some compact region. For these theories the criterion for the choice of the background metric is specified, and the boundary condition for the initial data set (q{sub ab}, P{sup ab}) is given in terms of the background metric. Having these boundary conditions it is shown that the symplectic structure and the constraint functionals are well defined. The conserved quantities associated with internal Killing vector fields are specified. Lastly the energy relative to a fixed background and the total energy of the theory have been given. It is also shown that the total energy of the theory is independent of the choice of the background.
Ergodicity and asymptotic stability of Feller semigroups on Polish metric spaces
NASA Astrophysics Data System (ADS)
Gong, FuZhou; Liu, Yuan
2015-06-01
We provide some sharp criteria for studying the ergodicity and asymptotic stability of general Feller semigroups on Polish metric spaces. As application, the 2D Navier-Stokes equations with degenerate stochastic forcing will be simply revisited.
Dissipative solitons in fiber lasers
NASA Astrophysics Data System (ADS)
Turitsyn, S. K.; Rosanov, N. N.; Yarutkina, I. A.; Bednyakova, A. E.; Fedorov, S. V.; Shtyrina, O. V.; Fedoruk, M. P.
2016-07-01
Dissipative solitons (also known as auto-solitons) are stable, nonlinear, time- or space-localized solitary waves that occur due to the balance between energy excitation and dissipation. We review the theory of dissipative solitons applied to fiber laser systems. The discussion context includes the classical Ginzburg-Landau and Maxwell-Bloch equations and their modifications that allow describing laser-cavity-produced waves. Practical examples of laser systems generating dissipative solitons are discussed.
Asymptotic Rayleigh instantaneous unit hydrograph
Troutman, B.M.; Karlinger, M.R.
1988-01-01
The instantaneous unit hydrograph for a channel network under general linear routing and conditioned on the network magnitude, N, tends asymptotically, as N grows large, to a Rayleigh probability density function. This behavior is identical to that of the width function of the network, and is proven under the assumption that the network link configuration is topologically random and the link hydraulic and geometric properties are independent and identically distributed random variables. The asymptotic distribution depends only on a scale factor, {Mathematical expression}, where ?? is a mean link wave travel time. ?? 1988 Springer-Verlag.
Wedge locality and asymptotic commutativity
NASA Astrophysics Data System (ADS)
Soloviev, M. A.
2014-05-01
In this paper, we study twist deformed quantum field theories obtained by combining the Wightman axiomatic approach with the idea of spacetime noncommutativity. We prove that the deformed fields with deformation parameters of opposite sign satisfy the condition of mutual asymptotic commutativity, which was used earlier in nonlocal quantum field theory as a substitute for relative locality. We also present an improved proof of the wedge localization property discovered for the deformed fields by Grosse and Lechner, and we show that the deformation leaves the asymptotic behavior of the vacuum expectation values in spacelike directions substantially unchanged.
Asymptotic Normality of Quadratic Estimators.
Robins, James; Li, Lingling; Tchetgen, Eric; van der Vaart, Aad
2016-12-01
We prove conditional asymptotic normality of a class of quadratic U-statistics that are dominated by their degenerate second order part and have kernels that change with the number of observations. These statistics arise in the construction of estimators in high-dimensional semi- and non-parametric models, and in the construction of nonparametric confidence sets. This is illustrated by estimation of the integral of a square of a density or regression function, and estimation of the mean response with missing data. We show that estimators are asymptotically normal even in the case that the rate is slower than the square root of the observations.
Lorentzian proper vertex amplitude: Asymptotics
NASA Astrophysics Data System (ADS)
Engle, Jonathan; Vilensky, Ilya; Zipfel, Antonia
2016-09-01
In previous work, the Lorentzian proper vertex amplitude for a spin-foam model of quantum gravity was derived. In the present work, the asymptotics of this amplitude are studied in the semiclassical limit. The starting point of the analysis is an expression for the amplitude as an action integral with action differing from that in the Engle-Pereira-Rovelli-Livine (EPRL) case by an extra "projector" term. This extra term scales linearly with spins only in the asymptotic limit, and is discontinuous on a (lower dimensional) submanifold of the integration domain in the sense that its value at each such point depends on the direction of approach. New tools are introduced to generalize stationary phase methods to this case. For the case of boundary data which can be glued to a nondegenerate Lorentzian 4-simplex, the asymptotic limit of the amplitude is shown to equal the single Feynman term, showing that the extra term in the asymptotics of the EPRL amplitude has been eliminated.
Asymptotic screened hydrogenic radial integrals
NASA Technical Reports Server (NTRS)
Olsgaard, D. A.; Khan, F.; Khandelwal, G. S.
1988-01-01
The usefulness of the screened hydrogenic model for the transitions of the helium sequence is studied. The screened hydrogenic radial dipole integral for discrete-discrete transitions from the initial state to the final state is asymptotically expanded to the lowest order such that the final quantum number n approaches infinity. The analytical expression obtained is in terms of confluent hypergeometric functions.
A dimensionless model of impact piezoelectric energy harvesting with dissipation
NASA Astrophysics Data System (ADS)
Fu, Xinlei; Liao, Wei-Hsin
2016-04-01
Impact excitation is common in the environment. Impact piezoelectric energy harvesting could realize frequency up-conversion. However, the dissipation mechanism in impact piezoelectric energy harvesting has not been investigated so far. There is no comprehensive model to be able to analyze the impact piezoelectric energy harvesting thoroughly. This paper is aimed to develop a generalized model that considers dissipation mechanism of impact piezoelectric energy harvesting. In this electromechanical model, Hertzian contact theory and impact dissipation mechanism are identified as constitutive mechanisms. The impact force is compared and the energy distribution is analyzed so that input energy corresponds to impact dissipated energy, structural damping dissipated energy and harvested electrical energy. We then nondimensionalize the developed model and define five dimensionless parameters with attributed physical meanings, including dimensionless parameters of impact dissipation, mass ratio, structural damping, electromechanical coupling, and electrical load. We conclude it is more accurate to consider impact dissipation mechanism to predict impact force and harvested energy. The guideline for improving harvested energy based on parametric studies of dimensionless model is to increase mass ratio, to minimize structural damping, to maximize electromechanical coupling, to use optimal load resistance for impedance matching, and to choose proper impact velocity .
Dissipation in deforming chaotic billiards
NASA Astrophysics Data System (ADS)
Barnett, Alexander Harvey
Chaotic billiards (hard-walled cavities) in two or more dimensions are paradigm systems in the fields of classical and quantum chaos. We study the dissipation (irreversible heating) rate in such billiard systems due to general shape deformations which are periodic in time. We are motivated by older studies of one-body nuclear dissipation and by anticipated mesoscopic applications. We review the classical and quantum linear response theories of dissipation rate and demonstrate their correspondence in the semiclassical limit. In both pictures, heating is a result of stochastic energy spreading. The heating rate can be expressed as a frequency-dependent friction coefficient μ(ω), which depends on billiard shape and deformation choice. We show that there is a special class of deformations for which μ vanishes as like a power law in the small- ω limit. Namely, for deformations which cause translations and dilations μ ~ ω4 whereas for those which cause rotations μ ~ ω2. This contrasts the generic case for which μ ~ ω4 We show how a systematic treatment of this special class leads to an improved version of the `wall formula' estimate for μ(0). We show that the special nature of dilation (a new result) is semiclassically equivalent to a quasi- orthogonality relation between the (undeformed) billiard quantum eigenstates on the boundary. This quasi- orthogonality forms the heart of a `scaling method' for the numerical calculation of quantum eigenstates, invented recently by Vergini and Saraceno. The scaling method is orders of magnitude more efficient than any other known billiard quantization method, however an adequate explanation for its success has been lacking until now. We explain the scaling method, its errors, and applications. We also present improvements to Heller's plane wave method. Two smaller projects conclude the thesis. Firstly, we give a new formalism for quantum point contact (QPC) conductance in terms of scattering cross-section in the half
Skyrmionic spin Seebeck effect via dissipative thermomagnonic torques
NASA Astrophysics Data System (ADS)
Kovalev, Alexey A.
2014-06-01
We derive thermomagnonic torque and its "β-type" dissipative correction from the stochastic Landau-Lifshitz-Gilbert equation. The β-type dissipative correction describes viscous coupling between magnetic dynamics and magnonic current and it stems from spin mistracking of the magnetic order. We show that thermomagnonic torque is important for describing temperature gradient induced motion of skyrmions in helical magnets while dissipative correction plays an essential role in generating transverse Magnus force. We propose to detect such skyrmionic motion by employing the transverse spin Seebeck effect geometry.
Viscosity measurement techniques in Dissipative Particle Dynamics
NASA Astrophysics Data System (ADS)
Boromand, Arman; Jamali, Safa; Maia, Joao M.
2015-11-01
In this study two main groups of viscosity measurement techniques are used to measure the viscosity of a simple fluid using Dissipative Particle Dynamics, DPD. In the first method, a microscopic definition of the pressure tensor is used in equilibrium and out of equilibrium to measure the zero-shear viscosity and shear viscosity, respectively. In the second method, a periodic Poiseuille flow and start-up transient shear flow is used and the shear viscosity is obtained from the velocity profiles by a numerical fitting procedure. Using the standard Lees-Edward boundary condition for DPD will result in incorrect velocity profiles at high values of the dissipative parameter. Although this issue was partially addressed in Chatterjee (2007), in this work we present further modifications (Lagrangian approach) to the original LE boundary condition (Eulerian approach) that will fix the deviation from the desired shear rate at high values of the dissipative parameter and decrease the noise to signal ratios in stress measurement while increases the accessible low shear rate window. Also, the thermostat effect of the dissipative and random forces is coupled to the dynamic response of the system and affects the transport properties like the viscosity and diffusion coefficient. We investigated thoroughly the dependency of viscosity measured by both Eulerian and Lagrangian methodologies, as well as numerical fitting procedures and found that all the methods are in quantitative agreement.
Tidal Energy Dissipation from Topex/Poseidon
NASA Technical Reports Server (NTRS)
Ray, Richard D.; Egbert, G. D.; Smith, David E. (Technical Monitor)
2000-01-01
In a recent paper ({\\it Nature, 405,} 775, 2000) we concluded that 25 to 30\\% of the ocean's tidal energy dissipation, or about 1 terawatt, occurs in the deep ocean, with the remaining 2.6 TW in shallow seas. The physical mechanism for deep-ocean dissipation is apparently scattering of the surface tide into internal modes; Munk and Wunsch have suggested that this mechanism may provide half the power needed for mixing the deep-ocean. This paper builds further evidence for $1\\pm 0.2$ TW of deep-ocean dissipation. The evidence is extracted from tidal elevations deduced from seven years of Topex/Poseidon satellite altimeter data. The dissipation rate Is formed as a balance between the rate of working by tidal forces and the energy flux divergence. While dynamical assumptions are required to compute fluxes, area integrals of the energy balance are, owing to the tight satellite constraints, remarkably insensitive to these assumptions. A large suite of tidal solutions based on a wide range of dynamical assumptions, on perturbations to bathymetric models, and on simulated elevation data are used to assess this sensitivity. These and Monte Carlo error fields from a generalized inverse model are used to establish error uncertainties.
Direct and indirect detection of dissipative dark matter
Fan, JiJi; Katz, Andrey; Shelton, Jessie E-mail: katz.andrey@gmail.com
2014-06-01
We study the constraints from direct detection and solar capture on dark matter scenarios with a subdominant dissipative component. This dissipative dark matter component in general has both a symmetric and asymmetric relic abundance. Dissipative dynamics allow this subdominant dark matter component to cool, resulting in its partial or total collapse into a smaller volume inside the halo (e.g., a dark disk) as well as a reduced thermal velocity dispersion compared to that of normal cold dark matter. We first show that these features considerably relax the limits from direct detection experiments on the couplings between standard model (SM) particles and dissipative dark matter. On the other hand, indirect detection of the annihilation of the symmetric dissipative dark matter component inside the Sun sets stringent and robust constraints on the properties of the dissipative dark matter. In particular, IceCube observations force dissipative dark matter particles with mass above 50 GeV to either have a small coupling to the SM or a low local density in the solar system, or to have a nearly asymmetric relic abundance. Possible helioseismology signals associated with purely asymmetric dissipative dark matter are discussed, with no present constraints.
Dissipative quantum trajectories in complex space: Damped harmonic oscillator
NASA Astrophysics Data System (ADS)
Chou, Chia-Chun
2016-10-01
Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton-Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation for the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.
Classical to quantum correspondence in dissipative directed transport
NASA Astrophysics Data System (ADS)
Carlo, Gabriel G.; Rivas, Alejandro M. F.; Spina, María E.
2015-11-01
We compare the quantum and classical properties of the (quantum) isoperiodic stable structures [(Q)ISSs], which organize the parameter space of a paradigmatic dissipative ratchet model, i.e., the dissipative modified kicked rotator. We study the spectral behavior of the corresponding classical Perron-Frobenius operators with thermal noise and the quantum superoperators without it for small ℏeff values. We find a remarkable similarity between the classical and quantum spectra. This finding significantly extends previous results—obtained for the mean currents and asymptotic distributions only—and, on the other hand, unveils a classical to quantum correspondence mechanism where the classical noise is qualitatively different from the quantum one. This is crucial not only for simple attractors but also for chaotic ones, where just analyzing the asymptotic distribution is revealed as insufficient. Moreover, we provide with a detailed characterization of relevant eigenvectors by means of the corresponding Weyl-Wigner distributions, in order to better identify similarities and differences. Finally, this model being generic, it allows us to conjecture that this classical to quantum correspondence mechanism is a universal feature of dissipative systems.
Asymptotic controllability and optimal control
NASA Astrophysics Data System (ADS)
Motta, M.; Rampazzo, F.
We consider a control problem where the state must approach asymptotically a target C while paying an integral cost with a non-negative Lagrangian l. The dynamics f is just continuous, and no assumptions are made on the zero level set of the Lagrangian l. Through an inequality involving a positive number p and a Minimum Restraint FunctionU=U(x) - a special type of Control Lyapunov Function - we provide a condition implying that (i) the system is asymptotically controllable, and (ii) the value function is bounded by U/p. The result has significant consequences for the uniqueness issue of the corresponding Hamilton-Jacobi equation. Furthermore it may be regarded as a first step in the direction of a feedback construction.
Composite operators in asymptotic safety
NASA Astrophysics Data System (ADS)
Pagani, Carlo; Reuter, Martin
2017-03-01
We study the role of composite operators in the asymptotic safety program for quantum gravity. By including in the effective average action an explicit dependence on new sources, we are able to keep track of operators which do not belong to the exact theory space and/or are normally discarded in a truncation. Typical examples are geometric operators such as volumes, lengths, or geodesic distances. We show that this setup allows us to investigate the scaling properties of various interesting operators via a suitable exact renormalization group equation. We test our framework in several settings including quantum Einstein gravity, the conformally reduced Einstein-Hilbert truncation, and two-dimensional quantum gravity. Finally, we briefly argue that our construction paves the way to approach observables in the asymptotic safety program.
Asymptotic safety goes on shell
NASA Astrophysics Data System (ADS)
Benedetti, Dario
2012-01-01
It is well known in quantum field theory that the off-shell effective action depends on the gauge choice and field parametrization used in calculating it. Nevertheless, the typical scheme in which the scenario of asymptotically safe gravity is investigated is an off-shell version of the functional renormalization group equation. Working with the Einstein-Hilbert truncation as a test bed, we develop a new scheme for the analysis of asymptotically safe gravity in which the on-shell part of the effective action is singled out and we show that the beta function for the essential coupling has no explicit gauge dependence. In order to reach our goal, we introduce several technical novelties, including a different decomposition of the metric fluctuations, a new implementation of the ghost sector and a new cut-off scheme. We find a nontrivial fixed point, with a value of the cosmological constant that is independent of the gauge-fixing parameters.
NASA Technical Reports Server (NTRS)
2002-01-01
The moon's gravity imparts tremendous energy to the Earth, raising tides throughout the global oceans. What happens to all this energy? This question has been pondered by scientists for over 200 years, and has consequences ranging from the history of the moon to the mixing of the oceans. Richard Ray at NASA's Goddard Space Flight Center, Greenbelt, Md. and Gary Egbert of the College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Ore. studied six years of altimeter data from the TOPEX/Poseidon satellite to address this question. According to their report in the June 15 issue of Nature, about 1 terawatt, or 25 to 30 percent of the total tidal energy dissipation, occurs in the deep ocean. The remainder occurs in shallow seas, such as on the Patagonian Shelf. 'By measuring sea level with the TOPEX/Poseidon satellite altimeter, our knowledge of the tides in the global ocean has been remarkably improved,' said Richard Ray, a geophysicist at Goddard. The accuracies are now so high that this data can be used to map empirically the tidal energy dissipation. (Red areas, above) The deep-water tidal dissipation occurs generally near rugged bottom topography (seamounts and mid-ocean ridges). 'The observed pattern of deep-ocean dissipation is consistent with topographic scattering of tidal energy into internal motions within the water column, resulting in localized turbulence and mixing', said Gary Egbert an associate professor at OSU. One important implication of this finding concerns the possible energy sources needed to maintain the ocean's large-scale 'conveyor-belt' circulation and to mix upper ocean heat into the abyssal depths. It is thought that 2 terawatts are required for this process. The winds supply about 1 terawatt, and there has been speculation that the tides, by pumping energy into vertical water motions, supply the remainder. However, all current general circulation models of the oceans ignore the tides. 'It is possible that properly
On asymptotically lacunary invariant statistical equivalent set sequences
NASA Astrophysics Data System (ADS)
Pancaroglu, Nimet; Nuray, Fatih; Savas, Ekrem
2013-10-01
In this paper, we define asymptotically invariant equivalence, strongly asymptotically invariant equivalence, asymptotically invariant statistical equivalence, asymptotically lacunary invariant statistical equivalence, strongly asymptotically lacunary invariant equivalence, asymptotically lacunary invariant equivalence (Wijsman sense) for sequences of sets. Also we investigate some relations between asymptotically lacunary invariant statistical equivalence and asymptotically invariant statistical equivalence for sequences of sets. We introduce some notions and theorems as follows, asymptotically lacunary invariant statistical equivalence, strongly asymptotically lacunary invariant equivalence, asymptotically lacunary invariant equivalence (Wijsman sense) for sequences of sets.
Enceladus' tidal dissipation revisited
NASA Astrophysics Data System (ADS)
Tobie, Gabriel; Behounkova, Marie; Choblet, Gael; Cadek, Ondrej; Soucek, Ondrej
2016-10-01
A series of chemical and physical evidence indicates that the intense activity at Enceladus' South Pole is related to a subsurface salty water reservoir underneath the tectonically active ice shell. The detection of a significant libration implies that this water reservoir is global and that the average ice shell thickness is about 20-25km (Thomas et al. 2016). The interpretation of gravity and topography data further predicts large variations in ice shell thickness, resulting in a shell potentially thinner than 5 km in the South Polar Terrain (SPT) (Cadek et al. 2016). Such an ice shell structure requires a very strong heat source in the interior, with a focusing mechanism at the SPT. Thermal diffusion through the ice shell implies that at least 25-30 GW is lost into space by passive diffusion, implying a very efficient dissipation mechanism in Enceladus' interior to maintain such an ocean/ice configuration thermally stable.In order to determine in which conditions such a large dissipation power may be generated, we model the tidal response of Enceladus including variable ice shell thickness. For the rock core, we consider a wide range of rheological parameters representative of water-saturated porous rock materials. We demonstrate that the thinning toward the South Pole leads to a strong increase in heat production in the ice shell, with a optimal thickness obtained between 1.5 and 3 km, depending on the assumed ice viscosity. Our results imply that the heat production in the ice shell within the SPT may be sufficient to counterbalance the heat loss by diffusion and to power eruption activity. However, outside the SPT, a strong dissipation in the porous core is required to counterbalance the diffusive heat loss. We show that about 20 GW can be generated in the core, for an effective viscosity of 1012 Pa.s, which is comparable to the effective viscosity estimated in water-saturated glacial tills on Earth. We will discuss the implications of this revisited tidal
A Lagrangian fluctuation-dissipation relation for scalar turbulence
NASA Astrophysics Data System (ADS)
Drivas, Theodore; Eyink, Gregory
2016-11-01
An exact relation is derived between the dissipation of scalar fluctuations and the variance of the scalar inputs (due to initial scalar values, scalar sources, and boundary fluxes) as those are sampled by stochastic Lagrangian trajectories. Previous work on the Kraichnan (1968) model of turbulent scalar advection has shown that anomalous scalar dissipation, non-vanishing in the limit of vanishing viscosity and diffusivity, is in that model due to Lagrangian spontaneous stochasticity, or non-determinism of the Lagrangian particle trajectories in the limit. We here extend this result to scalars advected by any incompressible velocity field. For fluid flows in domains without walls (e.g. periodic boxes) and for insulating/impermeable walls with zero scalar fluxes, we prove that anomalous scalar dissipation and spontaneous stochasticity are completely equivalent. For flows with imposed scalar values or non-vanishing scalar fluxes at the walls, spontaneous stochasticity still implies anomalous scalar dissipation but simple examples show that a distinct mechanism of non-vanishing dissipation can be thin scalar boundary layers near the walls. As an example, we consider turbulent Rayleigh-Benard convection. We here obtain an exact relation between steady-state thermal dissipation and the time for diffusive tracer particles released at the top or bottom wall to mix to their final uniform value near those walls. We show that an "ultimate regime" of turbulent convection as predicted by Kraichnan (1962) will occur at high Rayleigh numbers, unless this near-wall mixing time is asymptotically much longer than the large-scale circulation time.
Energy dissipation in flows through curved spaces
NASA Astrophysics Data System (ADS)
Debus, J.-D.; Mendoza, M.; Succi, S.; Herrmann, H. J.
2017-02-01
Fluid dynamics in intrinsically curved geometries is encountered in many physical systems in nature, ranging from microscopic bio-membranes all the way up to general relativity at cosmological scales. Despite the diversity of applications, all of these systems share a common feature: the free motion of particles is affected by inertial forces originating from the curvature of the embedding space. Here we reveal a fundamental process underlying fluid dynamics in curved spaces: the free motion of fluids, in the complete absence of solid walls or obstacles, exhibits loss of energy due exclusively to the intrinsic curvature of space. We find that local sources of curvature generate viscous stresses as a result of the inertial forces. The curvature- induced viscous forces are shown to cause hitherto unnoticed and yet appreciable energy dissipation, which might play a significant role for a variety of physical systems involving fluid dynamics in curved spaces.
Energy dissipation in flows through curved spaces
Debus, J.-D.; Mendoza, M.; Succi, S.; Herrmann, H. J.
2017-01-01
Fluid dynamics in intrinsically curved geometries is encountered in many physical systems in nature, ranging from microscopic bio-membranes all the way up to general relativity at cosmological scales. Despite the diversity of applications, all of these systems share a common feature: the free motion of particles is affected by inertial forces originating from the curvature of the embedding space. Here we reveal a fundamental process underlying fluid dynamics in curved spaces: the free motion of fluids, in the complete absence of solid walls or obstacles, exhibits loss of energy due exclusively to the intrinsic curvature of space. We find that local sources of curvature generate viscous stresses as a result of the inertial forces. The curvature- induced viscous forces are shown to cause hitherto unnoticed and yet appreciable energy dissipation, which might play a significant role for a variety of physical systems involving fluid dynamics in curved spaces. PMID:28195148
The effects of dissipation on topological mechanical systems
Xiong, Ye; Wang, Tianxiang; Tong, Peiqing
2016-01-01
We theoretically study the effects of isotropic dissipation in a topological mechanical system which is an analogue of Chern insulator in mechanical vibrational lattice. The global gauge invariance is still conserved in this system albeit it is destroyed by the dissipation in the quantum counterpart. The chiral edge states in this system are therefore robust against strong dissipation. The dissipation also causes a dispersion of damping for the eigenstates. It will modify the equation of motion of a wave packet by an extra effective force. After taking into account the Berry curvature in the wave vector space, the trace of a free wave packet in the real space should be curved, feinting to break the Newton’s first law. PMID:27605247
The effects of dissipation on topological mechanical systems
NASA Astrophysics Data System (ADS)
Xiong, Ye; Wang, Tianxiang; Tong, Peiqing
2016-09-01
We theoretically study the effects of isotropic dissipation in a topological mechanical system which is an analogue of Chern insulator in mechanical vibrational lattice. The global gauge invariance is still conserved in this system albeit it is destroyed by the dissipation in the quantum counterpart. The chiral edge states in this system are therefore robust against strong dissipation. The dissipation also causes a dispersion of damping for the eigenstates. It will modify the equation of motion of a wave packet by an extra effective force. After taking into account the Berry curvature in the wave vector space, the trace of a free wave packet in the real space should be curved, feinting to break the Newton’s first law.
The effects of dissipation on topological mechanical systems.
Xiong, Ye; Wang, Tianxiang; Tong, Peiqing
2016-09-08
We theoretically study the effects of isotropic dissipation in a topological mechanical system which is an analogue of Chern insulator in mechanical vibrational lattice. The global gauge invariance is still conserved in this system albeit it is destroyed by the dissipation in the quantum counterpart. The chiral edge states in this system are therefore robust against strong dissipation. The dissipation also causes a dispersion of damping for the eigenstates. It will modify the equation of motion of a wave packet by an extra effective force. After taking into account the Berry curvature in the wave vector space, the trace of a free wave packet in the real space should be curved, feinting to break the Newton's first law.
Approximate formula for the vertical asymptote of projectile motion in midair
NASA Astrophysics Data System (ADS)
Sergey Chudinov, Peter
2010-01-01
The classic problem of the motion of a point mass (projectile) thrown at an angle to the horizon is reviewed. The air drag force is taken into account with the drag factor assumed to be constant. An analytical approach is used for the investigation. An approximate formula is obtained for one of the characteristics of the motion - the vertical asymptote. The value of an asymptote is determined directly by the initial conditions of throwing. Analytically derived values of asymptotes in comparison with numerical values obtained by integrating the equations of motion are given. The motion of a baseball is presented as an example.
Energy dissipation of moved magnetic vortices
NASA Astrophysics Data System (ADS)
Magiera, Martin P.
2013-09-01
A two-dimensional easy-plane ferromagnetic substrate, interacting with a dipolar tip which is magnetised perpendicularly with respect to the easy plane is studied numerically by solving the Landau-Lifshitz Gilbert equation. The dipolar tip stabilises a vortex structure which is dragged through the system and dissipates energy. An analytical expression for the friction force in the v {\\rightarrow} 0 limit based on the Thiele equation is presented. The limitations of this result which predicts a diverging friction force in the thermodynamic limit, are demonstrated by a study of the size dependence of the friction force. While for small system sizes the dissipation depends logarithmically on the system size, it saturates at a specific velocity-dependent value. This size can be regarded as an effective vortex size and it is shown how this effective vortex size agrees with the infinite extension of a vortex in the thermodynamic limit. A magnetic friction number is defined which represents a general criterion for the validity of the Thiele equation and quantifies the degree of nonlinearity in the response of a driven spin configuration.
Polarizable water model for Dissipative Particle Dynamics
NASA Astrophysics Data System (ADS)
Pivkin, Igor; Peter, Emanuel
2015-11-01
Dissipative Particle Dynamics (DPD) is an efficient particle-based method for modeling mesoscopic behavior of fluid systems. DPD forces conserve the momentum resulting in a correct description of hydrodynamic interactions. Polarizability has been introduced into some coarse-grained particle-based simulation methods; however it has not been done with DPD before. We developed a new polarizable coarse-grained water model for DPD, which employs long-range electrostatics and Drude oscillators. In this talk, we will present the model and its applications in simulations of membrane systems, where polarization effects play an essential role.
Many-body dissipative particle dynamics simulation of liquid/vapor and liquid/solid interactions
NASA Astrophysics Data System (ADS)
Arienti, Marco; Pan, Wenxiao; Li, Xiaoyi; Karniadakis, George
2011-05-01
The combination of short-range repulsive and long-range attractive forces in many-body dissipative particle dynamics (MDPD) is examined at a vapor/liquid and liquid/solid interface. Based on the radial distribution of the virial pressure in a drop at equilibrium, a systematic study is carried out to characterize the sensitivity of the surface tension coefficient with respect to the inter-particle interaction parameters. For the first time, the approximately cubic dependence of the surface tension coefficient on the bulk density of the fluid is evidenced. In capillary flow, MDPD solutions are shown to satisfy the condition on the wavelength of an axial disturbance leading to the pinch-off of a cylindrical liquid thread; correctly, no pinch-off occurs below the cutoff wavelength. Moreover, in an example that illustrates the cascade of fluid dynamics behaviors from potential to inertial-viscous to stochastic flow, the dynamics of the jet radius is consistent with the power law predictions of asymptotic analysis. To model interaction with a solid wall, MDPD is augmented by a set of bell-shaped weight functions; hydrophilic and hydrophobic behaviors, including the occurrence of slip in the latter, are reproduced using a modification in the weight function that avoids particle clustering. The dynamics of droplets entering an inverted Y-shaped fracture junction is shown to be correctly captured in simulations parametrized by the Bond number, confirming the flexibility of MDPD in modeling interface-dominated flows.
The maximum drag reduction asymptote
NASA Astrophysics Data System (ADS)
Choueiri, George H.; Hof, Bjorn
2015-11-01
Addition of long chain polymers is one of the most efficient ways to reduce the drag of turbulent flows. Already very low concentration of polymers can lead to a substantial drag and upon further increase of the concentration the drag reduces until it reaches an empirically found limit, the so called maximum drag reduction (MDR) asymptote, which is independent of the type of polymer used. We here carry out a detailed experimental study of the approach to this asymptote for pipe flow. Particular attention is paid to the recently observed state of elasto-inertial turbulence (EIT) which has been reported to occur in polymer solutions at sufficiently high shear. Our results show that upon the approach to MDR Newtonian turbulence becomes marginalized (hibernation) and eventually completely disappears and is replaced by EIT. In particular, spectra of high Reynolds number MDR flows are compared to flows at high shear rates in small diameter tubes where EIT is found at Re < 100. The research leading to these results has received funding from the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme (FP7/2007-2013) under REA grant agreement n° [291734].
Asymptotically Free Gauge Theories. I
DOE R&D Accomplishments Database
Wilczek, Frank; Gross, David J.
1973-07-01
Asymptotically free gauge theories of the strong interactions are constructed and analyzed. The reasons for doing this are recounted, including a review of renormalization group techniques and their application to scaling phenomena. The renormalization group equations are derived for Yang-Mills theories. The parameters that enter into the equations are calculated to lowest order and it is shown that these theories are asymptotically free. More specifically the effective coupling constant, which determines the ultraviolet behavior of the theory, vanishes for large space-like momenta. Fermions are incorporated and the construction of realistic models is discussed. We propose that the strong interactions be mediated by a "color" gauge group which commutes with SU(3)xSU(3). The problem of symmetry breaking is discussed. It appears likely that this would have a dynamical origin. It is suggested that the gauge symmetry might not be broken, and that the severe infrared singularities prevent the occurrence of non-color singlet physical states. The deep inelastic structure functions, as well as the electron position total annihilation cross section are analyzed. Scaling obtains up to calculable logarithmic corrections, and the naive lightcone or parton model results follow. The problems of incorporating scalar mesons and breaking the symmetry by the Higgs mechanism are explained in detail.
Asymptotic density and effective negligibility
NASA Astrophysics Data System (ADS)
Astor, Eric P.
In this thesis, we join the study of asymptotic computability, a project attempting to capture the idea that an algorithm might work correctly in all but a vanishing fraction of cases. In collaboration with Hirschfeldt and Jockusch, broadening the original investigation of Jockusch and Schupp, we introduce dense computation, the weakest notion of asymptotic computability (requiring only that the correct answer is produced on a set of density 1), and effective dense computation, where every computation halts with either the correct answer or (on a set of density 0) a symbol denoting uncertainty. A few results make more precise the relationship between these notions and work already done with Jockusch and Schupp's original definitions of coarse and generic computability. For all four types of asymptotic computation, including generic computation, we demonstrate that non-trivial upper cones have measure 0, building on recent work of Hirschfeldt, Jockusch, Kuyper, and Schupp in which they establish this for coarse computation. Their result transfers to yield a minimal pair for relative coarse computation; we generalize their method and extract a similar result for relative dense computation (and thus for its corresponding reducibility). However, all of these notions of near-computation treat a set as negligible iff it has asymptotic density 0. Noting that this definition is not computably invariant, this produces some failures of intuition and a break with standard expectations in computability theory. For instance, as shown by Hamkins and Miasnikov, the halting problem is (in some formulations) effectively densely computable, even in polynomial time---yet this result appears fragile, as indicated by Rybalov. In independent work, we respond to this by strengthening the approach of Jockusch and Schupp to avoid such phenomena; specifically, we introduce a new notion of intrinsic asymptotic density, invariant under computable permutation, with rich relations to both
Asymptotic safety, emergence and minimal length
NASA Astrophysics Data System (ADS)
Percacci, Roberto; Vacca, Gian Paolo
2010-12-01
There seems to be a common prejudice that asymptotic safety is either incompatible with, or at best unrelated to, the other topics in the title. This is not the case. In fact, we show that (1) the existence of a fixed point with suitable properties is a promising way of deriving emergent properties of gravity, and (2) there is a sense in which asymptotic safety implies a minimal length. In doing so we also discuss possible signatures of asymptotic safety in scattering experiments.
Every composition operator is (mean) asymptotically Toeplitz
NASA Astrophysics Data System (ADS)
Shapiro, Joel H.
2007-09-01
Nazarov and Shapiro recently showed that, while composition operators on the Hardy space H2 can only trivially be Toeplitz, or even "Toeplitz plus compact," it is an interesting problem to determine which of them can be "asymptotically Toeplitz." I show here that if "asymptotically" is interpreted in, for example, the Cesaro (C,[alpha]) sense ([alpha]>0), then every composition operator on H2 becomes asymptotically Toeplitz.
Entanglement Created by Dissipation
Alharbi, Abdullah F.; Ficek, Zbigniew
2011-10-27
A technique for entangling closely separated atoms by the process of dissipative spontaneous emission is presented. The system considered is composed of two non-identical two-level atoms separated at the quarter wavelength of a driven standing wave laser field. At this atomic distance, only one of the atoms can be addressed by the laser field. In addition, we arrange the atomic dipole moments to be oriented relative to the inter-atomic axis such that the dipole-dipole interaction between the atoms is zero at this specific distance. It is shown that an entanglement can be created between the atoms on demand by tuning the Rabi frequency of the driving field to the difference between the atomic transition frequencies. The amount of the entanglement created depends on the ratio between the damping rates of the atoms, but is independent of the frequency difference between the atoms. We also find that the transient buildup of an entanglement between the atoms may differ dramatically for different initial atomic conditions.
Asymptotic conditions of motion for radiating charged particles
NASA Astrophysics Data System (ADS)
Anderson, James L.
1997-10-01
Approximate asymptotic conditions on the motion of compact, electrically charged particles are derived within the framework of general relativity using the Einstein-Infeld-Hoffmann (EIH) surface integral method. While superficially similar to the Abraham-Lorentz and Lorentz-Dirac equations, these conditions differ from them in several fundamental ways. They are not equations of motion in the usual sense but rather a set of conditions which these motions must obey asymptotically in the future of an initial starting time. And furthermore, they do not admit the runaway solutions of these other equations. As in the original EIH work, they are integrability conditions gotten from integrating the empty-space (i.e., sourceless) Einstein-Maxwell equations of general relativity over closed two-surfaces surrounding the sources of the fields appearing in these equations. No additional ad hoc assumptions, such as the form of a force law or the introduction of inertial reaction terms, are required for this purpose, nor is there a need for any infinite mass renormalizations such as are required in other derivations since all integrals are over surfaces and thus finite. In addition to being asymptotic, the conditions of motion derived here are also approximate and apply, as do the original EIH equations, only to slowly moving systems. A ``slowness'' parameter ɛ is identified as the ratio of the light travel time across the system divided by a characteristic time, e.g., a period. Use is made of both the method of matched asymptotic expansions and the method of multiple time scales to obtain an asymptotic expansion in ɛ and the expansion is carried to sufficiently high order ɛ7 to obtain the lowest-order radiation reaction terms. The resulting conditions of motion are shown to not allow runaway motions.
Asymptotic and Fredholm representations of discrete groups
NASA Astrophysics Data System (ADS)
Manuilov, V. M.; Mishchenko, A. S.
1998-10-01
A C^*-algebra servicing the theory of asymptotic representations and its embedding into the Calkin algebra that induces an isomorphism of K_1-groups is constructed. As a consequence, it is shown that all vector bundles over the classifying space B\\pi that can be obtained by means of asymptotic representations of a discrete group \\pi can also be obtained by means of representations of the group \\pi \\times {\\mathbb Z} into the Calkin algebra. A generalization of the concept of Fredholm representation is also suggested, and it is shown that an asymptotic representation can be regarded as an asymptotic Fredholm representation.
Thermal dissipation in quantum turbulence.
Kobayashi, Michikazu; Tsubota, Makoto
2006-10-06
The microscopic mechanism of thermal dissipation in quantum turbulence is numerically studied by solving the coupled system involving the Gross-Pitaevskii equation and the Bogoliubov-de Gennes equation. At low temperatures, the obtained dissipation does not work at scales greater than the vortex core size. However, as the temperature increases, dissipation works at large scales and it affects the vortex dynamics. We successfully obtain the mutual friction coefficients of the vortex in dilute Bose-Einstein condensates dynamics as functions of temperature.
Thermal Dissipation in Quantum Turbulence
Kobayashi, Michikazu; Tsubota, Makoto
2006-10-06
The microscopic mechanism of thermal dissipation in quantum turbulence is numerically studied by solving the coupled system involving the Gross-Pitaevskii equation and the Bogoliubov-de Gennes equation. At low temperatures, the obtained dissipation does not work at scales greater than the vortex core size. However, as the temperature increases, dissipation works at large scales and it affects the vortex dynamics. We successfully obtain the mutual friction coefficients of the vortex in dilute Bose-Einstein condensates dynamics as functions of temperature.
The asymptotic degrees of freedom of fluid flows
Foias, C.
1990-09-01
We have obtained rigorous estimates for the attractors of some basic dissipative differential equations which are within the physical or numerical ranges (e.g. 2D Navier-Stokes equations). We have shown that the ring laser cavity equations have a finite dimensional attractor. We have constructed inertial manifolds for a large class of dissipative differential equations (e.g. Kuramoto-Sivashinsky and Ginzberg-Landau equations). For a large class of equations including the 2D Navier-Stokes equations we have introduced several approximate intertial manifolds which yield new approximative ordinary differential equations with better error estimates then those of the usual Galerkin approximations. We have evidence that the new approximating schemes lead to computational improvements upon the Galerkin schemes. We have given a normal form for the Navier-Stokes which allows the explicit asymptotic integration of the equations. We have also proposed a new theoretical approach to decaying homogeneous turbulence. We also made some contribution to robust control theory which may be relevant to fluid dynamics.
Asymptotic invariants of homotopy groups
NASA Astrophysics Data System (ADS)
Manin, Fedor
We study the homotopy groups of a finite CW complex X via constraints on the geometry of representatives of their elements. For example, one can measure the "size" of alpha ∈ pi n (X) by the optimal Lipschitz constant or volume of a representative. By comparing the geometrical structure thus obtained with the algebraic structure of the group, one can define functions such as growth and distortion in pin(X), analogously to the way that such functions are studied in asymptotic geometric group theory. We provide a number of examples and techniques for studying these invariants, with a special focus on spaces with few rational homotopy groups. Our main theorem characterizes those X in which all non-torsion homotopy classes are undistorted, that is, their volume distortion functions, and hence also their Lipschitz distortion functions, are linear.
Satellite Movie Shows Erika Dissipate
This animation of visible and infrared imagery from NOAA's GOES-West satellite from Aug. 27 to 29 shows Tropical Storm Erika move through the Eastern Caribbean Sea and dissipate near eastern Cuba. ...
Dissipation, interaction, and relative entropy.
Gaveau, B; Granger, L; Moreau, M; Schulman, L S
2014-03-01
Many thermodynamic relations involve inequalities, with equality if a process does not involve dissipation. In this article we provide equalities in which the dissipative contribution is shown to involve the relative entropy (also called the Kullback-Leibler divergence). The processes considered are general time evolutions in both classical and quantum mechanics, and the initial state is sometimes thermal, sometimes partially so. As an application, the relative entropy is related to transport coefficients.
Power dissipation in automotive suspensions
NASA Astrophysics Data System (ADS)
Smith, Malcolm C.; Swift, Stuart J.
2011-02-01
For a standard quarter-car vehicle model and a road disturbance whose velocity profile is white noise, it is shown that the power dissipated in the suspension is proportional to the tyre vertical stiffness and the noise intensity, but is independent of all masses and suspension parameters. The dependence of this result on the modelling assumptions is explored. It is shown that the road disturbance model is ill-posed for the computation of power dissipation in the tyre and a modification is suggested. Computational results then indicate that the total power dissipation is still very insensitive to variations in vehicle and suspension parameters, but not tyre parameters, even though the suspension power dissipation and the tyre power dissipation vary individually. The extension of the result to half-car vehicle models is also considered. For both the pitch-plane and roll-plane models, it is found from numerical examples that the broad conclusion of large dependence of the total power dissipation on tyre parameters and small dependence on all other parameters remains. A brief discussion is included on the contribution to power loss due to rolling resistance.
Einstein-Yang-Mills theory: Asymptotic symmetries
NASA Astrophysics Data System (ADS)
Barnich, Glenn; Lambert, Pierre-Henry
2013-11-01
Asymptotic symmetries of the Einstein-Yang-Mills system with or without cosmological constant are explicitly worked out in a unified manner. In agreement with a recent conjecture, one finds a Virasoro-Kac-Moody type algebra not only in three dimensions but also in the four-dimensional asymptotically flat case.
On SLλ(I)-asymptotically statistical equivalent sequences
NASA Astrophysics Data System (ADS)
Gumus, Hafize; Savas, Ekrem
2012-09-01
This paper presents the notion of SLλ(I)-asymptotically statistical equivalence which is a natural combination of asymptotic I-equivalence and λ-statistical equivalence. We find its relation to I-asymptotically statistical convergence, strong λI-asymptotically equivalence and strong Cesàro I-asymptotically equivalence.
NASA Astrophysics Data System (ADS)
Notari, Alessio; Tywoniuk, Konrad
2016-12-01
We analyze in detail the background cosmological evolution of a scalar field coupled to a massless abelian gauge field through an axial term phi/fγ F ~F, such as in the case of an axion. Gauge fields in this case are known to experience tachyonic growth and therefore can backreact on the background as an effective dissipation into radiation energy density ρR, which can lead to inflation without the need of a flat potential. We analyze the system, for momenta k smaller than the cutoff fγ, including the backreaction numerically. We consider the evolution from a given static initial condition and explicitly show that, if fγ is smaller than the field excursion phi0 by about a factor of at least Script O (20), there is a friction effect which turns on before the field can fall down and which can then lead to a very long stage of inflation with a generic potential. In addition we find superimposed oscillations, which would get imprinted on any kind of perturbations, scalars and tensors. Such oscillations have a period of 4-5 efolds and an amplitude which is typically less than a few percent and decreases linearly with fγ. We also stress that the curvature perturbation on uniform density slices should be sensitive to slow-roll parameters related to ρR rather than dot phi2/2 and we discuss the existence of friction terms acting on the perturbations, although we postpone a calculation of the power spectrum and of non-gaussianity to future work and we simply define and compute suitable slow roll parameters. Finally we stress that this scenario may be realized in the axion case, if the coupling 1/fγ to U(1) (photons) is much larger than the coupling 1/fG to non-abelian gauge fields (gluons), since the latter sets the range of the potential and therefore the maximal allowed phi0~ fG.
Nonlinear Localized Dissipative Structures for Long-Time Solution of Wave Equation
2009-07-01
Fatemi, E., Engquist, B., and Osher, S., " Numerical Solution of the High Frequency Asymptotic Expansion for the Scalar Wave Equation ", Journal of...FINAL REPORT Grant Title: Nonlinear Localized Dissipative Structures for Long-Time Solution of Wave Equation By Dr. John Steinhoff Grant number... numerical method, "Wave Confinement" (WC), is developed to efficiently solve the linear wave equation . This is similar to the originally developed
Dynamics of nonlinear dissipative systems in the vicinity of resonance
NASA Astrophysics Data System (ADS)
Plaksiy, K. Y.; Mikhlin, Y. V.
2015-01-01
The behavior of nonlinear dissipative 2-DOF mechanical systems in the vicinity of resonance is studied in this paper. Namely, the free resonance vibrations of a spring-mass-pendulum system and the forced resonance vibrations of a 2-DOF dissipative system containing a nonlinear absorber are considered. A reduced system stated with respect to the system energy, the arctangent of the vibration amplitudes ratio, and the phase difference, is obtained and analyzed. The nonlinear normal mode approach is used in this analysis. Conditions for vibration energy localization are discussed.
Dissipation in small systems: Landau-Zener approach
NASA Astrophysics Data System (ADS)
Barra, Felipe; Esposito, Massimiliano
2016-06-01
We establish a stochastic thermodynamics for a Fermionic level driven by a time-dependent force and interacting with initially thermalized levels playing the role of a reservoir. The driving induces consecutive avoided crossings between system and reservoir levels described within Landau-Zener theory. We derive the resulting system dynamics and thermodynamics and identify energy, work, heat, entropy, and dissipation. Our theory perfectly reproduces the numerically exact quantum work statistics obtained using a two point measurements approach of the total energy and provides an explicit expression for the dissipation in terms of diabatic transitions.
Dissipation in small systems: Landau-Zener approach.
Barra, Felipe; Esposito, Massimiliano
2016-06-01
We establish a stochastic thermodynamics for a Fermionic level driven by a time-dependent force and interacting with initially thermalized levels playing the role of a reservoir. The driving induces consecutive avoided crossings between system and reservoir levels described within Landau-Zener theory. We derive the resulting system dynamics and thermodynamics and identify energy, work, heat, entropy, and dissipation. Our theory perfectly reproduces the numerically exact quantum work statistics obtained using a two point measurements approach of the total energy and provides an explicit expression for the dissipation in terms of diabatic transitions.
Mixing and dissipation in a geostrophic buoyancy-driven circulation
NASA Astrophysics Data System (ADS)
Vreugdenhil, Catherine A.; Gayen, Bishakhdatta; Griffiths, Ross W.
2016-08-01
Turbulent mixing and energy dissipation have important roles in the global circulation but are not resolved by ocean models. We use direct numerical simulations of a geostrophic circulation, resolving turbulence and convection, to examine the rates of dissipation and mixing. As a starting point, we focus on circulation in a rotating rectangular basin forced by a surface temperature difference but no wind stress. Emphasis is on the geostrophic regime for the horizontal circulation, but also on the case of strong buoyancy forcing (large Rayleigh number), which implies a turbulent convective boundary layer. The computed results are consistent with existing scaling theory that predicts dynamics and heat transport dependent on the relative thicknesses of thermal and Ekman boundary layers, hence on the relative roles of buoyancy and rotation. Scaling theory is extended to describe the volume-integrated rate of mixing, which is proportional to heat transport and decreases with increasing rotation rate or decreasing temperature difference. In contrast, viscous dissipation depends crucially on whether the thermal boundary layer is laminar or turbulent, with no direct Coriolis effect on the turbulence unless rotation is extremely strong. For strong forcing, in the geostrophic regime, the mechanical energy input from buoyancy goes primarily into mixing rather than dissipation. For a buoyancy-driven circulation in a basin comparable to the North Atlantic we estimate that the total rate of mixing accounts for over 95% of the mechanical energy supply, implying that buoyancy is an efficient driver of mixing in the oceans.
Detecting communities using asymptotical surprise
NASA Astrophysics Data System (ADS)
Traag, V. A.; Aldecoa, R.; Delvenne, J.-C.
2015-08-01
Nodes in real-world networks are repeatedly observed to form dense clusters, often referred to as communities. Methods to detect these groups of nodes usually maximize an objective function, which implicitly contains the definition of a community. We here analyze a recently proposed measure called surprise, which assesses the quality of the partition of a network into communities. In its current form, the formulation of surprise is rather difficult to analyze. We here therefore develop an accurate asymptotic approximation. This allows for the development of an efficient algorithm for optimizing surprise. Incidentally, this leads to a straightforward extension of surprise to weighted graphs. Additionally, the approximation makes it possible to analyze surprise more closely and compare it to other methods, especially modularity. We show that surprise is (nearly) unaffected by the well-known resolution limit, a particular problem for modularity. However, surprise may tend to overestimate the number of communities, whereas they may be underestimated by modularity. In short, surprise works well in the limit of many small communities, whereas modularity works better in the limit of few large communities. In this sense, surprise is more discriminative than modularity and may find communities where modularity fails to discern any structure.
Asymptotics of Simple Branching Populations
NASA Astrophysics Data System (ADS)
Huillet, Thierry; Kłopotowski, Andrzej; Porzio, Anna
1995-09-01
In this paper we study a simple deterministic tree structure: an initial individual generates a finite number of offspring, each of which has given integer valued lifetime, iterating the same procedure when dying. Three asymptotic distributions of this asynchronous deterministic branching procedure are considered: the generation distribution, the ability of individuals to generate offspring and the age distribution. Thermodynamic formalism is then developped to reveal the multifractal nature of the mass splitting associated to our process. On considère l'itération d'une structure déterministe arborescente selon laquelle un ancêtre engendre un nombre fini de descendants dont la durée de vie (à valeurs entières) est donnée. Dans un premier temps on s'intéresse aux trois distributions asymptotiques suivantes : répartition des générations, aptitude à engendrer des descendants et répartition selon l'âge. Ensuite nous développons le formalisme thermodynamique pour mettre en évidence le caractère multifractal de la scission d'une masse unitaire associée à cette arborescence.
Wave dissipation by muddy seafloors
NASA Astrophysics Data System (ADS)
Elgar, Steve; Raubenheimer, Britt
2008-04-01
Muddy seafloors cause tremendous dissipation of ocean waves. Here, observations and numerical simulations of waves propagating between 5- and 2-m water depths across the muddy Louisiana continental shelf are used to estimate a frequency- and depth-dependent dissipation rate function. Short-period sea (4 s) and swell (7 s) waves are shown to transfer energy to long-period (14 s) infragravity waves, where, in contrast with theories for fluid mud, the observed dissipation rates are highest. The nonlinear energy transfers are most rapid in shallow water, consistent with the unexpected strong increase of the dissipation rate with decreasing depth. These new results may explain why the southwest coast of India offers protection for fishing (and for the 15th century Portuguese fleet) only after large waves and strong currents at the start of the monsoon move nearshore mud banks from about 5- to 2-m water depth. When used with a numerical nonlinear wave model, the new dissipation rate function accurately simulates the large reduction in wave energy observed in the Gulf of Mexico.
Response of driven sessile drops with contact-line dissipation.
Bostwick, Joshua B; Steen, Paul H
2016-11-04
A partially-wetting sessile drop is driven by a sinusoidal pressure field that produces capillary waves on the liquid/gas interface. Response diagrams and phase shifts for the droplet, whose contact-line moves with contact-angle that is a smooth function of the contact line speed, are reported. Contact-line dissipation originating from the contact-line speed condition leads to damping for drops with finite contact-line mobility, even for inviscid fluids. The critical mobility and associated driving frequency to generate the largest contact-line dissipation is computed. Viscous dissipation is approximated using the irrotational flow and the critical Ohnesorge number bounding regions beyond which a given mode becomes over-damped is computed. Regions of modal coexistence where two modes can be simultaneously excited by a single forcing frequency are identified. Predictions compare favorably to related experiments on vibrated drops.
Prodanovic, Srdjan; Gracewski, Sheryl; Nam, Jong-Hoon
2015-01-01
The stereocilia bundle is the mechano-transduction apparatus of the inner ear. In the mammalian cochlea, the stereocilia bundles are situated in the subtectorial space (STS)—a micrometer-thick space between two flat surfaces vibrating relative to each other. Because microstructures vibrating in fluid are subject to high-viscous friction, previous studies considered the STS as the primary place of energy dissipation in the cochlea. Although there have been extensive studies on how metabolic energy is used to compensate the dissipation, much less attention has been paid to the mechanism of energy dissipation. Using a computational model, we investigated the power dissipation in the STS. The model simulates fluid flow around the inner hair cell (IHC) stereocilia bundle. The power dissipation in the STS because of the presence IHC stereocilia increased as the stimulating frequency decreased. Along the axis of the stimulating frequency, there were two asymptotic values of power dissipation. At high frequencies, the power dissipation was determined by the shear friction between the two flat surfaces of the STS. At low frequencies, the power dissipation was dominated by the viscous friction around the IHC stereocilia bundle—the IHC stereocilia increased the STS power dissipation by 50- to 100-fold. There exists a characteristic frequency for STS power dissipation, CFSTS, defined as the frequency where power dissipation drops to one-half of the low frequency value. The IHC stereocilia stiffness and the gap size between the IHC stereocilia and the tectorial membrane determine the characteristic frequency. In addition to the generally assumed shear flow, nonshear STS flow patterns were simulated. Different flow patterns have little effect on the CFSTS. When the mechano-transduction of the IHC was tuned near the vibrating frequency, the active motility of the IHC stereocilia bundle reduced the power dissipation in the STS. PMID:25650916
DISSIPATIVE DIVERGENCE OF RESONANT ORBITS
Batygin, Konstantin; Morbidelli, Alessandro
2013-01-01
A considerable fraction of multi-planet systems discovered by the observational surveys of extrasolar planets reside in mild proximity to first-order mean-motion resonances. However, the relative remoteness of such systems from nominal resonant period ratios (e.g., 2:1, 3:2, and 4:3) has been interpreted as evidence for lack of resonant interactions. Here, we show that a slow divergence away from exact commensurability is a natural outcome of dissipative evolution and demonstrate that libration of critical angles can be maintained tens of percent away from nominal resonance. We construct an analytical theory for the long-term dynamical evolution of dissipated resonant planetary pairs and confirm our calculations numerically. Collectively, our results suggest that a significant fraction of the near-commensurate extrasolar planets are in fact resonant and have undergone significant dissipative evolution.
Model of dissipative dielectric elastomers
NASA Astrophysics Data System (ADS)
Chiang Foo, Choon; Cai, Shengqiang; Jin Adrian Koh, Soo; Bauer, Siegfried; Suo, Zhigang
2012-02-01
The dynamic performance of dielectric elastomer transducers and their capability of electromechanical energy conversion are affected by dissipative processes, such as viscoelasticity, dielectric relaxation, and current leakage. This paper describes a method to construct a model of dissipative dielectric elastomers on the basis of nonequilibrium thermodynamics. We characterize the state of the dielectric elastomer with kinematic variables through which external loads do work, and internal variables that measure the progress of the dissipative processes. The method is illustrated with examples motivated by existing experiments of polyacrylate very-high-bond dielectric elastomers. This model predicts the dynamic response of the dielectric elastomer and the leakage current behavior. We show that current leakage can be significant under large deformation and for long durations. Furthermore, current leakage can result in significant hysteresis for dielectric elastomers under cyclic voltage.
Dissipative heavy-ion collisions
Feldmeier, H.T.
1985-01-01
This report is a compilation of lecture notes of a series of lectures held at Argonne National Laboratory in October and November 1984. The lectures are a discussion of dissipative phenomena as observed in collisions of atomic nuclei. The model is based on a system which has initially zero temperature and the initial energy is kinetic and binding energy. Collisions excite the nuclei, and outgoing fragments or the compound system deexcite before they are detected. Brownian motion is used to introduce the concept of dissipation. The master equation and the Fokker-Planck equation are derived. 73 refs., 59 figs. (WRF)
Quantum dissipative Rashba spin ratchets.
Smirnov, Sergey; Bercioux, Dario; Grifoni, Milena; Richter, Klaus
2008-06-13
We predict the possibility to generate a finite stationary spin current by applying an unbiased ac driving to a quasi-one-dimensional asymmetric periodic structure with Rashba spin-orbit interaction and strong dissipation. We show that under a finite coupling strength between the orbital degrees of freedom the electron dynamics at low temperatures exhibits a pure spin ratchet behavior, i.e., a finite spin current and the absence of charge transport in spatially asymmetric structures. It is also found that the equilibrium spin currents are not destroyed by the presence of strong dissipation.
Tumbling asteroid rotation with the YORP torque and inelastic energy dissipation
NASA Astrophysics Data System (ADS)
Breiter, S.; Murawiecka, M.
2015-05-01
The Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect and rotational energy dissipation due to inelastic deformations are two key mechanisms affecting rotation of tumbling asteroids in long term. Each of the effects used to be discussed separately. We present the first results concerning a simulation of their joint action. Asteroids (3103) Eger and (99942) Apophis, as well as their scaled variants, are used as test bodies. Plugging in the dissipation destroys limit cycles of the pure YORP, but creates a new asymptotic state of stationary tumbling with a fixed rotation period. The present model does not contradict finding Eger in the principal axis rotation. For Apophis, the model suggests that its current rotation state should be relatively young. In general, the fraction of initial conditions leading to the principal axis rotation is too small, compared to the actual data. The model requires a stronger energy dissipation and weaker YORP components in the nutation angle and obliquity.
Iacocca, Ezio; Dumas, Randy K; Bookman, Lake; Mohseni, Majid; Chung, Sunjae; Hoefer, Mark A; Akerman, Johan
2014-01-31
Magnetic dissipative droplets are localized, strongly nonlinear dynamical modes excited in nanocontact spin valves with perpendicular magnetic anisotropy. These modes find potential application in nanoscale structures for magnetic storage and computation, but dissipative droplet studies have so far been limited to extended thin films. Here, numerical and asymptotic analyses are used to demonstrate the existence and properties of novel solitons in confined structures. As a nanowire's width is decreased with a nanocontact of fixed size at its center, the observed modes undergo transitions from a fully localized two-dimensional droplet into a two-dimensional droplet edge mode and then a pulsating one-dimensional droplet. These solitons are interpreted as dissipative versions of classical, conservative solitons, allowing for an analytical description of the modes and the mechanisms of bifurcation. The presented results open up new possibilities for the study of low-dimensional solitons and droplet applications in nanostructures.
Parameter estimation in the presence of the most general Gaussian dissipative reservoir
NASA Astrophysics Data System (ADS)
Jarzyna, Marcin; Zwierz, Marcin
2017-01-01
We analyze the performance of quantum parameter estimation in the presence of the most general Gaussian dissipative reservoir. We derive lower bounds on the precision of phase estimation and a closely related problem of frequency estimation. For both problems we show that it is impossible to achieve the Heisenberg limit asymptotically in the presence of such a reservoir. However, we also find that for any fixed number of probes used in the setup there exists a Gaussian dissipative reservoir, which, in principle, allows for the Heisenberg-limited performance for that number of probes. We discuss a realistic implementation of a frequency estimation scheme in the presence of a Gaussian dissipative reservoir in a cavity system.
Self-organization in a driven dissipative plasma system
NASA Astrophysics Data System (ADS)
Shaikh, Dastgeer; Dasgupta, B.; Hu, Q.; Zank, G. P.
2010-02-01
We perform a fully self-consistent three-dimensional numerical simulation for a compressible, dissipative magnetoplasma driven by large-scale perturbations, that contain a fairly broad spectrum of characteristic modes, ranging from largest scales to intermediate scales and down to the smallest scales, where the energy of the system is dissipated by collisional (ohmic) and viscous dissipations. Additionally, our simulation includes nonlinear interactions amongst a wide range of fluctuations that are initialized with random spectral amplitudes, leading to the cascade of spectral energy in the inertial range spectrum, and takes into account large-scale as well as small-scale perturbations that may have been induced by the background plasma fluctuations, as well as the non-adiabatic exchange of energy leading to the migration of energy from the energy-containing modes or randomly injected energy driven by perturbations and further dissipated by the smaller scales. Besides demonstrating the comparative decays of the total energy and the dissipation rate of the energy, our results show the existence of a perpendicular component of the current, thus clearly confirming that the self-organized state is non-force free.
ENERGY DISSIPATION PROCESSES IN SOLAR WIND TURBULENCE
Wang, Y.; Wei, F. S.; Feng, X. S.; Sun, T. R.; Zuo, P. B.; Xu, X. J.; Zhang, J.
2015-12-15
Turbulence is a chaotic flow regime filled by irregular flows. The dissipation of turbulence is a fundamental problem in the realm of physics. Theoretically, dissipation ultimately cannot be achieved without collisions, and so how turbulent kinetic energy is dissipated in the nearly collisionless solar wind is a challenging problem. Wave particle interactions and magnetic reconnection (MR) are two possible dissipation mechanisms, but which mechanism dominates is still a controversial topic. Here we analyze the dissipation region scaling around a solar wind MR region. We find that the MR region shows unique multifractal scaling in the dissipation range, while the ambient solar wind turbulence reveals a monofractal dissipation process for most of the time. These results provide the first observational evidences for intermittent multifractal dissipation region scaling around a MR site, and they also have significant implications for the fundamental energy dissipation process.
Asymptotic unbounded root loci - Formulas and computation
NASA Technical Reports Server (NTRS)
Sastry, S. S.; Desoer, C. A.
1983-01-01
A new geometric way of computing the asymptotic behavior of unbounded root loci of a strictly proper linear time-invariant control system as loop gain goes to infinity is presented. Properties of certain restricted linear maps and nested restrictions of linear maps are developed, and formulas are obtained for the leading coefficient of the asymptotic values of the unbounded multivariable root loci are obtained in terms of eigenvalues of those maps. Published results and a certain simple null structure assumption are used to relate these asymptotic values to the structure at infinity of the Smith-McMillan form of the open loop transfer function. Explicit matrix formulas for the more abstract derived formulas are given and additional geometric insights are developed with orthogonal projections and singular value decomposition. Formulas for the pivots of the unbounded root loci are calculated and shown to have the same form as the coefficients of the unbounded asymptotic root loci.
On asymptotically generalized statistical equivalent set sequences
NASA Astrophysics Data System (ADS)
Savas, Ekrem
2013-10-01
In this paper we shall study the asymptotically λ-statistical equivalent (Wijsman sense) of multiple L. In addition to these definition, natural inclusion theorems shall also be presented. This approach has not been considered in any context before.
How nanomechanical systems can minimize dissipation.
Muratore-Ginanneschi, Paolo; Schwieger, Kay
2014-12-01
Information processing machines at the nanoscales are unavoidably affected by thermal fluctuations. Efficient design requires understanding how nanomachines can operate at minimal energy dissipation. Here we focus on mechanical systems controlled by smoothly varying potential forces. We show that optimal control equations come about in a natural way if the energy cost to manipulate the potential is taken into account. When such a cost becomes negligible, an optimal control strategy can be constructed by transparent geometrical methods which recover the solution of optimal mass transport equations in the overdamped limit. Our equations are equivalent to hierarchies of kinetic equations of a form well known in the theory of dilute gases. From our results, optimal strategies for energy efficient nanosystems may be devised by established techniques from kinetic theory.
Variational Derivation of Dissipative Equations
NASA Astrophysics Data System (ADS)
Sogo, Kiyoshi
2017-03-01
A new variational principle is formulated to derive various dissipative equations. Model equations considered are the damping equation, Bloch equation, diffusion equation, Fokker-Planck equation, Kramers equation and Smoluchowski equation. Each equation and its time reversal equation are simultaneously obtained in our variational principle.
On Some Numerical Dissipation Schemes
NASA Technical Reports Server (NTRS)
Swanson, R. C.; Radespiel, R.; Turkel, E.
1998-01-01
Several schemes for introducing an artificial dissipation into a central difference approximation to the Euler and Navier Stokes equations are considered. The focus of the paper is on the convective upwind and split pressure (CUSP) scheme, which is designed to support single interior point discrete shock waves. This scheme is analyzed and compared in detail with scalar dissipation and matrix dissipation (MATD) schemes. Resolution capability is determined by solving subsonic, transonic, and hypersonic flow problems. A finite-volume discretization and a multistage time-stepping scheme with multigrid are used to compute solutions to the flow equations. Numerical solutions are also compared with either theoretical solutions or experimental data. For transonic airfoil flows the best accuracy on coarse meshes for aerodynamic coefficients is obtained with a simple MATD scheme. The coarse-grid accuracy for the original CUSP scheme is improved by modifying the limiter function used with the scheme, giving comparable accuracy to that obtained with the MATD scheme. The modifications reduce the background dissipation and provide control over the regions where the scheme can become first order.
Estimates of M2 Tidal Energy Dissipation from TOPEX/Poseidon Altimeter Data
NASA Technical Reports Server (NTRS)
Egbert, Gary D.; Ray, Richard D.
2001-01-01
Most of the tidal energy dissipation in the ocean occurs in shallow seas, as has long been recognized. However, recent work has suggested that a significant fraction of the dissipation, perhaps 1 TW or more, occurs in the deep ocean. This paper builds further evidence for that conclusion. More than 6 years of data from the TOPEX/Poseidon satellite altimeter are used to map the tidal dissipation rate throughout the world ocean. The dissipation rate is estimated as a balance between the rate of working by tidal forces and the energy flux divergence, computed using currents derived by least squares fitting of the altimeter data and the shallow water equations. Such calculations require dynamical assumptions, in particular about the nature of dissipation. To assess sensitivity of dissipation estimates to input assumptions, a large suite of tidal inversions based on a wide range of drag parameterizations and employing both real and synthetic altimeter data are compared. These experiments and Monte Carlo error fields from a generalized inverse model are used to establish error uncertainties for the dissipation estimates. Owing to the tight constraints on tidal elevation fields provided by the altimeter, area integrals of the energy balance are remarkably insensitive to required dynamical assumptions. Tidal energy dissipation is estimated for all major shallow seas (excluding individual polar seas) and compared with previous model and data-based estimates. Dissipation in the open ocean is significantly tnhanced around major bathymetric features, in a manner consistent with simple theories the generation of baroclinic tides.
Avoiding dissipation in a system of three quantum harmonic oscillators
NASA Astrophysics Data System (ADS)
Manzano, Gonzalo; Galve, Fernando; Zambrini, Roberta
2013-03-01
We analyze the symmetries in an open quantum system composed by three coupled and detuned harmonic oscillators in the presence of a common heat bath. It is shown analytically how to engineer the couplings and frequencies of the system so as to have several degrees of freedom unaffected by decoherence, irrespective of the specific spectral density or initial state of the bath. This partial thermalization allows observing asymptotic entanglement at moderate temperatures, even in the nonresonant case. This latter feature cannot be seen in the simpler situation of only two oscillators, highlighting the richer structural variety of the three-body case. When departing from the strict conditions for partial thermalization, a hierarchical structure of dissipation rates for the normal modes is observed, leading to a long transient where quantum correlations such as the quantum discord are largely preserved, as well as to synchronous dynamics of the oscillators quadratures.
Fedosov, Dmitry A; Em Karniadakis, George; Caswell, Bruce
2008-04-14
The flows of dilute polymer solutions in micro- and nanoscale channels are of both fundamental and practical importance in variety of applications in which the channel gap is of the same order as the size of the suspended particles or macromolecules. In such systems depletion layers are observed near solid-fluid interfaces, even in equilibrium, and the imposition of flow results in further cross-stream migration of the particles. In this work we employ dissipative particle dynamics to study depletion and migration in dilute polymer solutions in channels several times larger than the radius of gyration (Rg) of bead-spring chains. We compare depletion layers for different chain models and levels of chain representation, solvent quality, and relative wall-solvent-polymer interactions. By suitable scaling the simulated depletion layers compare well with the asymptotic lattice theory solution of depletion near a repulsive wall. In Poiseuille flow, polymer migration across the streamlines increases with the Peclet and the Reynolds number until the center-of-mass distribution develops two symmetric off-center peaks which identify the preferred chain positions across the channel. These appear to be governed by the balance of wall-chain repulsive interactions and an off-center driving force of the type known as the Segre-Silberberg effect.
Dissipative particle dynamics model for colloid transport in porous media
Pan, W.; Tartakovsky, A. M.
2013-08-01
We present that the transport of colloidal particles in porous media can be effectively modeled with a new formulation of dissipative particle dynamics, which augments standard DPD with non-central dissipative shear forces between particles while preserving angular momentum. Our previous studies have demonstrated that the new formulation is able to capture accurately the drag forces as well as the drag torques on colloidal particles that result from the hydrodynamic retardation effect. In the present work, we use the new formulation to study the contact efficiency in colloid filtration in saturated porous media. Note that the present model include all transport mechanisms simultaneously, including gravitational sedimentation, interception and Brownian diffusion. Our results of contact efficiency show a good agreement with the predictions of the correlation equation proposed by Tufenkji and EliMelech, which also incorporate all transport mechanisms simultaneously without the additivity assumption.
Time course of sleep inertia dissipation in human performance and alertness
NASA Technical Reports Server (NTRS)
Jewett, M. E.; Wyatt, J. K.; Ritz-De Cecco, A.; Khalsa, S. B.; Dijk, D. J.; Czeisler, C. A.
1999-01-01
Alertness and performance on a wide variety of tasks are impaired immediately upon waking from sleep due to sleep inertia, which has been found to dissipate in an asymptotic manner following waketime. It has been suggested that behavioural or environmental factors, as well as sleep stage at awakening, may affect the severity of sleep inertia. In order to determine the time course of sleep inertia dissipation under normal entrained conditions, subjective alertness and cognitive throughput were measured during the first 4 h after habitual waketime from a full 8-h sleep episode on 3 consecutive days. We investigated whether this time course was affected by either sleep stage at awakening or behavioural/environmental factors. Sleep inertia dissipated in an asymptotic manner and took 2-4 h to near the asymptote. Saturating exponential functions fitted the sleep inertia data well, with time constants of 0.67 h for subjective alertness and 1.17 h for cognitive performance. Most awakenings occurred out of stage rapid eye movement (REM), 2 or 1 sleep, and no effect of sleep stage at awakening on either the severity of sleep inertia or the time course of its dissipation could be detected. Subjective alertness and cognitive throughput were significantly impaired upon awakening regardless of whether subjects got out of bed, ate breakfast, showered and were exposed to ordinary indoor room light (approximately 150 lux) or whether subjects participated in a constant routine (CR) protocol in which they remained in bed, ate small hourly snacks and were exposed to very dim light (10-15 lux). These findings allow for the refinement of models of alertness and performance, and have important implications for the scheduling of work immediately upon awakening in many occupational settings.
Asymptotic permanent profile of the ion acoustic wave driven by the Langmuir wave
NASA Astrophysics Data System (ADS)
Kaup, D. J.; Latifi, A.; Leon, J.
1992-08-01
We study the evolution of Langmuir waves coupled to the ion acoustic wave by means of the ponderomotive force in the Karpman limit (caviton equation). Using the spectral transform with singular dispersion relation, it is shown that the background noise (fluctuations in the ion density) is amplified and its time asymptotic behavior will be a static solution which is totally reflective for the Langmuir wave. Moreover, if the initial ion density contains a local depression, the asymptotic profile will contain a number of permanent localized density depressions (cavitons), static in the rest frame of the acoustic wave and entrained in its wake.
A dissipative model of solar system
NASA Astrophysics Data System (ADS)
Vladimir, V. G.
2009-04-01
rotation of planets, and the small tidal deformations arising under influence of gradients of gravitational forces. The method of division of movements receives the equations describing movements of the centers of weights of planets and their own rotations. In the offered model takes place a dissipation of the energy which source are internally viscous forces of each planet. The system supposes the first integral - the law of preservation of the kinetic moment concerning the centre of weights of system. As a result of deformations of planets in the law of the universal gravitation which has been written down for material points, there are small conservative amendments. The equations of movement describe movement of the centers of weights of planets and their rotation around of the centers of weights in view of the tidal phenomena and the dissipative forces. The connected system of the equations consists of 3N the vector equations of the second order representing the theorems of movement of the centers of weights of planets, and N the vector equations of the first order determining changes of the own kinetic moments of each planet. Stationary values of full mechanical energy on the variety set in integral of the kinetic moment, correspond to stationary movements - to rotations of system as firm body with constant angular speed around of the centre of weights of all system. Angular speed of stationary rotation is directed along a constant vector of the kinetic moment, and the axis of rotation is the main central axis of inertia of system. We shall notice, that deformations of planets in stationary movement are constant, as in system of coordinates rotating with constant angular speed centrifugal forces and forces of gravitational interaction of planets are constant. Stationary configurations of system are determined according to Routh`s technique as stationary points of the changed potential energy submitted by the sum potential energies of centrifugal and gravitational
Dissipative ring solitons with vorticity.
Soto-Crespo, J M; Akhmediev, N; Mejia-Cortés, C; Devine, N
2009-03-16
We study dissipative ring solitons with vorticity in the frame of the (2+1)-dimensional cubic-quintic complex Ginzburg-Landau equation. In dissipative media, radially symmetric ring structures with any vorticity m can be stable in a finite range of parameters. Beyond the region of stability, the solitons lose the radial symmetry but may remain stable, keeping the same value of the topological charge. We have found bifurcations into solitons with n-fold bending symmetry, with n independent on m. Solitons without circular symmetry can also display (m + 1)-fold modulation behaviour. A sequence of bifurcations can transform the ring soliton into a pulsating or chaotic state which keeps the same value of the topological charge as the original ring.
Global classical solutions of the Vlasov-Fokker-Planck equation with local alignment forces
NASA Astrophysics Data System (ADS)
Choi, Young-Pil
2016-07-01
In this paper, we are concerned with the global well-posedness and time-asymptotic decay of the Vlasov-Fokker-Planck equation with local alignment forces. The equation can be formally derived from an agent-based model for self-organized dynamics called the Motsch-Tadmor model with noises. We present the global existence and uniqueness of classical solutions to the equation around the global Maxwellian in the whole space. For the large-time behavior, we show the algebraic decay rate of solutions towards the equilibrium under suitable assumptions on the initial data. We also remark that the rate of convergence is exponential when the spatial domain is periodic. The main methods used in this paper are the classical energy estimates combined with hyperbolic-parabolic dissipation arguments.
Topological sigma models & dissipative hydrodynamics
NASA Astrophysics Data System (ADS)
Haehl, Felix M.; Loganayagam, R.; Rangamani, Mukund
2016-04-01
We outline a universal Schwinger-Keldysh effective theory which describes macroscopic thermal fluctuations of a relativistic field theory. The basic ingredients of our construction are three: a doubling of degrees of freedom, an emergent abelian symmetry associated with entropy, and a topological (BRST) supersymmetry imposing fluctuationdissipation theorem. We illustrate these ideas for a non-linear viscous fluid, and demonstrate that the resulting effective action obeys a generalized fluctuation-dissipation theorem, which guarantees a local form of the second law.
Asymptotic cost in document conversion
NASA Astrophysics Data System (ADS)
Blostein, Dorothea; Nagy, George
2012-01-01
In spite of a hundredfold decrease in the cost of relevant technologies, the role of document image processing systems is gradually declining due to the transition to an on-line world. Nevertheless, in some high-volume applications, document image processing software still saves millions of dollars by accelerating workflow, and similarly large savings could be realized by more effective automation of the multitude of low-volume personal document conversions. While potential cost savings, based on estimates of costs and values, are a driving force for new developments, quantifying such savings is difficult. The most important trend is that the cost of computing resources for DIA is becoming insignificant compared to the associated labor costs. An econometric treatment of document processing complements traditional performance evaluation, which focuses on assessing the correctness of the results produced by document conversion software. Researchers should look beyond the error rate for advancing both production and personal document conversion.
Asymptotic wave propagation in excitable media.
Bernus, Olivier; Vigmond, Edward
2015-07-01
Wave shape and velocity are important issues in reaction-diffusion systems, and are often the result of competition in media with heterogeneous conduction properties. Asymptotic wave front propagation at maximal conduction velocity has been previously reported in the context of anisotropic cardiac tissue, but it is unknown whether this is a universal property of excitable tissues where conduction velocity can be locally modulated by mechanisms other than anisotropy. Here, we investigate the impact of conduction heterogeneities and boundary effects on wave propagation in excitable media. Following a theoretical analysis, we find that wave-front cusps occur where local velocity is reduced and that asymptotic wave fronts propagate at the maximal translational conduction velocity. Simulations performed in different reaction-diffusion systems, including cardiac tissue, confirm our theoretical findings. We conclude that this property can be found in a wide range of reaction-diffusion systems with excitable dynamics and that asymptotic wave-front shapes can be predicted.
Quantum dissipation and CP violation in MINOS
NASA Astrophysics Data System (ADS)
Oliveira, R. L. N.; Guzzo, M. M.; de Holanda, P. C.
2014-03-01
We use the open quantum systems framework to analyze the MINOS data and perform this analysis considering two different dissipative models. In the first model, the dissipative parameter describes the decoherence effect and in the second, the dissipative parameter describes other dissipative effects including decoherence. With the second model it is possible to study CP violation since we consider Majorana neutrinos. The analysis from the muon neutrino and antineutrino beam assigns different values to all the parameters of the models, but is consistent between them. Assuming that neutrinos are equivalent to antineutrinos, the global analysis presents a nonvanishing Majorana CP phase depending on the energetic parametrization of the dissipative parameter.
Dissipative Particle Dynamics simulation of colloidal suspensions
NASA Astrophysics Data System (ADS)
Jamali, Safa; Boromand, Arman; Maia, Joao
2014-03-01
DPD as a mesoscale method was firstly proposed to study dynamics of suspensions under flow condition. However the proposed method failed to capture shear properties of suspensions because it lacked: first a potential to reproduce lubrication forces and second a clear definition for the colloid surface. Recently we reported a modified DPD method which defines colloidal particles as particles with hard core and a dissipative coat. An additional lubrication force was introduced to include the short-range hydrodynamics that are not captured in original DPD. The model was found to be able to reproduce shear properties of suspensions for a wide range of different systems, from monodisperse to bimodal with different volume fractions, compositions and size ratios. In present work our modified DPD method is employed to study both equilibrium and flow properties of colloidal suspension. Zero shear viscosity of suspension is measured using Green-Kubo expressions and the results are compared to theoretical predictions. Furthermore, structure formation in suspensions is studied in respect to energy landscape of the fluid both at rest and under flow.
Asymptotic stability of singularly perturbed differential equations
NASA Astrophysics Data System (ADS)
Artstein, Zvi
2017-02-01
Asymptotic stability is examined for singularly perturbed ordinary differential equations that may not possess a natural split into fast and slow motions. Rather, the right hand side of the equation is comprised of a singularly perturbed component and a regular one. The limit dynamics consists then of Young measures, with values being invariant measures of the fast contribution, drifted by the slow one. Relations between the asymptotic stability of the perturbed system and the limit dynamics are examined, and a Lyapunov functions criterion, based on averaging, is established.
Turbulent collision statistics of cloud droplets at low dissipation rates
NASA Astrophysics Data System (ADS)
Banerjee, Sandipan
Collisions of sedimenting droplets in a turbulent flow is of great importance in cloud physics. Collision efficiency and collision enhancement over gravitational collision by air turbulence govern the growth of the cloud droplets leading to warm rain initiation and precipitation dynamics. In this thesis we present direct numerical simulation (DNS) results for collision statistics of droplets in turbulent flows of low dissipation rates (in the range of 3 cm2/s3-100 cm2/s3) relevant to strato-cumulus clouds. First, we revisit the case of gravitational collision in still fluid to validate the details of the collision detection algorithm used in our code. We compare the collision statistics with either new analytical predictions regarding the percentages of different collision types, or results from published papers. The effect of initial conditions on the collision statistics and statistical uncertainties are analyzed both analytically and through the simulation data. Second, we consider the case of weak turbulence (as in strato-cumulus clouds). In this case the particle motion is mainly driven by gravity. The standard deviation (or the uncertainty) of the average collision statistics is examined analytically in terms of time correlation function of the data. We then report new DNS results of collision statistics in a turbulent flow, showing how air turbulence increases the geometric colli- sion statistics and the collision efficiency. We find that the collision-rate enhancement due to turbulence depends nonlinearly on the flow dissipation rate. This result calls for a more careful parameterization of the collision statistics in strato-cumulus clouds. Due to the low flow dissipation rate in stratocumulus clouds, a related challenge is low droplet Stokes number. Here the Stokes number is the ratio of droplet inertial response time to the flow Kolmogorov time. A very low Stokes number implies that the numerical integration time step is now governed by the droplet
Optimal control of an asymptotic model of flow separation
NASA Astrophysics Data System (ADS)
Qadri, Ubaid; Schmid, Peter; LFC-UK Team
2015-11-01
In the presence of surface imperfections, the boundary layer developing over an aircraft wing can separate and reattach, leading to a small separation bubble. We are interested in developing a low-order model that can be used to control the onset of separation at high Reynolds numbers typical of aircraft flight. In contrast to previous studies, we use a high Reynolds number asymptotic description of the Navier-Stokes equations to describe the motion of motion of the fluid. We obtain a steady solution to the nonlinear triple-deck equations for the separated flow over a small bump at high Reynolds numbers. We derive for the first time the adjoint of the nonlinear triple-deck equations and use it to study optimal control of the separated flow. We calculate the sensitivity of the properties of the separation bubble to local base flow modifications and steady forcing. We assess the validity of using this simplified asymptotic model by comparing our results with those obtained using the full Navier-Stokes equations.
Dimant
2000-01-24
Linearly unstable dissipative systems with quadratic nonlinearity occurring in plasma physics, optics, fluid mechanics, etc. are often modeled by a general set of three-wave mode-coupled ordinary differential equations for complex variables. Bounded attractors of the set approximate nonlinearly saturated turbulent states of real physical systems. Exact criteria for boundedness of the attractors are found. Fundamentally different kinds of asymptotic behavior of the wave triad are classified in the parameter space and quantitatively assessed.
Asymptotic theory of relativistic, magnetized jets
Lyubarsky, Yuri
2011-01-15
The structure of a relativistically hot, strongly magnetized jet is investigated at large distances from the source. Asymptotic equations are derived describing collimation and acceleration of the externally confined jet. Conditions are found for the transformation of the thermal energy into the fluid kinetic energy or into the Poynting flux. Simple scalings are presented for the jet collimation angle and Lorentz factors.
Asymptotic theory of relativistic, magnetized jets.
Lyubarsky, Yuri
2011-01-01
The structure of a relativistically hot, strongly magnetized jet is investigated at large distances from the source. Asymptotic equations are derived describing collimation and acceleration of the externally confined jet. Conditions are found for the transformation of the thermal energy into the fluid kinetic energy or into the Poynting flux. Simple scalings are presented for the jet collimation angle and Lorentz factors.
Lectures on renormalization and asymptotic safety
Nagy, Sandor
2014-11-15
A short introduction is given on the functional renormalization group method, putting emphasis on its nonperturbative aspects. The method enables to find nontrivial fixed points in quantum field theoretic models which make them free from divergences and leads to the concept of asymptotic safety. It can be considered as a generalization of the asymptotic freedom which plays a key role in the perturbative renormalization. We summarize and give a short discussion of some important models, which are asymptotically safe such as the Gross–Neveu model, the nonlinear σ model, the sine–Gordon model, and we consider the model of quantum Einstein gravity which seems to show asymptotic safety, too. We also give a detailed analysis of infrared behavior of such scalar models where a spontaneous symmetry breaking takes place. The deep infrared behavior of the broken phase cannot be treated within the framework of perturbative calculations. We demonstrate that there exists an infrared fixed point in the broken phase which creates a new scaling regime there, however its structure is hidden by the singularity of the renormalization group equations. The theory spaces of these models show several similar properties, namely the models have the same phase and fixed point structure. The quantum Einstein gravity also exhibits similarities when considering the global aspects of its theory space since the appearing two phases there show analogies with the symmetric and the broken phases of the scalar models. These results be nicely uncovered by the functional renormalization group method.
Layer tracking, asymptotics, and domain decomposition
NASA Technical Reports Server (NTRS)
Brown, D. L.; Chin, R. C. Y.; Hedstrom, G. W.; Manteuffel, T. A.
1991-01-01
A preliminary report is presented on the work on the tracking of internal layers in a singularly-perturbed convection-diffusion equation. It is shown why such tracking may be desirable, and it is also shown how to do it using domain decomposition based on asymptotic analysis.
On asymptotic properties of biharmonic Steklov eigenvalues
NASA Astrophysics Data System (ADS)
Liu, Genqian
2016-11-01
In this paper, by explicitly calculating the principal symbols of pseudodifferential operators, we establish two Weyl-type asymptotic formulas with sharp remainder estimates for the counting functions of the two classes of biharmonic Steklov eigenvalue problems of smooth bounded domains in a Riemannian manifold.
Asymptotic Distributions for Tests of Combined Significance.
ERIC Educational Resources Information Center
Becker, Betsy Jane
This paper discusses distribution theory and power computations for four common "tests of combined significance." These tests are calculated using one-sided sample probabilities or p values from independent studies (or hypothesis tests), and provide an overall significance level for the series of results. Noncentral asymptotic sampling…
Harnessing spin precession with dissipation.
Crisan, A D; Datta, S; Viennot, J J; Delbecq, M R; Cottet, A; Kontos, T
2016-01-27
Non-collinear spin transport is at the heart of spin or magnetization control in spintronics devices. The use of nanoscale conductors exhibiting quantum effects in transport could provide new paths for that purpose. Here we study non-collinear spin transport in a quantum dot. We use a device made out of a single-wall carbon nanotube connected to orthogonal ferromagnetic electrodes. In the spin transport signals, we observe signatures of out of equilibrium spin precession that are electrically tunable through dissipation. This could provide a new path to harness spin precession in nanoscale conductors.
Harnessing spin precession with dissipation
NASA Astrophysics Data System (ADS)
Crisan, A. D.; Datta, S.; Viennot, J. J.; Delbecq, M. R.; Cottet, A.; Kontos, T.
2016-01-01
Non-collinear spin transport is at the heart of spin or magnetization control in spintronics devices. The use of nanoscale conductors exhibiting quantum effects in transport could provide new paths for that purpose. Here we study non-collinear spin transport in a quantum dot. We use a device made out of a single-wall carbon nanotube connected to orthogonal ferromagnetic electrodes. In the spin transport signals, we observe signatures of out of equilibrium spin precession that are electrically tunable through dissipation. This could provide a new path to harness spin precession in nanoscale conductors.
Designing Biomimetic, Dissipative Material Systems
Balazs, Anna C.; Whitesides, George M.; Brinker, C. Jeffrey; Aranson, Igor S.; Chaikin, Paul; Dogic, Zvonimir; Glotzer, Sharon; Hammer, Daniel; Irvine, Darrell; Little, Steven R.; Olvera de la Cruz, Monica; Parikh, Atul N.; Stupp, Samuel; Szostak, Jack
2016-01-21
Throughout human history, new materials have been the foundation of transformative technologies: from bronze, paper, and ceramics to steel, silicon, and polymers, each material has enabled far-reaching advances. Today, another new class of materials is emerging—one with both the potential to provide radically new functions and to challenge our notion of what constitutes a “material”. These materials would harvest, transduce, or dissipate energy to perform autonomous, dynamic functions that mimic the behaviors of living organisms. Herein, we discuss the challenges and benefits of creating “dissipative” materials that can potentially blur the boundaries between living and non-living matter.
Tidal disruption of dissipative planetesimals
NASA Technical Reports Server (NTRS)
Mizuno, H.; Boss, A. P.
1985-01-01
A self-consistent numerical model is developed for the tidal disruption of a solid planetesimal. The planetesimal is treated as a highly viscous, slightly compressible fluid whose disturbed parts are an inviscid, pressureless fluid undergoing distortion and disruption. The distortions were constrained to being symmetrical above and below the equatorial plane. The tidal potential is expanded in terms of Legendre polynomials, which eliminates the center of mass acceleration effects, permitting definition of equations of motion in a noninertial frame. Consideration is given to viscous dissipation and to characteristics of the solid-atmosphere boundary. The model is applied to sample cases in one, two and three dimensions.
Entropy Splitting and Numerical Dissipation
NASA Technical Reports Server (NTRS)
Yee, H. C.; Vinokur, M.; Djomehri, M. J.
1999-01-01
A rigorous stability estimate for arbitrary order of accuracy of spatial central difference schemes for initial-boundary value problems of nonlinear symmetrizable systems of hyperbolic conservation laws was established recently by Olsson and Oliger (1994) and Olsson (1995) and was applied to the two-dimensional compressible Euler equations for a perfect gas by Gerritsen and Olsson (1996) and Gerritsen (1996). The basic building block in developing the stability estimate is a generalized energy approach based on a special splitting of the flux derivative via a convex entropy function and certain homogeneous properties. Due to some of the unique properties of the compressible Euler equations for a perfect gas, the splitting resulted in the sum of a conservative portion and a non-conservative portion of the flux derivative. hereafter referred to as the "Entropy Splitting." There are several potential desirable attributes and side benefits of the entropy splitting for the compressible Euler equations that were not fully explored in Gerritsen and Olsson. The paper has several objectives. The first is to investigate the choice of the arbitrary parameter that determines the amount of splitting and its dependence on the type of physics of current interest to computational fluid dynamics. The second is to investigate in what manner the splitting affects the nonlinear stability of the central schemes for long time integrations of unsteady flows such as in nonlinear aeroacoustics and turbulence dynamics. If numerical dissipation indeed is needed to stabilize the central scheme, can the splitting help minimize the numerical dissipation compared to its un-split cousin? Extensive numerical study on the vortex preservation capability of the splitting in conjunction with central schemes for long time integrations will be presented. The third is to study the effect of the non-conservative proportion of splitting in obtaining the correct shock location for high speed complex shock
Ray Tracing Modeling of Gravity Wave Propagation and Dissipation
NASA Astrophysics Data System (ADS)
Vadas, Sharon; Crowley, Geoff
In this paper, we describe a ray trace model which calculates the wavevector, location and phase of a gravity wave (GW) as it propagates in the lower atmosphere and thermosphere. If used for a discreet transient source (such as a deep convective plume), we describe how this model can calculate the body forcing and the heat/cooling that are created when the GWs within a wave packet dissipate in the thermosphere from kinematic viscosity and thermal diffusivity. Although the body force calculation requires only the divergence of the momentum flux, the heat/cooling calculation requires the reconstructed GW field (e.g., density, velocity perturbations), which in turn requires the GW dissipative polarization relations. We describe these relations. We then describe the results of a recent study involving GWs identified from TIDDBIT HF Doppler sounder data taken at Wallops Island, VI, USA. Using this ray trace model, we determine if the unusual neutral wind profile measured by a rocket experiment at high altitudes (~290-370 km) could have been caused by the propagation and dissipation of several waves observed by TIDDBIT at lower altitudes.
Damping and energy dissipation in soft tissue vibrations during running.
Khassetarash, Arash; Hassannejad, Reza; Enders, Hendrik; Ettefagh, Mir Mohammad
2015-01-21
It has been well accepted that the vibrations of soft tissue cannot be simulated by a single sinusoidal function. In fact, these vibrations are a combination of several vibration modes. In this study, these modes are extracted applying a recently developed method namely, partly ensemble empirical mode decomposition (PEEMD). Then, a methodology for estimating the damping properties and energy dissipation caused by damping for each mode is used. Applying this methodology on simulated signals demonstrates high accuracy. This methodology is applied to the acceleration signals of the gastrocnemius muscle during sprinting and the differences between the damping properties of different vibration modes were identified. The results were 1) the damping property of high-frequency mode was higher than that for low-frequency modes. 2) All identified modes were in under damped condition, therefore, the vibrations had an oscillatory nature. 3) The damping ratios of lower modes are about 100% increased compared to higher modes. 4) The energy dissipation occurred in lower modes were much more than that for higher mode; According to the power spectrum of the ground reaction force (GRF), which is the input force into the body, the recent finding supports the muscle tuning paradigm. It is suggested that the damping properties and energy dissipation can be used to distinguish between different running conditions (surface, fatigue, etc.).
Asymptotic self-restabilization of a continuous elastic structure
NASA Astrophysics Data System (ADS)
Bosi, F.; Misseroni, D.; Dal Corso, F.; Neukirch, S.; Bigoni, D.
2016-12-01
A challenge in soft robotics and soft actuation is the determination of an elastic system that spontaneously recovers its trivial path during postcritical deformation after a bifurcation. The interest in this behavior is that a displacement component spontaneously cycles around a null value, thus producing a cyclic soft mechanism. An example of such a system is theoretically proven through the solution of the elastica and a stability analysis based on dynamic perturbations. It is shown that the asymptotic self-restabilization is driven by the development of a configurational force, of similar nature to the Peach-Koehler interaction between dislocations in crystals, which is derived from the principle of least action. A proof-of-concept prototype of the discovered elastic system is designed, realized, and tested, showing that this innovative behavior can be obtained in a real mechanical apparatus.
Correspondence behavior of classical and quantum dissipative directed transport via thermal noise
NASA Astrophysics Data System (ADS)
Carlo, Gabriel G.; Ermann, Leonardo; Rivas, Alejandro M. F.; Spina, María E.
2016-04-01
We systematically study several classical-quantum correspondence properties of the dissipative modified kicked rotator, a paradigmatic ratchet model. We explore the behavior of the asymptotic currents for finite ℏeff values in a wide range of the parameter space. We find that the correspondence between the classical currents with thermal noise providing fluctuations of size ℏeff and the quantum ones without it is very good in general with the exception of specific regions. We systematically consider the spectra of the corresponding classical Perron-Frobenius operators and quantum superoperators. By means of an average distance between the classical and quantum sets of eigenvalues we find that the correspondence is unexpectedly quite uniform. This apparent contradiction is solved with the help of the Weyl-Wigner distributions of the equilibrium eigenvectors, which reveal the key role of quantum effects by showing surviving coherences in the asymptotic states.
Correspondence behavior of classical and quantum dissipative directed transport via thermal noise.
Carlo, Gabriel G; Ermann, Leonardo; Rivas, Alejandro M F; Spina, María E
2016-04-01
We systematically study several classical-quantum correspondence properties of the dissipative modified kicked rotator, a paradigmatic ratchet model. We explore the behavior of the asymptotic currents for finite ℏ_{eff} values in a wide range of the parameter space. We find that the correspondence between the classical currents with thermal noise providing fluctuations of size ℏ_{eff} and the quantum ones without it is very good in general with the exception of specific regions. We systematically consider the spectra of the corresponding classical Perron-Frobenius operators and quantum superoperators. By means of an average distance between the classical and quantum sets of eigenvalues we find that the correspondence is unexpectedly quite uniform. This apparent contradiction is solved with the help of the Weyl-Wigner distributions of the equilibrium eigenvectors, which reveal the key role of quantum effects by showing surviving coherences in the asymptotic states.
Natural approach to quantum dissipation
NASA Astrophysics Data System (ADS)
Taj, David; Öttinger, Hans Christian
2015-12-01
The dissipative dynamics of a quantum system weakly coupled to one or several reservoirs is usually described in terms of a Lindblad generator. The popularity of this approach is certainly due to the linear character of the latter. However, while such linearity finds justification from an underlying Hamiltonian evolution in some scaling limit, it does not rely on solid physical motivations at small but finite values of the coupling constants, where the generator is typically used for applications. The Markovian quantum master equations we propose are instead supported by very natural thermodynamic arguments. They themselves arise from Markovian master equations for the system and the environment which preserve factorized states and mean energy and generate entropy at a non-negative rate. The dissipative structure is driven by an entropic map, called modular, which introduces nonlinearity. The generated modular dynamical semigroup (MDS) guarantees for the positivity of the time evolved state the correct steady state properties, the positivity of the entropy production, and a positive Onsager matrix with symmetry relations arising from Green-Kubo formulas. We show that the celebrated Davies Lindblad generator, obtained through the Born and the secular approximations, generates a MDS. In doing so we also provide a nonlinear MDS which is supported by a weak coupling argument and is free from the limitations of the Davies generator.
Modular quantum-information processing by dissipation
NASA Astrophysics Data System (ADS)
Marshall, Jeffrey; Campos Venuti, Lorenzo; Zanardi, Paolo
2016-11-01
Dissipation can be used as a resource to control and simulate quantum systems. We discuss a modular model based on fast dissipation capable of performing universal quantum computation, and simulating arbitrary Lindbladian dynamics. The model consists of a network of elementary dissipation-generated modules and it is in principle scalable. In particular, we demonstrate the ability to dissipatively prepare all single-qubit gates, and the controlled-not gate; prerequisites for universal quantum computing. We also show a way to implement a type of quantum memory in a dissipative environment, whereby we can arbitrarily control the loss in both coherence, and concurrence, over the evolution. Moreover, our dissipation-assisted modular construction exhibits a degree of inbuilt robustness to Hamiltonian and, indeed, Lindbladian errors, and as such is of potential practical relevance.
Thermodynamic geometry of minimum-dissipation driven barrier crossing
NASA Astrophysics Data System (ADS)
Sivak, David A.; Crooks, Gavin E.
2016-11-01
We explore the thermodynamic geometry of a simple system that models the bistable dynamics of nucleic acid hairpins in single molecule force-extension experiments. Near equilibrium, optimal (minimum-dissipation) driving protocols are governed by a generalized linear response friction coefficient. Our analysis demonstrates that the friction coefficient of the driving protocols is sharply peaked at the interface between metastable regions, which leads to minimum-dissipation protocols that drive rapidly within a metastable basin, but then linger longest at the interface, giving thermal fluctuations maximal time to kick the system over the barrier. Intuitively, the same principle applies generically in free energy estimation (both in steered molecular dynamics simulations and in single-molecule experiments), provides a design principle for the construction of thermodynamically efficient coupling between stochastic objects, and makes a prediction regarding the construction of evolved biomolecular motors.
Thermodynamic geometry of minimum-dissipation driven barrier crossing.
Sivak, David A; Crooks, Gavin E
2016-11-01
We explore the thermodynamic geometry of a simple system that models the bistable dynamics of nucleic acid hairpins in single molecule force-extension experiments. Near equilibrium, optimal (minimum-dissipation) driving protocols are governed by a generalized linear response friction coefficient. Our analysis demonstrates that the friction coefficient of the driving protocols is sharply peaked at the interface between metastable regions, which leads to minimum-dissipation protocols that drive rapidly within a metastable basin, but then linger longest at the interface, giving thermal fluctuations maximal time to kick the system over the barrier. Intuitively, the same principle applies generically in free energy estimation (both in steered molecular dynamics simulations and in single-molecule experiments), provides a design principle for the construction of thermodynamically efficient coupling between stochastic objects, and makes a prediction regarding the construction of evolved biomolecular motors.
Dissipative discrete breathers: periodic, quasiperiodic, chaotic, and mobile.
Martínez, P J; Meister, M; Floría, L M; Falo, F
2003-06-01
The properties of discrete breathers in dissipative one-dimensional lattices of nonlinear oscillators subject to periodic driving forces are reviewed. We focus on oscillobreathers in the Frenkel-Kontorova chain and rotobreathers in a ladder of Josephson junctions. Both types of exponentially localized solutions are easily obtained numerically using adiabatic continuation from the anticontinuous limit. Linear stability (Floquet) analysis allows the characterization of different types of bifurcations experienced by periodic discrete breathers. Some of these bifurcations produce nonperiodic localized solutions, namely, quasiperiodic and chaotic discrete breathers, which are generally impossible as exact solutions in Hamiltonian systems. Within a certain range of parameters, propagating breathers occur as attractors of the dissipative dynamics. General features of these excitations are discussed and the Peierls-Nabarro barrier is addressed. Numerical scattering experiments with mobile breathers reveal the existence of two-breather bound states and allow a first glimpse at the intricate phenomenology of these special multibreather configurations.
Efficient Schmidt number scaling in dissipative particle dynamics
NASA Astrophysics Data System (ADS)
Krafnick, Ryan C.; García, Angel E.
2015-12-01
Dissipative particle dynamics is a widely used mesoscale technique for the simulation of hydrodynamics (as well as immersed particles) utilizing coarse-grained molecular dynamics. While the method is capable of describing any fluid, the typical choice of the friction coefficient γ and dissipative force cutoff rc yields an unacceptably low Schmidt number Sc for the simulation of liquid water at standard temperature and pressure. There are a variety of ways to raise Sc, such as increasing γ and rc, but the relative cost of modifying each parameter (and the concomitant impact on numerical accuracy) has heretofore remained undetermined. We perform a detailed search over the parameter space, identifying the optimal strategy for the efficient and accuracy-preserving scaling of Sc, using both numerical simulations and theoretical predictions. The composite results recommend a parameter choice that leads to a speed improvement of a factor of three versus previously utilized strategies.
Influence of dissipation on two-atom dispersion interactions
NASA Astrophysics Data System (ADS)
Barcellona, Pablo; Buhmann, Stefan Yoshi
2015-03-01
We consider the dispersion interaction between two neutral, ground-state atoms at zero and finite temperature by means of a dynamical approach. Our result differs from the previous ones obtained with time-independent perturbation theory because it correctly accounts for the influence of dissipation via the atomic decay rates. Modern measurements of Casimir force seem to suggest a suppressed influence of dissipation. Our new result shows similar features and can hence help resolve the Drude-plasma debate. We also consider the interaction between a ground-state atom and an excited atom. There are discordant results in the literature for the retarded potential: one oscillating and one monotonous. Our dynamical result uniquely leads to the oscillating result when taking into account the decay rates. This work was supported by the DFG (Grant BU 1803/3-1).
Quantum speed meter based on dissipative coupling
NASA Astrophysics Data System (ADS)
Vyatchanin, Sergey P.; Matsko, Andrey B.
2017-01-01
We consider dissipative coupling Fabry-Perot cavity, i.e. its input mirror transmittance depends on position of probe mass. We show that dissipative coupling provide possibility to realize quantum speed meter by natural way, without additional setup for subtraction of position x(t) and delayed position x(t-τ). Quantum speed meter is a quantum non demolition (QND) meter which allow to overcome Standatd Quantum Limit — we show it for speed meter based on dissipative coupling.
Konow, Nicolai; Roberts, Thomas J
2015-04-07
During downhill running, manoeuvring, negotiation of obstacles and landings from a jump, mechanical energy is dissipated via active lengthening of limb muscles. Tendon compliance provides a 'shock-absorber' mechanism that rapidly absorbs mechanical energy and releases it more slowly as the recoil of the tendon does work to stretch muscle fascicles. By lowering the rate of muscular energy dissipation, tendon compliance likely reduces the risk of muscle injury that can result from rapid and forceful muscle lengthening. Here, we examine how muscle-tendon mechanics are modulated in response to changes in demand for energy dissipation. We measured lateral gastrocnemius (LG) muscle activity, force and fascicle length, as well as leg joint kinematics and ground-reaction force, as turkeys performed drop-landings from three heights (0.5-1.5 m centre-of-mass elevation). Negative work by the LG muscle-tendon unit during landing increased with drop height, mainly owing to greater muscle recruitment and force as drop height increased. Although muscle strain did not increase with landing height, ankle flexion increased owing to increased tendon strain at higher muscle forces. Measurements of the length-tension relationship of the muscle indicated that the muscle reached peak force at shorter and likely safer operating lengths as drop height increased. Our results indicate that tendon compliance is important to the modulation of energy dissipation by active muscle with changes in demand and may provide a mechanism for rapid adjustment of function during deceleration tasks of unpredictable intensity.
Dissipative entanglement of quantum spin fluctuations
NASA Astrophysics Data System (ADS)
Benatti, F.; Carollo, F.; Floreanini, R.
2016-06-01
We consider two non-interacting infinite quantum spin chains immersed in a common thermal environment and undergoing a local dissipative dynamics of Lindblad type. We study the time evolution of collective mesoscopic quantum spin fluctuations that, unlike macroscopic mean-field observables, retain a quantum character in the thermodynamical limit. We show that the microscopic dissipative dynamics is able to entangle these mesoscopic degrees of freedom, through a purely mixing mechanism. Further, the behaviour of the dissipatively generated quantum correlations between the two chains is studied as a function of temperature and dissipation strength.
Dissipation-induced instabilities and symmetry
NASA Astrophysics Data System (ADS)
Kirillov, Oleg N.; Verhulst, Ferdinand
2011-02-01
The paradox of destabilization of a conservative or non-conservative system by small dissipation, or Ziegler's paradox (1952), has stimulated a growing interest in the sensitivity of reversible and Hamiltonian systems with respect to dissipative perturbations. Since the last decade it has been widely accepted that dissipation-induced instabilities are closely related to singularities arising on the stability boundary, associated with Whitney's umbrella. The first explanation of Ziegler's paradox was given (much earlier) by Oene Bottema in 1956. The aspects of the mechanics and geometry of dissipation-induced instabilities with an application to rotor dynamics are discussed.
Geometric Integration of Weakly Dissipative Systems
NASA Astrophysics Data System (ADS)
Modin, K.; Führer, C.; Soöderlind, G.
2009-09-01
Some problems in mechanics, e.g. in bearing simulation, contain subsystems that are conservative as well as weakly dissipative subsystems. Our experience is that geometric integration methods are often superior for such systems, as long as the dissipation is weak. Here we develop adaptive methods for dissipative perturbations of Hamiltonian systems. The methods are "geometric" in the sense that the form of the dissipative perturbation is preserved. The methods are linearly explicit, i.e., they require the solution of a linear subsystem. We sketch an analysis in terms of backward error analysis and numerical comparisons with a conventional RK method of the same order is given.
Dissipation of sleep pressure is stable across adolescence.
Tarokh, L; Carskadon, M A; Achermann, P
2012-08-02
The sleep electroencephalogram (EEG) undergoes many changes during adolescence. We assessed whether sleep homeostasis is altered across adolescent development using two measures: the dissipation of slow-wave activity (SWA, 0.6-4.6Hz) across the night and the rate of build-up of SWA in the first non-rapid eye movement (NREM) sleep episode. Furthermore, we examined the association between homeostatic and circadian measures, by correlating the build-up of SWA in the first non-rapid eye movement (NREM) sleep episode with circadian phase. Finally, we compared the dissipation of SWA in individuals with (PH+) and without (PH-) a parental history of alcohol abuse/dependence. Twenty children (8 PH+) and 25 teens (10 PH+) underwent two consecutive polysomnographic recordings at ages 9/10 and 15/16 years and again 1.5-3 years later. Thirteen young adults (ages 20-23 years; no PH+) were assessed one time. The decay of Process S was modeled for each individual at each assessment using data from both recordings. Four parameters of Process S were derived for EEG derivation C3/A2: time constant of the decay, lower asymptote (LA), the level of S at sleep onset (S(SO)), and S(SO) minus LA. We found no change in these parameters between assessments for the children and teen cohorts. Between-subject analysis of the follow-up assessment for children (ages 11-13 years) and the initial assessment for teens (ages 15/16 years) showed no difference in these parameters, nor did follow-up assessment of teens (ages 17-19 years) compared to the single assessment of young adults (ages 20-23 years). Similarly, we observed no developmental changes in the rate of the build-up of SWA in the first NREM sleep episode for our within- and between-subject analyses, or a correlation between this measure and circadian phase for either cohort. With regard to parental alcohol history, we found no difference in the dissipation of sleep pressure between PH+ and PH- children and teens. These results indicate
Dissipative adaptation in driven self-assembly.
England, Jeremy L
2015-11-01
In a collection of assembling particles that is allowed to reach thermal equilibrium, the energy of a given microscopic arrangement and the probability of observing the system in that arrangement obey a simple exponential relationship known as the Boltzmann distribution. Once the same thermally fluctuating particles are driven away from equilibrium by forces that do work on the system over time, however, it becomes significantly more challenging to relate the likelihood of a given outcome to familiar thermodynamic quantities. Nonetheless, it has long been appreciated that developing a sound and general understanding of the thermodynamics of such non-equilibrium scenarios could ultimately enable us to control and imitate the marvellous successes that living things achieve in driven self-assembly. Here, I suggest that such a theoretical understanding may at last be emerging, and trace its development from historic first steps to more recent discoveries. Focusing on these newer results, I propose that they imply a general thermodynamic mechanism for self-organization via dissipation of absorbed work that may be applicable in a broad class of driven many-body systems.
Soap film vibration: origin of the dissipation.
Acharige, Sébastien Kosgodagan; Elias, Florence; Derec, Caroline
2014-11-07
We investigate the complex dispersion relationship of a transverse antisymmetric wave on a horizontal soap film. Experimentally, the complex wave number k at a fixed forcing frequency is determined by measuring the vibrating amplitude of the soap film: the wavelength (linked to the real part of k) is determined by the spatial variation of the amplitude; the decay length (linked to the imaginary part of k) is determined by analyzing the resonance curves of the vibrating wave as a function of frequency. Theoretically, we compute the complex dispersion relationship taking into account the physical properties of the bulk liquid and gas phase, and of the gas-liquid interfaces. The comparison between the computation (developed to the leading order under our experimental conditions) and the experimental results confirms that the phase velocity is fixed by the interplay between surface tension, and liquid and air inertia, as reported in previous studies. Moreover, we show that the attenuation of the transverse antisymmetric wave originates from the viscous dissipation in the gas phase surrounding the liquid film. This result is an important step in understanding the propagation of an acoustic wave in liquid foam, using a bottom-up approach.
Granular flows on a dissipative base.
Louge, Michel Y; Valance, Alexandre; Lancelot, Paul; Delannay, Renaud; Artières, Olivier
2015-08-01
We study inclined channel flows of sand over a sensor-enabled composite geotextile fabric base that dissipates granular fluctuation energy. We record strain of the fabric along the flow direction with imbedded fiber-optic Bragg gratings, flow velocity on the surface by correlating grain position in successive images, flow thickness with the streamwise shift of an oblique laser light sheet, velocity depth profile through a transparent side wall using a high-speed camera, and overall discharge rate. These independent measurements at inclinations between 33∘ and 37∘ above the angle of repose at 32.1±0.8∘ are consistent with a mass flow rate scaling as the 3/2 power of the flow depth, which is markedly different than flows on a rigid bumpy boundary. However, this power changes to 5/2 when flows are forced on the sand bed below its angle of repose. Strain measurements imply that the mean solid volume fraction in the flowing layer above the angle of repose is 0.268±0.033, independent of discharge rate or inclination.
Granular flows on a dissipative base
NASA Astrophysics Data System (ADS)
Louge, Michel Y.; Valance, Alexandre; Lancelot, Paul; Delannay, Renaud; Artières, Olivier
2015-08-01
We study inclined channel flows of sand over a sensor-enabled composite geotextile fabric base that dissipates granular fluctuation energy. We record strain of the fabric along the flow direction with imbedded fiber-optic Bragg gratings, flow velocity on the surface by correlating grain position in successive images, flow thickness with the streamwise shift of an oblique laser light sheet, velocity depth profile through a transparent side wall using a high-speed camera, and overall discharge rate. These independent measurements at inclinations between 33∘ and 37∘ above the angle of repose at 32.1 ±0 .8∘ are consistent with a mass flow rate scaling as the 3 /2 power of the flow depth, which is markedly different than flows on a rigid bumpy boundary. However, this power changes to 5 /2 when flows are forced on the sand bed below its angle of repose. Strain measurements imply that the mean solid volume fraction in the flowing layer above the angle of repose is 0.268 ±0.033 , independent of discharge rate or inclination.
Brane model with two asymptotic regions
NASA Astrophysics Data System (ADS)
Lubo, Musongela
2005-02-01
Some brane models rely on a generalization of the Melvin magnetic universe including a complex scalar field among the sources. We argue that the geometric interpretation of Kip. S. Thorne of this geometry restricts the kind of potential a complex scalar field can display to keep the same asymptotic behavior. While a finite energy is not obtained for a Mexican hat potential in this interpretation, this is the case for a potential displaying a broken phase and an unbroken one. We use for technical simplicity and illustrative purposes an ad hoc potential which however shares some features with those obtained in some supergravity models. We construct a sixth dimensional cylindrically symmetric solution which has two asymptotic regions: the Melvin-like metric on one side and a flat space displaying a conical singularity on the other. The causal structure of the configuration is discussed. Unfortunately, gravity is not localized on the brane.
Asymptotics of Determinants of Bessel Operators
NASA Astrophysics Data System (ADS)
Basor, Estelle L.; Ehrhardt, Torsten
For aL∞(+)∩L1(+) the truncated Bessel operator Bτ(a) is the integral operator acting on L2[0,τ] with the kernel
The Asymptotic Safety Scenario in Quantum Gravity.
Niedermaier, Max; Reuter, Martin
2006-01-01
The asymptotic safety scenario in quantum gravity is reviewed, according to which a renormalizable quantum theory of the gravitational field is feasible which reconciles asymptotically safe couplings with unitarity. The evidence from symmetry truncations and from the truncated flow of the effective average action is presented in detail. A dimensional reduction phenomenon for the residual interactions in the extreme ultraviolet links both results. For practical reasons the background effective action is used as the central object in the quantum theory. In terms of it criteria for a continuum limit are formulated and the notion of a background geometry self-consistently determined by the quantum dynamics is presented. Self-contained appendices provide prerequisites on the background effective action, the effective average action, and their respective renormalization flows.
Asymptotic scaling in turbulent pipe flow.
McKeon, B J; Morrison, J F
2007-03-15
The streamwise velocity component in turbulent pipe flow is assessed to determine whether it exhibits asymptotic behaviour that is indicative of high Reynolds numbers. The asymptotic behaviour of both the mean velocity (in the form of the log law) and that of the second moment of the streamwise component of velocity in the outer and overlap regions is consistent with the development of spectral regions which indicate inertial scaling. It is shown that an 'inertial sublayer' in physical space may be considered as a spatial analogue of the inertial subrange in the velocity spectrum and such behaviour only appears for Reynolds numbers R+>5 x 10(3), approximately, much higher than was generally thought.
Brane model with two asymptotic regions
Lubo, Musongela
2005-02-15
Some brane models rely on a generalization of the Melvin magnetic universe including a complex scalar field among the sources. We argue that the geometric interpretation of Kip. S. Thorne of this geometry restricts the kind of potential a complex scalar field can display to keep the same asymptotic behavior. While a finite energy is not obtained for a Mexican hat potential in this interpretation, this is the case for a potential displaying a broken phase and an unbroken one. We use for technical simplicity and illustrative purposes an ad hoc potential which however shares some features with those obtained in some supergravity models. We construct a sixth dimensional cylindrically symmetric solution which has two asymptotic regions: the Melvin-like metric on one side and a flat space displaying a conical singularity on the other. The causal structure of the configuration is discussed. Unfortunately, gravity is not localized on the brane.
Asymptotic Dynamics of Attractive-Repulsive Swarms
NASA Astrophysics Data System (ADS)
Leverentz, Andrew J.; Topaz, Chad M.; Bernoff, Andrew J.
2009-01-01
We classify and predict the asymptotic dynamics of a class of swarming models. The model consists of a conservation equation in one dimension describing the movement of a population density field. The velocity is found by convolving the density with a kernel describing attractive-repulsive social interactions. The kernel's first moment and its limiting behavior at the origin determine whether the population asymptotically spreads, contracts, or reaches steady state. For the spreading case, the dynamics approach those of the porous medium equation. The widening, compactly supported population has edges that behave like traveling waves whose speed, density, and slope we calculate. For the contracting case, the dynamics of the cumulative density approach those of Burgers' equation. We derive an analytical upper bound for the finite blow-up time after which the solution forms one or more delta-functions.
NASA Technical Reports Server (NTRS)
Busemann, A.; Vinh, N. X.; Culp, R. D.
1976-01-01
The problem of determining the trajectories, partially or wholly contained in the atmosphere of a spherical, nonrotating planet, is considered. The exact equations of motion for three-dimensional, aerodynamically affected flight are derived. Modified Chapman variables are introduced and the equations are transformed into a set suitable for analytic integration using asymptotic expansions. The trajectory is solved in two regions: the outer region, where the force may be considered a gravitational field with aerodynamic perturbations, and the inner region, where the force is predominantly aerodynamic, with gravity as a perturbation. The two solutions are matched directly. A composite solution, valid everywhere, is constructed by additive composition. This approach of directly matched asymptotic expansions applied to the exact equations of motion couched in terms of modified Chapman variables yields an analytical solution which should prove to be a powerful tool for aerodynamic orbit calculations.
Non-asymptotic Analysis of Bandlimited Functions
2012-01-12
Illustration of Theorem 10 with c = 1000 and n = 670. 44 References [1] Richard K. Miller, Anthony N. Michel, Ordinary Differential Equations, Dover ...Publications, Inc., 1982. [2] Yoel Shkolnisky, Mark Tygert, Vladimir Rokhlin, Approximation of Ban - dlimited Functions. [3] Andreas Glaser, Xiangtao Liu...A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, Dover Publications, 1964. [22] M.V. Fedoryuk, Asymptotic
Variational principles for dissipative waves
NASA Astrophysics Data System (ADS)
Dodin, I. Y.; Ruiz, D. E.
2016-10-01
Variational methods are a powerful tool in plasma theory. However, their applications are typically restricted to conservative systems or require doubling of variables, which often contradicts the purpose of the variational approach altogether. We show that these restrictions can be relaxed for some classes of dynamical systems that are of practical interest in plasma physics, particularly including dissipative plasma waves. Applications will be discussed to calculating dispersion relations and modulational dynamics of individual plasma waves and wave ensembles. The work was supported by the NNSA SSAA Program through DOE Research Grant No. DE-NA0002948, by the U.S. DOE through Contract No. DE-AC02-09CH11466, and by the U.S. DOD NDSEG Fellowship through Contract No. 32-CFR-168a.
Dissipative Dynamics with Exotic Beams
NASA Astrophysics Data System (ADS)
di Toro, M.; Colonna, M.; Greco, V.; Ferini, G.; Rizzo, C.; Rizzo, J.; Baran, V.; Wolter, H. H.; Zielinska-Pfabe, M.
2008-04-01
Heavy Ion Collisions (HIC) represent a unique tool to probe the in-medium nuclear interaction in regions away from saturation and at high nucleon momenta. In this report we present a selection of reaction observables particularly sensitive to the isovector part of the interaction, i.e. to the symmetry term of the nuclear Equation of State (EoS) At low and Fermi energies the behavior of the symmetry energy around saturation influences dissipation and fragment production mechanisms. Predictions are shown for fusion, deep-inelastic and fragmentation collisions induced by neutron rich projectiles. At all energies the isospin transport data are supplying valuable information on value and slope of the symmetry term below saturation. The importance of studying violent collisions with radioactive beams in this energy range is finally stressed.
Unravelling tidal dissipation in gaseous giant planets
NASA Astrophysics Data System (ADS)
Guenel, M.; Mathis, S.; Remus, F.
2014-06-01
Context. Tidal dissipation in planetary interiors is one of the key physical mechanisms that drive the evolution of star-planet and planet-moon systems. New constraints on this dissipation are now obtained both in the solar and exo-planetary systems. Aims: Tidal dissipation in planets is intrinsically related to their internal structure. Indeed, the dissipation behaves very differently when we compare its properties in solid and fluid planetary layers. Since planetary interiors consist of both types of regions, it is necessary to be able to assess and compare the respective intensity of the reservoir of dissipation in each type of layers. Therefore, in the case of giant planets, the respective contribution of the potential central dense rocky/icy core and of the deep convective fluid envelope must be computed as a function of the mass and the radius of the core. This will allow us to obtain their respective strengths. Methods: Using a method that evaluates the reservoir of dissipation associated to each region, which is a frequency-average of complex tidal Love numbers, we compared the respective contributions of the central core and of the fluid envelope. Results: For Jupiter- and Saturn-like planets, we show that the viscoelastic dissipation in the core could dominate the turbulent friction acting on tidal inertial waves in the envelope. However, the fluid dissipation would not be negligible. This demonstrates that it is necessary to build complete models of tidal dissipation in planetary interiors from their deep interior to their surface without any arbitrary assumptions. Conclusions: We demonstrate how important it is to carefully evaluate the respective strength of each type of dissipation mechanism in planetary interiors and to go beyond the usually adopted ad-hoc models. We confirm the significance of tidal dissipation in the potential dense core of gaseous giant planets.
Forced synchronization of a self-sustained chaotic oscillator.
González Salas, J S; Campos Cantón, E; Ordaz Salazar, F C; Campos Cantón, I
2008-06-01
This work presents a forced synchronization phenomenon like the asymptotic correlated behavior between chaotic oscillators forced by an external signal. Different kinds of forced synchronization are presented and given a theoretical justification explaining why it is possible to find some of them. Numerical results are presented for different cases such as antisymmetric, lag, phase, and identical forced synchronization.
Asymptotic dynamics of the exceptional Bianchi cosmologies
NASA Astrophysics Data System (ADS)
Hewitt, C. G.; Horwood, J. T.; Wainwright, J.
2003-05-01
In this paper we give, for the first time, a qualitative description of the asymptotic dynamics of a class of non-tilted spatially homogeneous (SH) cosmologies, the so-called exceptional Bianchi cosmologies, which are of Bianchi type VI$_{-1/9}$. This class is of interest for two reasons. Firstly, it is generic within the class of non-tilted SH cosmologies, being of the same generality as the models of Bianchi types VIII and IX. Secondly, it is the SH limit of a generic class of spatially inhomogeneous $G_{2}$ cosmologies. Using the orthonormal frame formalism and Hubble-normalized variables, we show that the exceptional Bianchi cosmologies differ from the non-exceptional Bianchi cosmologies of type VI$_{h}$ in two significant ways. Firstly, the models exhibit an oscillatory approach to the initial singularity and hence are not asymptotically self-similar. Secondly, at late times, although the models are asymptotically self-similar, the future attractor for the vacuum-dominated models is the so-called Robinson-Trautman SH model instead of the vacuum SH plane wave models.
Asymptotically flat space-times: an enigma
NASA Astrophysics Data System (ADS)
Newman, Ezra T.
2016-07-01
We begin by emphasizing that we are dealing with standard Einstein or Einstein-Maxwell theory—absolutely no new physics has been inserted. The fresh item is that the well-known asymptotically flat solutions of the Einstein-Maxwell theory are transformed to a new coordinate system with surprising and (seemingly) inexplicable results. We begin with the standard description of (Null) asymptotically flat space-times described in conventional Bondi-coordinates. After transforming the variables (mainly the asymptotic Weyl tensor components) to a very special set of Newman-Unti (NU) coordinates, we find a series of relations totally mimicking standard Newtonian classical mechanics and Maxwell theory. The surprising and troubling aspect of these relations is that the associated motion and radiation does not take place in physical space-time. Instead these relations takes place in an unusual inherited complex four-dimensional manifold referred to as H-space that has no immediate relationship with space-time. In fact these relations appear in two such spaces, H-space and its dual space \\bar{H}.
Some asymptotic properties of duplication graphs
NASA Astrophysics Data System (ADS)
Raval, Alpan
2003-12-01
Duplication graphs are graphs that grow by duplication of existing vertices, and are important models of biological networks, including protein-protein interaction networks and gene regulatory networks. Three models of graph growth are studied: pure duplication growth, and two two-parameter models in which duplication forms one element of the growth dynamics. A power-law degree distribution is found to emerge in all three models. However, the parameter space of the latter two models is characterized by a range of parameter values for which duplication is the predominant mechanism of graph growth. For parameter values that lie in this “duplication-dominated” regime, it is shown that the degree distribution either approaches zero asymptotically, or approaches a nonzero power-law degree distribution very slowly. In either case, the approach to the true asymptotic degree distribution is characterized by a dependence of the scaling exponent on properties of the initial degree distribution. It is therefore conjectured that duplication-dominated, scale-free networks may contain identifiable remnants of their early structure. This feature is inherited from the idealized model of pure duplication growth, for which the exact finite-size degree distribution is found and its asymptotic properties studied.
Asymptotic form of the Kohn-Sham correlation potential
Joubert, D. P.
2007-07-15
The density-functional correlation potential of a finite system is shown to asymptotically approach a nonzero constant along a nodal surface of the energetically highest occupied orbital and zero everywhere else. This nonuniform asymptotic form of the correlation potential exactly cancels the nonuniform asymptotic behavior of the exact exchange potential discussed by Della Sala and Goerling [Phys. Rev. Lett. 89, 33003 (2002)]. The sum of the exchange and correlation potentials therefore asymptotically tends to -1/r everywhere, consistent with the asymptotic form of the Kohn-Sham potential as analyzed by Almbladh and von Barth [Phys. Rev. B 31, 3231 (1985)].
Energy dissipation in fragmented geomaterials associated with impacting oscillators
NASA Astrophysics Data System (ADS)
Khudyakov, Maxim; Pasternak, Elena; Dyskin, Arcady
2016-04-01
In wave propagation through fragmented geomaterials forced by periodic loadings, the elements (fragments) strike against each other when passing through the neutral position (position with zero mutual rotation), quickly damping the oscillations. Essentially the impacts act as shock absorbers albeit localised at the neutral points. In order to analyse the vibrations of and wave propagation in such structures, a differential equation of a forced harmonic oscillator was investigated, where the each time the system passes through the neutral point the velocity gets reduced by multiplying it with the restitution coefficient which characterise the impact of the fragments. In forced vibrations the impact times depend on both the forced oscillations and the restitution coefficient and form an irregular sequence. Numerical solution of the differential equation was performed using Mathematica software. Along with vibration diagrams, the dependence of the energy dissipation on the ratio of the forcing frequency to the natural frequency was obtained. For small positive values of the restitution coefficient (less than 0.5), the asymmetric oscillations were found, and the phase of the forced vibrations determined the direction of the asymmetry. Also, at some values of the forcing frequencies and the restitution coefficient chaotic behaviour was found.
Sudden Viscous Dissipation of Compressing Turbulence
Davidovits, Seth; Fisch, Nathaniel J.
2016-03-11
Here we report compression of turbulent plasma can amplify the turbulent kinetic energy, if the compression is fast compared to the viscous dissipation time of the turbulent eddies. A sudden viscous dissipation mechanism is demonstrated, whereby this amplified turbulent kinetic energy is rapidly converted into thermal energy, suggesting a new paradigm for fast ignition inertial fusion.
Dissipation of anomalous pressures in the subsurface
NASA Astrophysics Data System (ADS)
Muggeridge, Ann; Abacioglu, Yafes; England, William; Smalley, Craig
2004-11-01
Zones of anomalous pressure, higher and lower than hydrostatic pressure, have been observed in many sedimentary basins around the world. These normally consist of groups of pressure compartments: volumes of higher-permeability rock surrounded on all sides by lower-permeability barriers. Knowledge of the timescales over which these abnormal pressures are maintained and the mechanisms by which they dissipate is critical for understanding how fluids, such as oil and gas, move in the subsurface. Existing analytic solutions investigate pressure dissipation through low-permeability barriers on top of or underneath an isolated pressure compartment. There are no analytic solutions describing pressure dissipation through lateral barriers, such as faults, or investigating the impact of groups of pressure compartments on the rate of pressure dissipation. This paper presents simple analytic models to investigate pressure dissipation through barriers, such as faults, forming the sides of pressure compartments. The timescales are compared with a solution for pressure dissipation through barriers on top of and underneath the compartment. It also investigates analytically the rate of pressure dissipation from groups of pressure compartments. Lateral seal permeabilities of 10-19 m2 may delay pressure equilibration for millions of years provided the compartment has a sufficiently high fluid storage capacity. Factors contributing toward a high fluid storage capacity include a high fluid compressibility (as is the case in hydrocarbon reservoirs) and a high porosity. The grouping of abnormally pressured compartments into "megacompartment complexes" may delay pressure dissipation for hundreds of millions of years.
Dissipation function in a magnetic field (Review)
NASA Astrophysics Data System (ADS)
Gurevich, V. L.
2015-07-01
The dissipation function is introduced to describe the behavior of the system of harmonic oscillations interacting with the environment (thermostat). This is a quadratic function of generalized velocities, which determines the rate of dissipation of the mechanical energy in the system. It was assumed earlier (Landau, Lifshitz) that the dissipation function can be introduced only in the absence of magnetic field. In the present review based on the author's studies, it has been shown how the dissipation function can be introduced in the presence of a magnetic field B. In a magnetic field, both dissipative and nondissipative responses arise as a response to perturbation and are expressed in terms of kinetic coefficients. The matrix of nondissipative coefficients can be obtained to determine an additional term formally including it into the equations of motion, which still satisfy the energy conservation law. Then, the dissipative part of the matrix can be considered in exactly the same way as without magnetic field, i.e., it defines the dissipation loss. As examples, the propagation and absorption of ultrasound in a metal or a semiconductor in a magnetic field have been considered using two methods: (i) the method based on the phenomenological theory using the equations of the theory of elasticity and (ii) the method based on the microscopic approach by analyzing and solving the kinetic equation. Both examples are used to illustrate the approach with the dissipation function.
asymptoticMK: A Web-Based Tool for the Asymptotic McDonald-Kreitman Test.
Haller, Benjamin C; Messer, Philipp W
2017-03-24
The McDonald-Kreitman (MK) test is a widely used method for quantifying the role of positive selection in molecular evolution. One key shortcoming of this test lies in its sensitivity to the presence of slightly deleterious mutations, which can severely bias its estimates. An asymptotic version of the MK test was recently introduced that addresses this problem by evaluating polymorphism levels for different mutation frequencies separately, and then extrapolating a function fitted to that data. Here we present asymptoticMK, a web-based implementation of this asymptotic McDonald-Kreitman test. Our web service provides a simple R-based interface into which the user can upload the required data (polymorphism and divergence data for the genomic test region and a neutrally evolving reference region). The web service then analyzes the data and provides plots of the test results. This service is free to use, open-source, and available at http://benhaller.com/messerlab/asymptoticMK.html. We provide results from simulations to illustrate the performance and robustness of the asymptoticMK test under a wide range of model parameters.
Precisely Timing Dissipative Quantum Information Processing
NASA Astrophysics Data System (ADS)
Kastoryano, M. J.; Wolf, M. M.; Eisert, J.
2013-03-01
Dissipative engineering constitutes a framework within which quantum information processing protocols are powered by system-environment interaction rather than by unitary dynamics alone. This framework embraces noise as a resource and, consequently, offers a number of advantages compared to one based on unitary dynamics alone, e.g., that the protocols are typically independent of the initial state of the system. However, the time independent nature of this scheme makes it difficult to imagine precisely timed sequential operations, conditional measurements, or error correction. In this work, we provide a path around these challenges, by introducing basic dissipative gadgets which allow us to precisely initiate, trigger, and time dissipative operations while keeping the system Liouvillian time independent. These gadgets open up novel perspectives for thinking of timed dissipative quantum information processing. As an example, we sketch how measurement-based computation can be simulated in the dissipative setting.
Precisely timing dissipative quantum information processing.
Kastoryano, M J; Wolf, M M; Eisert, J
2013-03-15
Dissipative engineering constitutes a framework within which quantum information processing protocols are powered by system-environment interaction rather than by unitary dynamics alone. This framework embraces noise as a resource and, consequently, offers a number of advantages compared to one based on unitary dynamics alone, e.g., that the protocols are typically independent of the initial state of the system. However, the time independent nature of this scheme makes it difficult to imagine precisely timed sequential operations, conditional measurements, or error correction. In this work, we provide a path around these challenges, by introducing basic dissipative gadgets which allow us to precisely initiate, trigger, and time dissipative operations while keeping the system Liouvillian time independent. These gadgets open up novel perspectives for thinking of timed dissipative quantum information processing. As an example, we sketch how measurement-based computation can be simulated in the dissipative setting.
Theory of harmonic dissipation in disordered solids
NASA Astrophysics Data System (ADS)
Damart, T.; Tanguy, A.; Rodney, D.
2017-02-01
Mechanical spectroscopy, i.e., cyclic deformations at varying frequencies, is used theoretically and numerically to compute dissipation in model glasses. From a normal mode analysis, we show that in the high-frequency terahertz regime where dissipation is harmonic, the quality factor (or loss angle) can be expressed analytically. This expression is validated through nonequilibrium molecular dynamics simulations applied to a model of amorphous silica (SiO2). Dissipation is shown to arise from nonaffine relaxations triggered by the applied strain through the excitation of vibrational eigenmodes that act as damped harmonic oscillators. We discuss an asymmetry vector field, which encodes the information about the structural origin of dissipation computed by mechanical spectroscopy. In the particular case of silica, we find that the motion of oxygen atoms, which induce a deformation of the Si-O-Si bonds, is the main contributor to harmonic energy dissipation.
Abnormal single or composite dissipative solitons generation
NASA Astrophysics Data System (ADS)
Zhong, Xianqiong; Liu, Dingyao; Cheng, Ke; Sheng, Jianan
2016-12-01
The evolution dynamics of the initial finite energy Airy pulses and Airy pulse pairs are numerically investigated in the cubic-quintic complex Ginzberg-Laudau equation governed dissipative system. Depending on different initial excitations and system parameters, abnormal double, triple, and quadruple composite dissipative solitons as well as single dissipative solitons can be observed. The composite dissipative solitons may consist of identical or different types of pulsating solitons. Moreover, the creeping solitons and the single ordinary pulsating solitons can even appear in the parameter regions where originally the other types of pulsating solitons exist. Besides, before evolving into each abnormal dissipative soliton, the initial finite energy Airy pulse or pulse pairs generally exhibit very interesting and unique early evolution behavior.
Exploring quantum phases by driven dissipation
NASA Astrophysics Data System (ADS)
Lang, Nicolai; Büchler, Hans Peter
2015-07-01
Dephasing and decay are the intrinsic dissipative processes prevalent in any open quantum system and the dominant mechanisms for the loss of coherence and entanglement. This inadvertent effect not only can be overcome but can even be capitalized on in a dissipative quantum simulation by means of tailored couplings between the quantum system and the environment. In this context it has been demonstrated that universal quantum computation can be performed using purely dissipative elements, and furthermore, the efficient preparation of highly entangled states is possible. In this article, we are interested in nonequilibrium phase transitions appearing in purely dissipative systems and the exploration of quantum phases in terms of a dissipative quantum simulation. To elucidate these concepts, we scrutinize exemplarily two paradigmatic models: the transverse-field Ising model and the considerably more complex Z2 lattice gauge theory. We show that the nonequilibrium phase diagrams parallel the quantum phase diagrams of the Hamiltonian "blueprint" theories.
Dissipative-particle-dynamics model of biofilm growth
Xu, Zhijie; Meakin, Paul; Tartakovsky, Alexandre M.; Scheibe, Timothy D.
2011-06-13
A dissipative particle dynamics (DPD) model for the quantitative simulation of biofilm growth controlled by substrate (nutrient) consumption, advective and diffusive substrate transport, and hydrodynamic interactions with fluid flow (including fragmentation and reattachment) is described. The model was used to simulate biomass growth, decay, and spreading. It predicts how the biofilm morphology depends on flow conditions, biofilm growth kinetics, the rheomechanical properties of the biofilm and adhesion to solid surfaces. The morphology of the model biofilm depends strongly on its rigidity and the magnitude of the body force that drives the fluid over the biofilm.
A Variational Approach to the Analysis of Dissipative Electromechanical Systems
Allison, Andrew; Pearce, Charles E. M.; Abbott, Derek
2014-01-01
We develop a method for systematically constructing Lagrangian functions for dissipative mechanical, electrical, and electromechanical systems. We derive the equations of motion for some typical electromechanical systems using deterministic principles that are strictly variational. We do not use any ad hoc features that are added on after the analysis has been completed, such as the Rayleigh dissipation function. We generalise the concept of potential, and define generalised potentials for dissipative lumped system elements. Our innovation offers a unified approach to the analysis of electromechanical systems where there are energy and power terms in both the mechanical and electrical parts of the system. Using our novel technique, we can take advantage of the analytic approach from mechanics, and we can apply these powerful analytical methods to electrical and to electromechanical systems. We can analyse systems that include non-conservative forces. Our methodology is deterministic, and does does require any special intuition, and is thus suitable for automation via a computer-based algebra package. PMID:24586221
A variational approach to the analysis of dissipative electromechanical systems.
Allison, Andrew; Pearce, Charles E M; Abbott, Derek
2014-01-01
We develop a method for systematically constructing Lagrangian functions for dissipative mechanical, electrical, and electromechanical systems. We derive the equations of motion for some typical electromechanical systems using deterministic principles that are strictly variational. We do not use any ad hoc features that are added on after the analysis has been completed, such as the Rayleigh dissipation function. We generalise the concept of potential, and define generalised potentials for dissipative lumped system elements. Our innovation offers a unified approach to the analysis of electromechanical systems where there are energy and power terms in both the mechanical and electrical parts of the system. Using our novel technique, we can take advantage of the analytic approach from mechanics, and we can apply these powerful analytical methods to electrical and to electromechanical systems. We can analyse systems that include non-conservative forces. Our methodology is deterministic, and does does require any special intuition, and is thus suitable for automation via a computer-based algebra package.
Asymptotic properties of mathematical models of excitability.
Biktasheva, I V; Simitev, R D; Suckley, R; Biktashev, V N
2006-05-15
We analyse small parameters in selected models of biological excitability, including Hodgkin-Huxley (Hodgkin & Huxley 1952 J. Physiol.117, 500-544) model of nerve axon, Noble (Noble 1962 J. Physiol.160, 317-352) model of heart Purkinje fibres and Courtemanche et al. (Courtemanche et al. 1998 Am. J. Physiol.275, H301-H321) model of human atrial cells. Some of the small parameters are responsible for differences in the characteristic time-scales of dynamic variables, as in the traditional singular perturbation approaches. Others appear in a way which makes the standard approaches inapplicable. We apply this analysis to study the behaviour of fronts of excitation waves in spatially extended cardiac models. Suppressing the excitability of the tissue leads to a decrease in the propagation speed, but only to a certain limit; further suppression blocks active propagation and leads to a passive diffusive spread of voltage. Such a dissipation may happen if a front propagates into a tissue recovering after a previous wave, e.g. re-entry. A dissipated front does not recover even when the excitability restores. This has no analogy in FitzHugh-Nagumo model and its variants, where fronts can stop and then start again. In two spatial dimensions, dissipation accounts for breakups and self-termination of re-entrant waves in excitable media with Courtemanche et al. kinetics.
Pullback Asymptotic Behavior of Solutions for a 2D Non-autonomous Non-Newtonian Fluid
NASA Astrophysics Data System (ADS)
Liu, Guowei
2016-10-01
This paper studies the pullback asymptotic behavior of solutions for the non-autonomous incompressible non-Newtonian fluid in 2D bounded domains. Firstly, with a little high regularity of the force, the semigroup method and ɛ -regularity method are used to establish the existence of compact pullback absorbing sets. Then, with a minimal regularity of the force, by verifying the flattening property also known as the "Condition (C)", the author proves the existence of pullback attractors for the universe of fixed bounded sets and for the another universe given by a tempered condition. Furthermore, the regularity of pullback attractors is given.
Asymptotic modal analysis and statistical energy analysis
NASA Technical Reports Server (NTRS)
Dowell, Earl H.
1992-01-01
Asymptotic Modal Analysis (AMA) is a method which is used to model linear dynamical systems with many participating modes. The AMA method was originally developed to show the relationship between statistical energy analysis (SEA) and classical modal analysis (CMA). In the limit of a large number of modes of a vibrating system, the classical modal analysis result can be shown to be equivalent to the statistical energy analysis result. As the CMA result evolves into the SEA result, a number of systematic assumptions are made. Most of these assumptions are based upon the supposition that the number of modes approaches infinity. It is for this reason that the term 'asymptotic' is used. AMA is the asymptotic result of taking the limit of CMA as the number of modes approaches infinity. AMA refers to any of the intermediate results between CMA and SEA, as well as the SEA result which is derived from CMA. The main advantage of the AMA method is that individual modal characteristics are not required in the model or computations. By contrast, CMA requires that each modal parameter be evaluated at each frequency. In the latter, contributions from each mode are computed and the final answer is obtained by summing over all the modes in the particular band of interest. AMA evaluates modal parameters only at their center frequency and does not sum the individual contributions from each mode in order to obtain a final result. The method is similar to SEA in this respect. However, SEA is only capable of obtaining spatial averages or means, as it is a statistical method. Since AMA is systematically derived from CMA, it can obtain local spatial information as well.
Asymptotics of loop quantum gravity fusion coefficients
NASA Astrophysics Data System (ADS)
Alesci, Emanuele; Bianchi, Eugenio; Magliaro, Elena; Perini, Claudio
2010-05-01
The fusion coefficients from SO(3) to SO(4) play a key role in the definition of spin foam models for the dynamics in loop quantum gravity. In this paper we give a simple analytic formula of the Engle-Pereira-Rovelli-Livine fusion coefficients. We study the large spin asymptotics and show that they map SO(3) semiclassical intertwiners into SU(2)L × SU(2)R semiclassical intertwiners. This non-trivial property opens the possibility for an analysis of the semiclassical behavior of the model.
Vacuum Potential and its Asymptotic Variation
NASA Astrophysics Data System (ADS)
Dahal, Pravin
2016-09-01
The possible form of existence of dark energy is explained and the relation for its asymptotic variation is given. This has two huge implications in the understanding of the Universe. The first is that the theory predicts that the Universe should be in negative pressure state in the very early period as required for inflation and spontaneous symmetry breaking. The second is that the theory gives the reasonable answer to the astrophysical evidence of dark energy dominating the Universe. The author is presenting his research in the nature of dark energy. Some of the work is submitted for publication in the journal and is currently under review.
The Two Isotropic Asymptotes of Fiber Composites,
1988-03-01
Voigt and Reuss models of summed stiffness and compliance. The compliance quasi-isotropic asymptote, which >’-:’ has evidently not been discussed in the...i,j,e)de o0 The resulting pseudo -isotropic compliance (series-model) Hooke’s law matrix is similar but not identical to Eq. (3): W(1) W(4) 0 a aIE...given by 1 W( ) 14) E : - Vc Wc 4W(5) 2[W(1) - W()] (8) c W() W(14 12 Direct formulas for the pseudo -isctrcpic moduli, in terms of the ply 1s natural
Asymptotic Theory for Nonparametric Confidence Intervals.
1982-07-01
distributions. Ann. Math Statist. 14, 56-62. 24. ROY, S.N. and POTTHOFF, R.F. (1958). Confidence bounds on vector analogues of the "ratio of the mean" and...fl c,~_________ 14L TITLE feed &MV) S. TYPE or REPORT a PeftOo COVx:REC Asympeocic Theory for Nonaparuetric Technical Report Confidence Intevals 6...S..C-0S78 UNCLASSIFIED TŗU *uuuuumuuumhhhhmhhhm_4 ASYMPTOTIC THEORY FOR NONPARAMETRIC CONFIDENCE INTERVALS by Peter W. Glynn TECHNICAL REPORT NO. 63
The aging of a surface and the evolution of conservative and dissipative nanoscale interactions.
Amadei, Carlo A; Tang, Tzu Chieh; Chiesa, Matteo; Santos, Sergio
2013-08-28
A method to monitor variations in the conservative and dissipative forces in dynamic atomic force microscopy is proposed in order to investigate the effects of exposing a surface to different sets of environmental conditions for prolonged periods of time. The variations are quantified by proposing and defining two metrics, one for conservative and another for dissipative interactions. Mica and graphite are chosen as model samples because they are atomically flat and easy to cleave. It is found that long term exposure to high relative humidity (RH), i.e., 90% > RH > 70%, affects the magnitude and distance dependencies of the forces, as quantified by the respective metrics, more drastically than the actual environmental conditions at which the samples are probed. Attenuated total reflectance infrared spectroscopy experiments further indicate that accumulation of water and carbonates on the surfaces with time is responsible for the variations in force measurements. This study has implications in surface functionality, reactivity, and longevity.
Particle Acceleration in Dissipative Pulsar Magnetospheres
NASA Technical Reports Server (NTRS)
Kazanas, Z.; Kalapotharakos, C.; Harding, A.; Contopoulos, I.
2012-01-01
Pulsar magnetospheres represent unipolar inductor-type electrical circuits at which an EM potential across the polar cap (due to the rotation of their magnetic field) drives currents that run in and out of the polar cap and close at infinity. An estimate ofthe magnitude of this current can be obtained by dividing the potential induced across the polar cap V approx = B(sub O) R(sub O)(Omega R(sub O)/c)(exp 2) by the impedance of free space Z approx eq 4 pi/c; the resulting polar cap current density is close to $n {GJ} c$ where $n_{GJ}$ is the Goldreich-Julian (GJ) charge density. This argument suggests that even at current densities close to the GJ one, pulsar magnetospheres have a significant component of electric field $E_{parallel}$, parallel to the magnetic field, a condition necessary for particle acceleration and the production of radiation. We present the magnetic and electric field structures as well as the currents, charge densities, spin down rates and potential drops along the magnetic field lines of pulsar magnetospheres which do not obey the ideal MHD condition $E cdot B = 0$. By relating the current density along the poloidal field lines to the parallel electric field via a kind of Ohm's law $J = sigma E_{parallel}$ we study the structure of these magnetospheres as a function of the conductivity $sigma$. We find that for $sigma gg OmegaS the solution tends to the (ideal) Force-Free one and to the Vacuum one for $sigma 11 OmegaS. Finally, we present dissipative magnetospheric solutions with spatially variable $sigma$ that supports various microphysical properties and are compatible with the observations.
Scattering of traveling spots in dissipative systems.
Nishiura, Yasumasa; Teramoto, Takashi; Ueda, Kei-Ichi
2005-12-01
One of the fundamental questions for self-organization in pattern formation is how spatial periodic structure is spontaneously formed starting from a localized fluctuation. It is known in dissipative systems that splitting dynamics is one of the driving forces to create many particle-like patterns from a single seed. On the way to final state there occur many collisions among them and its scattering manner is crucial to predict whether periodic structure is realized or not. We focus on the colliding dynamics of traveling spots arising in a three-component system and study how the transition of scattering dynamics is brought about. It has been clarified that hidden unstable patterns called "scattors" and their stable and unstable manifolds direct the traffic flow of orbits before and after collisions. The collision process in general can be decomposed into several steps and each step is controlled by such a scattor, in other words, a network among scattors forms the backbone for scattering dynamics. A variety of input-output relations comes from the complexity of the network as well as high Morse indices of the scattor. The change of transition manners is caused by the switching of the network from one structure to another, and such a change is caused by the singularities of scattors. We illustrate a typical example of the change of transition caused by the destabilization of the scattor. A new instability of the scattor brings a new destination for the orbit resulting in a new input-output relation, for instance, Hopf instability for the scattor of peanut type brings an annihilation.
In this article, we consider the least-squares approach for estimating parameters of a spatial variogram and establish consistency and asymptotic normality of these estimators under general conditions. Large-sample distributions are also established under a sp...
Asymptotic behavior of a flat plate wake
NASA Technical Reports Server (NTRS)
Weygandt, James H.; Mehta, Rabindra D.
1989-01-01
An experimental study has been conducted to investigate the far-field, self-similar properties of a flat plate wake. A plane turbulent wake was generated at the trailing edge of a smooth splitter plate separating two legs of a Mixing Layer Wind Tunnel, with both initial boundary layers tripped. For the present study, both legs were operated at a free-steam velocity in the test section of 15 m/s, giving a Reynolds number based on wake momentum thickness of about 1750. Single profile measurements were obtained at five streamwise locations using a Pitot probe for the mean velocity measurements and a single cross-wire probe for the turbulence data, which included statistics up to third order. The mean flow data indicated a self-similar behavior beyond a streamwise distance equivalent to about 350 wake momentum thicknesses. However, the turbulence data show better collapse beyond a distance equivalent to about 500 momentum thicknesses, with all the measured peak Reynolds stresses achieving constant, asymptotic levels. The asymptotic mean flow behavior and peak primary stress levels agree well with theoretical predictions based on a constant eddy viscosity model. The present data also agree reasonably well with previous measurements, of which only one set extends into the self-similar region. Detailed comparisons with previous data are presented and discussed in this report.
Relaxing the parity conditions of asymptotically flat gravity
NASA Astrophysics Data System (ADS)
Compère, Geoffrey; Dehouck, François
2011-12-01
Four-dimensional asymptotically flat spacetimes at spatial infinity are defined from first principles without imposing parity conditions or restrictions on the Weyl tensor. The Einstein-Hilbert action is shown to be a correct variational principle when it is supplemented by an anomalous counterterm which breaks asymptotic translation, supertranslation and logarithmic translation invariance. Poincaré transformations as well as supertranslations and logarithmic translations are associated with finite and conserved charges which represent the asymptotic symmetry group. Lorentz charges as well as logarithmic translations transform anomalously under a change of regulator. Lorentz charges are generally nonlinear functionals of the asymptotic fields but reduce to well-known linear expressions when parity conditions hold. We also define a covariant phase space of asymptotically flat spacetimes with parity conditions but without restrictions on the Weyl tensor. In this phase space, the anomaly plays classically no dynamical role. Supertranslations are pure gauge and the asymptotic symmetry group is the expected Poincaré group.
Turbulence at high resolution: intense events in dissipation, enstrophy and acceleration
NASA Astrophysics Data System (ADS)
Yeung, P. K.; Zhai, X. M.; Sreenivasan, K. R.
2014-11-01
Access to the Blue Waters supercomputer under the NSF Track 1 Petascale Resource Allocations program has allowed us to conduct an 81923 simulation of forced isotropic turbulence, with Taylor-scale Reynolds number close to 1300, and grid spacing at about 1.5 Kolmogorov scales. Extreme fluctuations in dissipation and enstrophy (over 10,000 times the mean) are observed, and found to scale similarly and occur together. Conditional sampling based on both dissipation and enstrophy shows that such extreme events in these variables are directly associated with strong intermittency in the fluid particle acceleration, which reaches values well beyond 100 standard deviations. An attempt is made to characterize in detail the formation of events of intense dissipation and enstrophy, including the transport, production and dissipation terms in the dissipation and enstrophy transport equations, as well as the nature of local flow conditions in principal strain-rate axes. Statistics of dissipation and enstrophy averaged over 3D sub-domains of linear size in the inertial range are also available. Both high Reynolds number and good small-scale resolution are important factors in these results. Supported by NSF Grant ACI-1036170.
Dissipative dark matter and the Andromeda plane of satellites
Randall, Lisa; Scholtz, Jakub E-mail: jscholtz@physics.harvard.edu
2015-09-01
We show that dissipative dark matter can potentially explain the large observed mass to light ratio of the dwarf satellite galaxies that have been observed in the recently identified planar structure around Andromeda, which are thought to result from tidal forces during a galaxy merger. Whereas dwarf galaxies created from ordinary disks would be dark matter poor, dark matter inside the galactic plane not only provides a source of dark matter, but one that is more readily bound due to the dark matter's lower velocity. This initial N-body study shows that with a thin disk of dark matter inside the baryonic disk, mass-to-light ratios as high as O(90) can be generated when tidal forces pull out patches of sizes similar to the scales of Toomre instabilities of the dark disk. A full simulation will be needed to confirm this result.
Asymptotic behaviour of solutions of semilinear parabolic equations
Egorov, Yu V; Kondratiev, V A
2008-04-30
The asymptotic behaviour of solutions of a second-order semilinear parabolic equation is analyzed in a cylindrical domain that is bounded in the space variables. The dominant term of the asymptotic expansion of the solution as t{yields}+{infinity} is found. It is shown that the solution of this problem is asymptotically equivalent to the solution of a certain non-linear ordinary differential equation. Bibliography: 8 titles.
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.
The Asymptotic Distribution of Mortality Rates in Competing Risks Analyses,
1979-12-01
For a sample of individuals from an animal or human population under observation in a clinical trial or life test, mortality rates are defined for...model, these mortality rates are shown to have an asymptotic normal distribution. An expression for the asymptotic correlation between a pair of... mortality rates is thus obtained and a necessary and sufficient condition for their asymptotic independence is investigated in some general situations with
Strongly nonlinear stress waves in dissipative metamaterials
NASA Astrophysics Data System (ADS)
Xu, Yichao; Nesterenko, Vitali F.
2017-01-01
We present the results of measurements and numerical simulations of stress wave propagation in a one-dimensional strongly nonlinear dissipative metamaterial composed of steel disks and Nitrile O-rings. The incoming bell shape stress wave is generated by the strikers with different masses. Numerical modeling including a viscous dissipative term to describe dynamic behavior of O-rings is developed to predict the wave amplitude, shape and propagation speed of stress waves. The viscous dissipation prevented the incoming pulse from splitting into trains of solitary waves typical for non-dissipative strongly nonlinear discrete systems. The linear momentum and energy from the striker were completely transferred into this strongly nonlinear "soft" metamaterial.
Dissipative quantum computing with open quantum walks
Sinayskiy, Ilya; Petruccione, Francesco
2014-12-04
An open quantum walk approach to the implementation of a dissipative quantum computing scheme is presented. The formalism is demonstrated for the example of an open quantum walk implementation of a 3 qubit quantum circuit consisting of 10 gates.
Open Boundary Conditions for Dissipative MHD
Meier, E T
2011-11-10
In modeling magnetic confinement, astrophysics, and plasma propulsion, representing the entire physical domain is often difficult or impossible, and artificial, or 'open' boundaries are appropriate. A novel open boundary condition (BC) for dissipative MHD, called Lacuna-based open BC (LOBC), is presented. LOBC, based on the idea of lacuna-based truncation originally presented by V.S. Ryaben'kii and S.V. Tsynkov, provide truncation with low numerical noise and minimal reflections. For hyperbolic systems, characteristic-based BC (CBC) exist for separating the solution into outgoing and incoming parts. In the hyperbolic-parabolic dissipative MHD system, such separation is not possible, and CBC are numerically unstable. LOBC are applied in dissipative MHD test problems including a translating FRC, and coaxial-electrode plasma acceleration. Solution quality is compared to solutions using CBC and zero-normal derivative BC. LOBC are a promising new open BC option for dissipative MHD.
Dissipation and θ 13 in neutrino oscillations
NASA Astrophysics Data System (ADS)
Oliveira, R. L. N.; Guzzo, M. M.
2013-05-01
We obtain a complete survival and transition probability involving three neutrino flavors when dissipation effects in vacuum are taken into consideration. In an approach that presents decoherence and relaxation effects, we study the behavior of the probabilities obtained from complete positivity constraints. Making the von Neumann entropy increase in time, many cases can be obtained and studied with the Lindblad master equation with addition of only one or two parameters related to dissipation. New possibilities are obtained when we take into account two decoherence parameters with different magnitudes which are given by reactor and accelerator neutrino oscillation experiments. We also present a model with only one parameter that has an important symmetry property, which can be used when the effective matter potential is important. Furthermore, the dissipation effects can contribute to the appearance of neutrinos that can hide or imitate the θ 13 effects and we study these possibilities showing that dissipative effects have an important role in three-neutrino oscillations.
The additive effect of harmonics on conservative and dissipative interactions
NASA Astrophysics Data System (ADS)
Santos, Sergio; Gadelrab, Karim R.; Barcons, Victor; Font, Josep; Stefancich, Marco; Chiesa, Matteo
2012-12-01
Multifrequency atomic force microscopy holds promise as a tool for chemical and topological imaging with nanoscale resolution. Here, we solve the equation of motion exactly for the fundamental mode in terms of the cantilever mean deflection, the fundamental frequency of oscillation, and the higher harmonic amplitudes and phases. The fundamental frequency provides information about the mean force, dissipation, and variations in the magnitude of the attractive and the repulsive force components during an oscillation cycle. The contributions of the higher harmonics to the position, velocity, and acceleration can be added gradually where the details of the true instantaneous force are recovered only when tens of harmonics are included. A formalism is developed here to decouple and quantify the viscous term of the force in the short and long range. It is also shown that the viscosity independent paths on tip approach and tip retraction can also be decoupled by simply acquiring a FFT at two different cantilever separations. The two paths correspond to tip distances at which metastability is present as, for example, in the presence of capillary interactions and where there is surface energy hysteresis.
Asymptotic geometric phase and purity for phase qubit dispersively coupled to lossy LC circuit
Mohamed, A.-B.A.; Obada, A.-S.F.
2011-09-15
Analytical descriptions of the geometric phases (GPs) for the total system and subsystems are studied for a current biased Josephson phase qubit strongly coupled to a lossy LC circuit in the dispersive limit. It is found that, the GP and purity depend on the damping parameter which leads to the phenomenon of GP death. Coherence parameter delays the phenomenon of a regular sequence of deaths and births of the GP. The asymptotic behavior of the GP and the purity for the qubit-LC resonator state closely follow that for the qubit state, but however, for the LC circuit these asymptotic values are equal to zero. - Highlights: > The model of a current biased Josephson phase qubit, strongly coupled to loss LC circuit, is considered. > Analytical descriptions of the geometric phase (GP) of this model, in the dispersive limit, are studied. > The GP and purity depend on the dissipation which leads to the GP death phenomenon. > Coherence parameter delays the phenomenon of a regular sequence of deaths and births of the GP.
Fundamental molecules of life are pigments which arose and evolved to dissipate the solar spectrum
NASA Astrophysics Data System (ADS)
Michaelian, K.; Simeonov, A.
2015-02-01
The driving force behind the origin and evolution of life has been the thermodynamic imperative of increasing the entropy production of the biosphere through increasing the global solar photon dissipation rate. In the upper atmosphere of today, oxygen and ozone derived from life processes are performing the short wavelength UVC and UVB dissipation. On Earth's surface, water and organic pigments in water facilitate the near UV and visible photon dissipation. The first organic pigments probably formed, absorbed, and dissipated at those photochemically active wavelengths in the UVC that could have reached Earth's surface during the Archean. Proliferation of these pigments can be understood as an autocatalytic photochemical process obeying non-equilibrium thermodynamic directives related to increasing solar photon dissipation rate. Under these directives, organic pigments would have evolved over time to increase the global photon dissipation rate by; (1) increasing the ratio of their effective photon cross sections to their physical size, (2) decreasing their electronic excited state life times, (3) quenching radiative de-excitation channels (e.g. fluorescence), (4) covering ever more completely the prevailing solar spectrum, and (5) proliferating and dispersing to cover an ever greater surface area of Earth. From knowledge of the evolution of the spectrum of G-type stars, and considering the most probable history of the transparency of Earth's atmosphere, we construct the most probable Earth surface solar spectrum as a function of time and compare this with the history of molecular absorption maxima obtained from the available data in the literature. This comparison supports the conjecture that many fundamental molecules of life are pigments which arose and evolved to dissipate the solar spectrum, supports the thermodynamic dissipation theory for the origin of life, constrains models for Earth's early atmosphere, and sheds some new light on the origin of
Asymptotic method for analysis of a conical shell under local loading
NASA Astrophysics Data System (ADS)
Nerubailo, B. V.; Ol'shanskii, V. P.
2007-06-01
Differential equations of the general theory describing the stress-strain state of conical shells are very complicated, and when computing the exact solution of the problem by analytic methods one encounters severe or even so far insurmountable difficulties. Therefore, in the present paper we develop an approach based on the method of asymptotic synthesis of the stressed state, which has already proved efficient when solving similar problems for cylindrical shells [1, 2]. We essentially use the fourth-order differential equations obtained by Kan [3], which describe the ground state and the boundary effect. Earlier, such equations have already been used to solve problems concerning force and thermal actions on weakly conical shells [4-6]. By applying the asymptotic synthesis method to these equations, we manage to obtain sufficiently accurate closed-form solutions.
Green's function asymptotics and sharp interpolation inequalities
NASA Astrophysics Data System (ADS)
Zelik, S. V.; Ilyin, A. A.
2014-04-01
A general method is proposed for finding sharp constants for the embeddings of the Sobolev spaces H^m(\\mathscr{M}) on an n-dimensional Riemannian manifold \\mathscr{M} into the space of bounded continuous functions, where m\\gt n/2. The method is based on an analysis of the asymptotics with respect to the spectral parameter of the Green's function of an elliptic operator of order 2m whose square root has domain determining the norm of the corresponding Sobolev space. The cases of the n-dimensional torus {T}^n and the n-dimensional sphere {S}^n are treated in detail, as well as certain manifolds with boundary. In certain cases when \\mathscr{M} is compact, multiplicative inequalities with remainder terms of various types are obtained. Inequalities with correction terms for periodic functions imply an improvement for the well-known Carlson inequalities. Bibliography: 28 titles.
Loop Quantum Gravity and Asymptotically Flat Spaces
NASA Astrophysics Data System (ADS)
Arnsdorf, Matthias
2002-12-01
Remarkable progress has been made in the field of non-perturbative (loop) quantum gravity in the last decade or so and it is now a rigorously defined kinematical theory (c.f. [5] for a review and references). We are now at the stage where physical applications of loop quantum gravity can be studied and used to provide checks for the consistency of the quantisation programme. Equally, old fundamental problems of canonical quantum gravity such as the problem of time or the interpretation of quantum cosmology need to be reevaluated seriously. These issues can be addressed most profitably in the asymptotically flat sector of quantum gravity. Indeed, it is likely that we should obtain a quantum theory for this special case even if it is not possible to quantise full general relativity. The purpose of this summary is to advertise the extension of loop quantum gravity to this sector that was developed in [1]...
Nucleosynthesis in asymptotic giant branch stars
El Eid, Mounib F.
2014-05-09
The nucleosynthesis in asymptotic giant branch stars (briefly: AGB)is a challenging and fascinating subject in the theory of stellar evolution and important for observations as well. This is because about of half the heavy elements beyond iron are synthesized during thermal pulsation phases of these stars. Furthermore, the understanding of the production of the heavy elements and some light elements like carbon and fluorine represent a powerful tool to get more insight into the internal structure of these stars. The diversity of nuclear processing during the AGB phases may also motivate experimental activities in measuring important nuclear reactions. In this contribution, we emphasize several interesting feature of the nucleosynthesis in AGB stars which still needs further elaboration especially from theoretical point of view.
Universality and asymptotic scaling in drilling percolation
NASA Astrophysics Data System (ADS)
Grassberger, Peter
2017-01-01
We present simulations of a three-dimensional percolation model studied recently by K. J. Schrenk et al. [Phys. Rev. Lett. 116, 055701 (2016), 10.1103/PhysRevLett.116.055701], obtained with a new and more efficient algorithm. They confirm most of their results in spite of larger systems and higher statistics used in the present Rapid Communication, but we also find indications that the results do not yet represent the true asymptotic behavior. The model is obtained by replacing the isotropic holes in ordinary Bernoulli percolation by randomly placed and oriented cylinders, with the constraint that the cylinders are parallel to one of the three coordinate axes. We also speculate on possible generalizations.
Asymptotic Linear Stability of Solitary Water Waves
NASA Astrophysics Data System (ADS)
Pego, Robert L.; Sun, Shu-Ming
2016-12-01
We prove an asymptotic stability result for the water wave equations linearized around small solitary waves. The equations we consider govern irrotational flow of a fluid with constant density bounded below by a rigid horizontal bottom and above by a free surface under the influence of gravity neglecting surface tension. For sufficiently small amplitude waves, with waveform well-approximated by the well-known sech-squared shape of the KdV soliton, solutions of the linearized equations decay at an exponential rate in an energy norm with exponential weight translated with the wave profile. This holds for all solutions with no component in (that is, symplectically orthogonal to) the two-dimensional neutral-mode space arising from infinitesimal translational and wave-speed variation of solitary waves. We also obtain spectral stability in an unweighted energy norm.
The asymptotics of large constrained graphs
NASA Astrophysics Data System (ADS)
Radin, Charles; Ren, Kui; Sadun, Lorenzo
2014-05-01
We show, through local estimates and simulation, that if one constrains simple graphs by their densities ɛ of edges and τ of triangles, then asymptotically (in the number of vertices) for over 95% of the possible range of those densities there is a well-defined typical graph, and it has a very simple structure: the vertices are decomposed into two subsets V1 and V2 of fixed relative size c and 1 - c, and there are well-defined probabilities of edges, gjk, between vj ∈ Vj, and vk ∈ Vk. Furthermore the four parameters c, g11, g22 and g12 are smooth functions of (ɛ, τ) except at two smooth ‘phase transition’ curves.
Chiral fermions in asymptotically safe quantum gravity.
Meibohm, J; Pawlowski, J M
2016-01-01
We study the consistency of dynamical fermionic matter with the asymptotic safety scenario of quantum gravity using the functional renormalisation group. Since this scenario suggests strongly coupled quantum gravity in the UV, one expects gravity-induced fermion self-interactions at energies of the Planck scale. These could lead to chiral symmetry breaking at very high energies and thus to large fermion masses in the IR. The present analysis which is based on the previous works (Christiansen et al., Phys Rev D 92:121501, 2015; Meibohm et al., Phys Rev D 93:084035, 2016), concludes that gravity-induced chiral symmetry breaking at the Planck scale is avoided for a general class of NJL-type models. We find strong evidence that this feature is independent of the number of fermion fields. This finding suggests that the phase diagram for these models is topologically stable under the influence of gravitational interactions.
Rubidium-rich asymptotic giant branch stars.
García-Hernández, D A; García-Lario, P; Plez, B; D'Antona, F; Manchado, A; Trigo-Rodríguez, J M
2006-12-15
A long-debated issue concerning the nucleosynthesis of neutron-rich elements in asymptotic giant branch (AGB) stars is the identification of the neutron source. We report intermediate-mass (4 to 8 solar masses) AGB stars in our Galaxy that are rubidium-rich as a result of overproduction of the long-lived radioactive isotope (87)Rb, as predicted theoretically 40 years ago. This finding represents direct observational evidence that the (22)Ne(alpha,n)(25)Mg reaction must be the dominant neutron source in these stars. These stars challenge our understanding of the late stages of the evolution of intermediate-mass stars and would have promoted a highly variable Rb/Sr environment in the early solar nebula.
Nucleosynthesis in asymptotic giant branch stars
NASA Astrophysics Data System (ADS)
El Eid, Mounib F.
2014-05-01
The nucleosynthesis in asymptotic giant branch stars (briefly: AGB)is a challenging and fascinating subject in the theory of stellar evolution and important for observations as well. This is because about of half the heavy elements beyond iron are synthesized during thermal pulsation phases of these stars. Furthermore, the understanding of the production of the heavy elements and some light elements like carbon and fluorine represent a powerful tool to get more insight into the internal structure of these stars. The diversity of nuclear processing during the AGB phases may also motivate experimental activities in measuring important nuclear reactions. In this contribution, we emphasize several interesting feature of the nucleosynthesis in AGB stars which still needs further elaboration especially from theoretical point of view.
Reliable dissipative control of high-speed train with probabilistic time-varying delays
NASA Astrophysics Data System (ADS)
Kaviarasan, B.; Sakthivel, R.; Shi, Y.
2016-12-01
This paper investigates the reliable dissipative control problem for high-speed trains (HSTs) under probabilistic time-varying sampling with a known upper bound on the sampling intervals. In particular, random variables obeying the Bernoulli distribution are considered to account for the probabilistic time-varying delays. Based on Lyapunov-Krasovskii functional approach which considers full use of the available information about actual sampling pattern, a new set of sufficient condition is established to guarantee that the HST can well track the desired speed and the relative spring displacement between the two neighbouring carriages is asymptotically stable and the corresponding error system is strictly ?-dissipative. The existence condition of the dissipativity-based reliable sampled-data controller is obtained in terms of a set of linear matrix inequalities which are delay-distribution-dependent, i.e. the solvability of the condition depends on not only the variation range of the delay but also the probability distribution of it. Moreover, different control processes for the HST system can be obtained from the proposed design procedure and hence it can reduce the time and cost. Finally, the effectiveness and benefits of the proposed control law is demonstrated through a numerical example by taking the experimental values of Japan Shinkansen HST.
Vortex formation and dynamics in two-dimensional driven-dissipative condensates
NASA Astrophysics Data System (ADS)
Hebenstreit, F.
2016-12-01
We investigate the real-time evolution of lattice bosons in two spatial dimensions whose dynamics is governed by a Markovian quantum master equation. We employ the Wigner-Weyl phase space quantization and derive the functional integral for open quantum many-body systems that determines the time evolution of the Wigner function. Using the truncated Wigner approximation, in which quantum fluctuations are only taken into account in the initial state whereas the dynamics is governed by classical evolution equations, we study the buildup of long-range correlations due to the action of non-Hermitean quantum jump operators that constitute a mechanism for dissipative cooling. Starting from an initially disordered state corresponding to a vortex condensate, the dissipative process results in the annihilation of vortex-antivortex pairs and the establishment of quasi-long-range order at late times. We observe that a finite vortex density survives the cooling process, which disagrees with the analytically constructed vortex-free Bose-Einstein condensate at asymptotic times. This indicates that quantum fluctuations beyond the truncated Wigner approximation need to be included to fully capture the physics of dissipative Bose-Einstein condensation.
Global Asymptotic Behavior of Iterative Implicit Schemes
NASA Technical Reports Server (NTRS)
Yee, H. C.; Sweby, P. K.
1994-01-01
The global asymptotic nonlinear behavior of some standard iterative procedures in solving nonlinear systems of algebraic equations arising from four implicit linear multistep methods (LMMs) in discretizing three models of 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODEs) is analyzed using the theory of dynamical systems. The iterative procedures include simple iteration and full and modified Newton iterations. The results are compared with standard Runge-Kutta explicit methods, a noniterative implicit procedure, and the Newton method of solving the steady part of the ODEs. Studies showed that aside from exhibiting spurious asymptotes, all of the four implicit LMMs can change the type and stability of the steady states of the differential equations (DEs). They also exhibit a drastic distortion but less shrinkage of the basin of attraction of the true solution than standard nonLMM explicit methods. The simple iteration procedure exhibits behavior which is similar to standard nonLMM explicit methods except that spurious steady-state numerical solutions cannot occur. The numerical basins of attraction of the noniterative implicit procedure mimic more closely the basins of attraction of the DEs and are more efficient than the three iterative implicit procedures for the four implicit LMMs. Contrary to popular belief, the initial data using the Newton method of solving the steady part of the DEs may not have to be close to the exact steady state for convergence. These results can be used as an explanation for possible causes and cures of slow convergence and nonconvergence of steady-state numerical solutions when using an implicit LMM time-dependent approach in computational fluid dynamics.
NASA Astrophysics Data System (ADS)
Mai-Duy, N.; Phan-Thien, N.; Khoo, B. C.
2015-04-01
In the Dissipative Particle Dynamics (DPD) simulation of suspension, the fluid (solvent) and colloidal particles are replaced by a set of DPD particles and therefore their relative sizes (as measured by their exclusion zones) can affect the maximal packing fraction of the colloidal particles. In this study, we investigate roles of the conservative, dissipative and random forces in this relative size ratio (colloidal/solvent). We propose a mechanism of adjusting the DPD parameters to properly model the solvent phase (the solvent here is supposed to have the same isothermal compressibility to that of water).
Large Deviations and Gallavotti-Cohen Principle for Dissipative PDEs with Rough Noise
NASA Astrophysics Data System (ADS)
Jakšić, V.; Nersesyan, V.; Pillet, C.-A.; Shirikyan, A.
2015-05-01
We study a class of dissipative PDEs perturbed by an unbounded kick force. Under some natural assumptions, the restrictions of solutions to integer times form a homogeneous Markov process. Assuming that the noise is rough with respect to the space variables and has a non-degenerate law, we prove that the system in question satisfies a large deviation principle (LDP) in τ-topology. Under some additional hypotheses, we establish a Gallavotti-Cohen type symmetry for the rate function of an entropy production functional and the strict positivity and finiteness of the mean entropy production rate in the stationary regime. The latter result is applicable to PDEs with strong nonlinear dissipation.
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.
NASA Astrophysics Data System (ADS)
Jrad, Hanen; Dion, Jean Luc; Renaud, Franck; Tawfiq, Imad; Haddar, Mohamed
2016-10-01
This paper focuses on energy losses caused by inner damping and friction in an elastomeric rotational joint. A description of the design of a new experimental device intended to characterize dynamic stiffness in rotational elastomeric joint is presented. An original method based on Lagrange's equations, which allows accurately measuring forces and torques only with accelerometers, is proposed in order to identify dissipated energy in the rotational elastomeric joint. A rheological model developed taking into account dependence of the torque and the angular displacement (rotation). Experimental results and simulations used to quantify the dissipated energy in order to evaluate the damping ratio are presented and discussed.
Diffraction and Dissipation of Atmospheric Waves in the Vicinity of Caustics
NASA Astrophysics Data System (ADS)
Godin, O. A.
2015-12-01
A large and increasing number of ground-based and satellite-borne instruments has been demonstrated to reliably reveal ionospheric manifestations of natural hazards such as large earthquakes, strong tsunamis, and powerful tornadoes. To transition from detection of ionospheric manifestations of natural hazards to characterization of the hazards for the purposes of improving early warning systems and contributing to disaster recovery, it is necessary to relate quantitatively characteristics of the observed ionospheric disturbances and the underlying natural hazard and, in particular, accurately model propagation of atmospheric waves from the ground or ocean surface to the ionosphere. The ray theory has been used extensively to model propagation of atmospheric waves and proved to be very efficient in elucidating the effects of atmospheric variability on ionospheric signatures of natural hazards. However, the ray theory predicts unphysical, divergent values of the wave amplitude and needs to be modified in the vicinity of caustics. This paper presents an asymptotic theory that describes diffraction, focusing and increased dissipation of acoustic-gravity waves in the vicinity of caustics and turning points. Air temperature, viscosity, thermal conductivity, and wind velocity are assumed to vary gradually with height and horizontal coordinates, and slowness of these variations determines the large parameter of the problem. Uniform asymptotics of the wave field are expressed in terms of Airy functions and their derivatives. The geometrical, or Berry, phase, which arises in the consistent WKB approximation for acoustic-gravity waves, plays an important role in the caustic asymptotics. In addition to the wave field in the vicinity of the caustic, these asymptotics describe wave reflection from the caustic and the evanescent wave field beyond the caustic. The evanescent wave field is found to play an important role in ionospheric manifestations of tsunamis.
Gaussian and mean curvatures for discrete asymptotic nets
NASA Astrophysics Data System (ADS)
Schief, W. K.
2017-04-01
We propose discretisations of Gaussian and mean curvatures of surfaces parametrised in terms of asymptotic coordinates and examine their relevance in the context of integrable discretisations of classical classes of surfaces and their underlying integrable systems. We also record discrete analogues of the classical relation between the Gaussian curvature of hyperbolic surfaces and the torsion of their asymptotic lines.
Scattering in an external electric field asymptotically constant in time
Adachi, Tadayoshi; Ishida, Atsuhide
2011-06-15
We show the asymptotic completeness for two-body quantum systems in an external electric field asymptotically non-zero constant in time. One of the main ingredients of this paper is to give some propagation estimates for physical propagators generated by time-dependent Hamiltonians which govern the systems under consideration.
Asymptotic expansions for the reciprocal of the gamma function
NASA Astrophysics Data System (ADS)
Withers, Christopher S.; Nadarajah, Saralees
2014-05-01
Asymptotic expansions are derived for the reciprocal of the gamma function. We show that the coefficients of the expansion are the same, up to a sign change, as the asymptotic expansions for the gamma function obtained by exponentiating the expansions of its logarithm due to Stirling and de Moivre. Expressions for the coefficients are given in terms of Bell polynomials.
Jung, Gerhard; Schmid, Friederike
2016-05-28
Exact values for bulk and shear viscosity are important to characterize a fluid, and they are a necessary input for a continuum description. Here we present two novel methods to compute bulk viscosities by non-equilibrium molecular dynamics simulations of steady-state systems with periodic boundary conditions - one based on frequent particle displacements and one based on the application of external bulk forces with an inhomogeneous force profile. In equilibrium simulations, viscosities can be determined from the stress tensor fluctuations via Green-Kubo relations; however, the correct incorporation of random and dissipative forces is not obvious. We discuss different expressions proposed in the literature and test them at the example of a dissipative particle dynamics fluid.
Self-gravity and dissipation in polar rings
NASA Technical Reports Server (NTRS)
Dubinski, John; Christodoulou, Dimitris M.
1994-01-01
Studies of inclined rings inside galaxy potentials have mostly considered the influence of self-gravity and viscous dissipation separately. In this study, we construct models of highly inclined ('polar') rings in an external potential including both self-gravity and dissipation due to a drag force. We do not include pressure forces and thus ignore shock heating that dominates the evolution of gaseous rings inside strongly nonspherical potentials. We adopt an oblate spheroidal scale-free logarithmic potential with axis ratio q = 0.85 and an initial inclination of 80 deg for the self-gravitating rings. We find that stellar (dissipationless) rings suffer from mass loss during their evolution. Mass loss also drives a secular change of the mean inclination toward the poles of the potential. As much as half of the ring mass escapes in the process and forms an inner and an outer shell of precessing orbits. If the remaining mass is more than approximately 0.02 of the enclosed galaxy mass, rings remain bound and do not fall apart from differential precession. The rings precess at a constant rate for more than a precession period tau(sub p) finding the configuration predicted by Sparke in 1986 which warps at larger radii toward the poles of the potential. We model shear viscosity with a velocity-dependent drag force and find that nuclear inflow dominates over self-gravity if the characteristic viscous inflow time scale tau(sub vi) is shorter than approximately 25(tau(sub p)). Rings with (tau(sub vi))/(tau(sub p)) less than or approximately equal to 25 collapse toward the nucleus of the potential within one precession period independent of the amount of self-gravity. Our results imply that stars and gas in real polar rings exhibit markedly different dynamical evolutions.
Asymptotic approximations to posterior distributions via conditional moment equations
Yee, J.L.; Johnson, W.O.; Samaniego, F.J.
2002-01-01
We consider asymptotic approximations to joint posterior distributions in situations where the full conditional distributions referred to in Gibbs sampling are asymptotically normal. Our development focuses on problems where data augmentation facilitates simpler calculations, but results hold more generally. Asymptotic mean vectors are obtained as simultaneous solutions to fixed point equations that arise naturally in the development. Asymptotic covariance matrices flow naturally from the work of Arnold & Press (1989) and involve the conditional asymptotic covariance matrices and first derivative matrices for conditional mean functions. When the fixed point equations admit an analytical solution, explicit formulae are subsequently obtained for the covariance structure of the joint limiting distribution, which may shed light on the use of the given statistical model. Two illustrations are given. ?? 2002 Biometrika Trust.
On the asymptotics of the α-Farey transfer operator
NASA Astrophysics Data System (ADS)
Kautzsch, J.; Kesseböhmer, M.; Samuel, T.; Stratmann, B. O.
2015-01-01
We study the asymptotics of iterates of the transfer operator for non-uniformly hyperbolic α-Farey maps. We provide a family of observables which are Riemann integrable, locally constant and of bounded variation, and for which the iterates of the transfer operator, when applied to one of these observables, is not asymptotic to a constant times the wandering rate on the first element of the partition α. Subsequently, sufficient conditions on observables are given under which this expected asymptotic holds. In particular, we obtain an extension theorem which establishes that, if the asymptotic behaviour of iterates of the transfer operator is known on the first element of the partition α, then the same asymptotic holds on any compact set bounded away from the indifferent fixed point.
Eigenvalue spectrum of the spheroidal harmonics: A uniform asymptotic analysis
NASA Astrophysics Data System (ADS)
Hod, Shahar
2015-06-01
The spheroidal harmonics Slm (θ ; c) have attracted the attention of both physicists and mathematicians over the years. These special functions play a central role in the mathematical description of diverse physical phenomena, including black-hole perturbation theory and wave scattering by nonspherical objects. The asymptotic eigenvalues {Alm (c) } of these functions have been determined by many authors. However, it should be emphasized that all the previous asymptotic analyzes were restricted either to the regime m → ∞ with a fixed value of c, or to the complementary regime | c | → ∞ with a fixed value of m. A fuller understanding of the asymptotic behavior of the eigenvalue spectrum requires an analysis which is asymptotically uniform in both m and c. In this paper we analyze the asymptotic eigenvalue spectrum of these important functions in the double limit m → ∞ and | c | → ∞ with a fixed m / c ratio.
Asymptotic Properties of Some Classes of Generalized Functions
NASA Astrophysics Data System (ADS)
Drozhzhinov, Yu N.; Zav'yalov, B. I.
1986-02-01
This paper studies the connection between the asymptotic and quasi-asymptotic properties at infinity of slowly increasing generalized functions with supports on the half-line and the asymptotic and quasi-asymptotic properties of the real parts of their Laplace and Fourier transforms in a neighborhood of the origin. The study is caried out in the scale of regularly varying self-similar functions. The results are applied to the study of the asymptotic properties of solutions of linear passive systems, and also to the study of the connection between Abel and Cesàro convergence (with respect to a self-similar weight) of the Fourier-Stieltjes series of nonnegative measures. Bibliography: 13 titles.
Large gauge symmetries and asymptotic states in QED
NASA Astrophysics Data System (ADS)
Gabai, Barak; Sever, Amit
2016-12-01
Large Gauge Transformations (LGT) are gauge transformations that do not vanish at infinity. Instead, they asymptotically approach arbitrary functions on the conformal sphere at infinity. Recently, it was argued that the LGT should be treated as an infinite set of global symmetries which are spontaneously broken by the vacuum. It was established that in QED, the Ward identities of their induced symmetries are equivalent to the Soft Photon Theorem. In this paper we study the implications of LGT on the S-matrix between physical asymptotic states in massive QED. In appose to the naively free scattering states, physical asymptotic states incorporate the long range electric field between asymptotic charged particles and were already constructed in 1970 by Kulish and Faddeev. We find that the LGT charge is independent of the particles' momenta and may be associated to the vacuum. The soft theorem's manifestation as a Ward identity turns out to be an outcome of not working with the physical asymptotic states.
Energy dissipation in sheared granular flows
Karion, A.; Hunt, M.L.
1999-11-01
Granular material flows describe flows of solid particles in which the interstitial fluid plays a negligible role in the flow mechanics. Examples include the transport of coal, food products, detergents, pharmaceutical tablets, and toner particles in high-speed printers. Using a two-dimensional discrete element computer simulation of a bounded, gravity-free Couette flow of particles, the heat dissipation rate per unit area is calculated as a function of position in the flow as well as overall solid fraction. The computation results compare favorably with the kinetic theory analysis for rough disks. The heat dissipation rate is also measured for binary mixtures of particles for different small to large solid fraction ratios, and for diameter ratios of ten, five, and two. The dissipation rates increase significantly with overall solid fraction as well as local strain rates and granular temperatures. The thermal energy equation is solved for a Couette flow with one adiabatic wall and one at constant temperature. Solutions use the simulation measurements of the heat dissipation rate, solid fraction, and granular temperature to show that the thermodynamic temperature increases with solid fraction and decreases with particle conductivity. In mixtures, both the dissipation rate and the thermodynamic temperature increase with size ratio and with decreasing ratio of small to large particles.
Dissipative compensators for flexible spacecraft control
NASA Technical Reports Server (NTRS)
Joshi, S. M.; Maghami, P. G.
1990-01-01
The problem of controller design for flexible spacecraft is addressed. Model-based compensators, which rely on the knowledge of the system parameters to tune the state estimator, are considered. The instability mechanisms resulting from high sensitivity to parameter uncertainties are investigated. Dissipative controllers, which use collocated actuators and sensors, are also considered, and the robustness properties of constant-gain dissipative controllers in the presence of unmodeled elastic-mode dynamics, sensor/actuator nonlinearities, and actuator dynamics are summarized. In order to improve the performance without sacrificing robustness, a class of dissipative dynamic compensators is proposed and is shown to retain robust stability in the presence of second-order actuator dynamics if acceleration feedback is employed. A class of dissipative dynamic controllers is proposed which consists of a low-authority, constant-gain controller and a high-authority dynamic compensator. A procedure for designing an optimal dissipative dynamic compensator is given which minimizes a quadratic performance criterion. Such compensators offer the promise of better performance while still retaining robust stability.
Intermittent energy dissipation by turbulent reconnection
NASA Astrophysics Data System (ADS)
Fu, H. S.; Vaivads, A.; Khotyaintsev, Y. V.; André, M.; Cao, J. B.; Olshevsky, V.; Eastwood, J. P.; Retinò, A.
2017-01-01
Magnetic reconnection—the process responsible for many explosive phenomena in both nature and laboratory—is efficient at dissipating magnetic energy into particle energy. To date, exactly how this dissipation happens remains unclear, owing to the scarcity of multipoint measurements of the "diffusion region" at the sub-ion scale. Here we report such a measurement by Cluster—four spacecraft with separation of 1/5 ion scale. We discover numerous current filaments and magnetic nulls inside the diffusion region of magnetic reconnection, with the strongest currents appearing at spiral nulls (O-lines) and the separatrices. Inside each current filament, kinetic-scale turbulence is significantly increased and the energy dissipation, E' ṡ j, is 100 times larger than the typical value. At the jet reversal point, where radial nulls (X-lines) are detected, the current, turbulence, and energy dissipations are surprisingly small. All these features clearly demonstrate that energy dissipation in magnetic reconnection occurs at O-lines but not X-lines.
Dynamical properties of breaking waves: dissipation, air entrainment and spray generation
NASA Astrophysics Data System (ADS)
Deike, Luc; Melville, W. Kendall; Popinet, Stephane
2016-11-01
Wave breaking in the ocean is of fundamental importance in order to quantify wave dissipation and air-sea interaction, including gas and momentum exchange, and to improve parametrization for ocean-atmosphere exchange in weather and climate models. Here, we present 2D and 3D direct numerical simulations of breaking waves, compared with laboratory measurements. The dissipation due to breaking in the 2D and 3D simulations is found to be in good agreement with experimental observations and inertial-scaling arguments. We discuss the transition from a 2D to a 3D flow during breaking. We present a model for air entrainment and bubble statistics that describes well the experimental and numerical data, and is based on turbulent fragmentation of the bubbles and a balance between buoyancy forces and viscous dissipation. Finally we discuss the generation of large drops during the impact and splashing process.
Topological protection of multiparticle dissipative transport
NASA Astrophysics Data System (ADS)
Loehr, Johannes; Loenne, Michael; Ernst, Adrian; de Las Heras, Daniel; Fischer, Thomas M.
2016-06-01
Topological protection allows robust transport of localized phenomena such as quantum information, solitons and dislocations. The transport can be either dissipative or non-dissipative. Here, we experimentally demonstrate and theoretically explain the topologically protected dissipative motion of colloidal particles above a periodic hexagonal magnetic pattern. By driving the system with periodic modulation loops of an external and spatially homogeneous magnetic field, we achieve total control over the motion of diamagnetic and paramagnetic colloids. We can transport simultaneously and independently each type of colloid along any of the six crystallographic directions of the pattern via adiabatic or deterministic ratchet motion. Both types of motion are topologically protected. As an application, we implement an automatic topologically protected quality control of a chemical reaction between functionalized colloids. Our results are relevant to other systems with the same symmetry.
Novel dissipative properties of the master equation
NASA Astrophysics Data System (ADS)
Hong, Liu; Jia, Chen; Zhu, Yi; Yong, Wen-An
2016-10-01
Recent studies have shown that the entropy production rate for the master equation consists of two non-negative terms: the adiabatic and non-adiabatic parts, where the non-adiabatic part is also known as the free energy dissipation rate. In this paper, we present some nonzero lower bounds for the free energy, the entropy production rate, and its adiabatic and non-adiabatic parts. These nonzero lower bounds not only reveal some novel dissipative properties for nonequilibrium dynamics which are much stronger than the second law of thermodynamics, but also impose some new constraints on thermodynamic constitutive relations. Moreover, we also give a mathematical application of the nonzero lower bounds by studying the long-time behavior of the master equation. Extensions to the Tsallis statistics are also discussed, including the nonzero lower bounds for the Tsallis-type free energy and its dissipation rate.
Topological protection of multiparticle dissipative transport
Loehr, Johannes; Loenne, Michael; Ernst, Adrian; de las Heras, Daniel; Fischer, Thomas M.
2016-01-01
Topological protection allows robust transport of localized phenomena such as quantum information, solitons and dislocations. The transport can be either dissipative or non-dissipative. Here, we experimentally demonstrate and theoretically explain the topologically protected dissipative motion of colloidal particles above a periodic hexagonal magnetic pattern. By driving the system with periodic modulation loops of an external and spatially homogeneous magnetic field, we achieve total control over the motion of diamagnetic and paramagnetic colloids. We can transport simultaneously and independently each type of colloid along any of the six crystallographic directions of the pattern via adiabatic or deterministic ratchet motion. Both types of motion are topologically protected. As an application, we implement an automatic topologically protected quality control of a chemical reaction between functionalized colloids. Our results are relevant to other systems with the same symmetry. PMID:27249049
Observed eddy dissipation in the Agulhas Current
NASA Astrophysics Data System (ADS)
Braby, Laura; Backeberg, Björn C.; Ansorge, Isabelle; Roberts, Michael J.; Krug, Marjolaine; Reason, Chris J. C.
2016-08-01
Analyzing eddy characteristics from a global data set of automatically tracked eddies for the Agulhas Current in combination with surface drifters as well as geostrophic currents from satellite altimeters, it is shown that eddies from the Mozambique Channel and south of Madagascar dissipate as they approach the Agulhas Current. By tracking the offshore position of the current core and its velocity at 30°S in relation to eddies, it is demonstrated that eddy dissipation occurs through a transfer of momentum, where anticyclones consistently induce positive velocity anomalies, and cyclones reduce the velocities and cause offshore meanders. Composite analyses of the anticyclonic (cyclonic) eddy-current interaction events demonstrate that the positive (negative) velocity anomalies propagate downstream in the Agulhas Current at 44 km/d (23 km/d). Many models are unable to represent these eddy dissipation processes, affecting our understanding of the Agulhas Current.
Dissipation in non-equilibrium turbulence
NASA Astrophysics Data System (ADS)
Bos, Wouter; Rubinstein, Robert
2016-11-01
For about a decade, experimental and numerical studies have reported on the existence of an anomalous behaviour of the viscous dissipation rate in unsteady turbulence (see for instance Vassilicos, Annu. Rev. Fluid Mech. 2015). It appears that the short-time transient dynamics can be described by a universal power law, incompatible with Taylor's 1935 dissipation rate estimate. We show that these results can be explained using a non-equilibrium energy distribution, obtained from a low-frequency perturbative expansion of simple spectral closure. The resulting description is fairly simple. In particular, during the transient, according to the predictions, the normalized dissipation rate Cɛ evolves as a function of the Taylor-scale Reynolds number Rλ following the relation Cɛ Rλ- 15 / 14 , in close agreement with experimental and numerical observations.
Basin topology in dissipative chaotic scattering.
Seoane, Jesús M; Aguirre, Jacobo; Sanjuán, Miguel A F; Lai, Ying-Cheng
2006-06-01
Chaotic scattering in open Hamiltonian systems under weak dissipation is not only of fundamental interest but also important for problems of current concern such as the advection and transport of inertial particles in fluid flows. Previous work using discrete maps demonstrated that nonhyperbolic chaotic scattering is structurally unstable in the sense that the algebraic decay of scattering particles immediately becomes exponential in the presence of weak dissipation. Here we extend the result to continuous-time Hamiltonian systems by using the Henon-Heiles system as a prototype model. More importantly, we go beyond to investigate the basin structure of scattering dynamics. A surprising finding is that, in the common case where multiple destinations exist for scattering trajectories, Wada basin boundaries are common and they appear to be structurally stable under weak dissipation, even when other characteristics of the nonhyperbolic scattering dynamics are not. We provide numerical evidence and a geometric theory for the structural stability of the complex basin topology.
Open Quantum Walks and Dissipative Quantum Computing
NASA Astrophysics Data System (ADS)
Petruccione, Francesco
2012-02-01
Open Quantum Walks (OQWs) have been recently introduced as quantum Markov chains on graphs [S. Attal, F. Petruccione, C. Sabot, and I. Sinayskiy, E-print: http://hal.archives-ouvertes.fr/hal-00581553/fr/]. The formulation of the OQWs is exclusively based upon the non-unitary dynamics induced by the environment. It will be shown that OQWs are a very useful tool for the formulation of dissipative quantum computing and quantum state preparation. In particular, it will be shown how to implement single qubit gates and the CNOT gate as OQWs on fully connected graphs. Also, OQWS make possible the dissipative quantum state preparation of arbitrary single qubit states and of all two-qubit Bell states. Finally, it will be shown how to reformulate efficiently a discrete time version of dissipative quantum computing in the language of OQWs.
Minimal Joule dissipation models of magnetospheric convection
NASA Astrophysics Data System (ADS)
Barbosa, D. D.
This paper gives a topical review of theoretical models of magnetospheric convection based on the concept of minimal Joule dissipation. A two-dimensional slab model of the ionosphere featuring an enhanced conductivity auroral oval is used to compute high-latitude electric fields and currents. Mathematical methods used in the modeling include Fourier analysis, fast Fourier transforms, and variational calculus. Also, conformal transformations are introduced in the analysis, which enable the auroral oval to be represented as a nonconcentric, crescent-shaped figure. Convection patterns appropriate to geomagnetic quiet and disturbed conditions are computed, the differentiating variable being the relative amount of power dissipated in the magnetospheric ring current. When ring current dissipation is small, the convection electric field is restricted to high latitudes (shielding regime), and when it is large, a significant penetration of the field to low latitudes occurs, accompanied by an increase in the ratio of the region I current to the region 2 current.
Minimal Joule dissipation models of magnetospheric convection
NASA Technical Reports Server (NTRS)
Barbosa, D. D.
1988-01-01
This paper gives a topical review of theoretical models of magnetospheric convection based on the concept of minimal Joule dissipation. A two-dimensional slab model of the ionosphere featuring an enhanced conductivity auroral oval is used to compute high-latitude electric fields and currents. Mathematical methods used in the modeling include Fourier analysis, fast Fourier transforms, and variational calculus. Also, conformal transformations are introduced in the analysis, which enable the auroral oval to be represented as a nonconcentric, crescent-shaped figure. Convection patterns appropriate to geomagnetic quiet and disturbed conditions are computed, the differentiating variable being the relative amount of power dissipated in the magnetospheric ring current. When ring current dissipation is small, the convection electric field is restricted to high latitudes (shielding regime), and when it is large, a significant penetration of the field to low latitudes occurs, accompanied by an increase in the ratio of the region I current to the region 2 current.
Heat dissipation guides activation in signaling proteins
Weber, Jeffrey K.; Shukla, Diwakar; Pande, Vijay S.
2015-01-01
Life is fundamentally a nonequilibrium phenomenon. At the expense of dissipated energy, living things perform irreversible processes that allow them to propagate and reproduce. Within cells, evolution has designed nanoscale machines to do meaningful work with energy harnessed from a continuous flux of heat and particles. As dictated by the Second Law of Thermodynamics and its fluctuation theorem corollaries, irreversibility in nonequilibrium processes can be quantified in terms of how much entropy such dynamics produce. In this work, we seek to address a fundamental question linking biology and nonequilibrium physics: can the evolved dissipative pathways that facilitate biomolecular function be identified by their extent of entropy production in general relaxation processes? We here synthesize massive molecular dynamics simulations, Markov state models (MSMs), and nonequilibrium statistical mechanical theory to probe dissipation in two key classes of signaling proteins: kinases and G-protein–coupled receptors (GPCRs). Applying machinery from large deviation theory, we use MSMs constructed from protein simulations to generate dynamics conforming to positive levels of entropy production. We note the emergence of an array of peaks in the dynamical response (transient analogs of phase transitions) that draw the proteins between distinct levels of dissipation, and we see that the binding of ATP and agonist molecules modifies the observed dissipative landscapes. Overall, we find that dissipation is tightly coupled to activation in these signaling systems: dominant entropy-producing trajectories become localized near important barriers along known biological activation pathways. We go on to classify an array of equilibrium and nonequilibrium molecular switches that harmonize to promote functional dynamics. PMID:26240354
Dissipative dark matter explains rotation curves
NASA Astrophysics Data System (ADS)
Foot, R.
2015-06-01
Dissipative dark matter, where dark matter particles interact with a massless (or very light) boson, is studied. Such dark matter can arise in simple hidden sector gauge models, including those featuring an unbroken U (1 )' gauge symmetry, leading to a dark photon. Previous work has shown that such models can not only explain the large scale structure and cosmic microwave background, but potentially also dark matter phenomena on small scales, such as the inferred cored structure of dark matter halos. In this picture, dark matter halos of disk galaxies not only cool via dissipative interactions but are also heated via ordinary supernovae (facilitated by an assumed photon-dark photon kinetic mixing interaction). This interaction between the dark matter halo and ordinary baryons, a very special feature of these types of models, plays a critical role in governing the physical properties of the dark matter halo. Here, we further study the implications of this type of dissipative dark matter for disk galaxies. Building on earlier work, we develop a simple formalism which aims to describe the effects of dissipative dark matter in a fairly model independent way. This formalism is then applied to generic disk galaxies. We also consider specific examples, including NGC 1560 and a sample of dwarf galaxies from the LITTLE THINGS survey. We find that dissipative dark matter, as developed here, does a fairly good job accounting for the rotation curves of the galaxies considered. Not only does dissipative dark matter explain the linear rise of the rotational velocity of dwarf galaxies at small radii, but it can also explain the observed wiggles in rotation curves which are known to be correlated with corresponding features in the disk gas distribution.
Estimating Energy Dissipation Due to Wave Breaking in the Surf Zone Using Infrared Imagery
NASA Astrophysics Data System (ADS)
Carini, Roxanne J.
Wave breaking is the largest forcing mechanism in the surf zone. Therefore, quantifying energy dissipation due to wave breaking is important for improving models that seek to predict nearshore circulation, wave-current interactions, air-sea gas exchange, erosion and accretion of sediment, and storm surge. Wave energy dissipation is difficult to measure with in situ instruments, and even the most reliable estimates are limited to point measurements. Using remote sensing technologies, specifically infrared (IR) imagery, the high spatial and temporal variability of wave breaking may be sampled. Duncan (1981) proposed a model (D81) for dissipation on a wave-by-wave basis, based on wave slope and roller length, the crest-perpendicular length of the aerated region of a breaking wave. The wave roller is composed of active foam, which, in thermal IR images, appears brighter than the surrounding water and the residual foam, the foam left behind in the wake of a breaking wave. Using IR imagery taken during the Surf Zone Optics 2010 experiment at Duck, NC, and exploiting the distinct signature of active foam, a retrieval algorithm was developed to identify and extract breaking wave roller length. Roller length was then used to estimate dissipation rate via the D81 formulation. The D81 dissipation rate estimates compare reasonably to in situ dissipation estimates at a point. When the D81 estimates are compared to the bulk energy flux into the surf zone, it is found that wave breaking dissipates approximately 25-36% of the incoming wave energy. The D81 dissipation rate estimates also agree closely with those from a dissipation parameterization proposed by Janssen and Battjes (2007) (JB07) and commonly applied within larger nearshore circulation models. The JB07 formulation, however, requires additional physical parameters (wave height and water depth) that are often sparsely sampled and are difficult to attain from remote sensing alone. The power of the D81 formulation lies in
The effects of nonextensivity on quantum dissipation
Choi, Jeong Ryeol
2014-01-01
Nonextensive dynamics for a quantum dissipative system described by a Caldirola-Kanai (CK) Hamiltonian is investigated in SU(1,1) coherent states. To see the effects of nonextensivity, the system is generalized through a modification fulfilled by replacing the ordinary exponential function in the standard CK Hamiltonian with the q-exponential function. We confirmed that the time behavior of the system is somewhat different depending on the value of q which is the degree of nonextensivity. The effects of q on quantum energy dissipation and other parameters are illustrated and discussed in detail. PMID:24468727
Dissipation in Relativistic Pair-Plasma Reconnection
NASA Technical Reports Server (NTRS)
Hesse, Michael; Zenitani, Seiji
2007-01-01
We present an investigation of the relativistic dissipation in magnetic reconnection. The investigated system consists of an electron-positron plasma. A relativistic generalization of Ohm's law is derived. We analyze a set of numerical simulations, composed of runs with and without guide magnetic field, and of runs with different species temperatures. The calculations indicate that the thermal inertia-based dissipation process survives in relativistic plasmas. For anti-parallel reconnection, it is found that the pressure tensor divergence remains the sole contributor to the reconnection electric field, whereas relativistic guide field reconnection exhibits a similarly important role of the bulk inertia terms.
Free power dissipation from functional line integration
NASA Astrophysics Data System (ADS)
Brader, Joseph M.; Schmidt, Matthias
2015-09-01
Power functional theory provides an exact generalisation of equilibrium density functional theory to non-equilibrium systems undergoing Brownian many-body dynamics. Practical implementation of this variational approach demands knowledge of an excess (over ideal gas) dissipation functional. Using functional line integration (i.e. the operation inverse to functional differentiation), we obtain an exact expression for the excess free power dissipation, which involves the pair interaction potential and the two-body, equal-time density correlator. This provides a basis for the development of approximation schemes.
Dissipation in relativistic pair-plasma reconnection
Hesse, Michael; Zenitani, Seiji
2007-11-15
An investigation into the relativistic dissipation in magnetic reconnection is presented. The investigated system consists of an electron-positron plasma. A relativistic generalization of Ohm's law is derived. A set of numerical simulations is analyzed, composed of runs with and without guide magnetic field, and of runs with different species temperatures. The calculations indicate that the thermal inertia-based dissipation process survives in relativistic plasmas. For antiparallel reconnection, it is found that the pressure tensor divergence remains the sole contributor to the reconnection electric field, whereas relativistic guide field reconnection exhibits a similarly important role of the bulk inertia terms.
Entropy production and the geometry of dissipative evolution equations
NASA Astrophysics Data System (ADS)
Reina, Celia; Zimmer, Johannes
2015-11-01
Purely dissipative evolution equations are often cast as gradient flow structures, z ˙=K (z ) D S (z ) , where the variable z of interest evolves towards the maximum of a functional S according to a metric defined by an operator K . While the functional often follows immediately from physical considerations (e.g., the thermodynamic entropy), the operator K and the associated geometry does not necessarily do so (e.g., Wasserstein geometry for diffusion). In this paper, we present a variational statement in the sense of maximum entropy production that directly delivers a relationship between the operator K and the constraints of the system. In particular, the Wasserstein metric naturally arises here from the conservation of mass or energy, and depends on the Onsager resistivity tensor, which, itself, may be understood as another metric, as in the steepest entropy ascent formalism. This variational principle is exemplified here for the simultaneous evolution of conserved and nonconserved quantities in open systems. It thus extends the classical Onsager flux-force relationships and the associated variational statement to variables that do not have a flux associated to them. We further show that the metric structure K is intimately linked to the celebrated Freidlin-Wentzell theory of stochastically perturbed gradient flows, and that the proposed variational principle encloses an infinite-dimensional fluctuation-dissipation statement.
Nonlinear evolution of a baroclinic wave and imbalanced dissipation
NASA Astrophysics Data System (ADS)
Nadiga, Balu
2015-11-01
The question of how ocean circulation equilibrates in the presence of continuous large-scale forcing and a tendency of geostrophic turbulence to confine energy to large and intermediate scales is considered. By considering the nonlinear evolution of an unstable baroclinic wave at small Rossby and Froude numbers (small aspect ratio domain) at high resolutions, it is shown that submesoscale instabilities provide an interior pathway between the energetic oceanic mesoscales and smaller unbalanced scales. An estimate of the magnitude of this pathway is presented. Phenomenology-wise, mesoscale shear and strain resulting from the primary baroclinic instability drive frontogenesis; fronts in turn support ageostrophic secondary circulation and instabilities. These two processes together lead to a quick rise in dissipation rate which then reaches a peak and begins to fall as frontogenesis slows down; eventually balanced and imbalanced modes decouple. Dissipation of balanced energy by imbalanced processes is shown to scale exponentially with Rossby number of the base flow. Further, a break is seen in the total energy (TE) spectrum at small scales with a transition from k-3 to k - 5 / 3 reminiscent of the atmospheric spectra of Nastrom & Gage. For details see JFM 756, 965-1006.
Nuclear Dissipation via Peripheral Collisions with Relativistic Radioactive Actinides Beams
Schmitt, C.; Heinz, A.; Jurado, B.; Kelic, A.; Schmidt, K.-H.
2007-05-22
Peripheral collisions with radioactive actinide beams at relativistic energies are proposed as a relevant approach for the study of dissipation in nuclear matter. The characteristics of the systems resulting from the primary fragmentation of such beams are particularly well suited for probing the controversial existence of a sizeable delay in fission. Thanks to the radioactive beam facility at GSI an unusually large set of data involving about 60 secondary unstable projectiles between At and U has been collected under identical conditions. The properties of the set-up enabled the coincident measurement of the atomic number of both fission fragments, permitting a judicious classification of the data. The width of the fission-fragment charge distribution is shown to establish a thermometer at the saddle point which is directly related to the transient delay caused by the friction force. From a comparison with realistic model calculations, the dissipation strength at small deformation and the transient time are inferred. The present strategy is promoted as a complementary approach that avoids some complex problems inherent to conventional techniques. Combined to the paramount size of the data set, it sheds light on contradictory conclusions that have been published in the past. There is at this point no definite consensus on our understanding of the damping process in fission.
Delayed correlation between turbulent energy injection and dissipation.
Pearson, Bruce R; Yousef, Tarek A; Haugen, Nils Erland L; Brandenburg, Axel; Krogstad, Per-Age
2004-11-01
The dimensionless kinetic energy dissipation rate C(epsilon) is estimated from numerical simulations of statistically stationary isotropic box turbulence that is slightly compressible. The Taylor microscale Reynolds number (Re(lambda)) range is 20< or approximately equal to Re(lambda) < or approximately equal to 220 and the statistical stationarity is achieved with a random phase forcing method. The strong Re(lambda) dependence of C(epsilon) abates when Re(lambda) approximately 100 after which C(epsilon) slowly approaches approximately 0.5, a value slightly different from previously reported simulations but in good agreement with experimental results. If C(epsilon) is estimated at a specific time step from the time series of the quantities involved it is necessary to account for the time lag between energy injection and energy dissipation. Also, the resulting value can differ from the ensemble averaged value by up to +/-30%. This may explain the spread in results from previously published estimates of C(epsilon).
Mechanical stiffness and dissipation in ultrananocrystalline diamond micro-resonators.
Sumant, A. V.; Adiga, V. P.; Suresh, S.; Gudeman, C.; Auciello, O.; Carlis, J. A.; Carpick, R. W.
2009-01-01
We have characterized mechanical properties of ultrananocrystalline diamond (UNCD) thin films grown using the hot filament chemical vapor deposition (HFCVD) technique at 680 C, significantly lower than the conventional growth temperature of {approx}800 C. The films have {approx}4.3% sp{sup 2} content in the near-surface region as revealed by near edge x-ray absorption fine structure spectroscopy. The films, {approx}1 {micro}m thick, exhibit a net residual compressive stress of 370 {+-} 1 MPa averaged over the entire 150 mm wafer. UNCD microcantilever resonator structures and overhanging ledges were fabricated using lithography, dry etching, and wet release techniques. Overhanging ledges of the films released from the substrate exhibited periodic undulations due to stress relaxation. This was used to determine a biaxial modulus of 838 {+-} 2 GPa. Resonant excitation and ring-down measurements in the kHz frequency range of the microcantilevers were conducted under ultrahigh vacuum (UHV) conditions in a customized UHV atomic force microscope system to determine Young's modulus as well as mechanical dissipation of cantilever structures at room temperature. Young's modulus is found to be 790 {+-} 30 GPa. Based on these measurements, Poisson's ratio is estimated to be 0.057 {+-} 0.038. The quality factors (Q) of these resonators ranged from 5000 to 16000. These Q values are lower than theoretically expected from the intrinsic properties of diamond. The results indicate that surface and bulk defects are the main contributors to the observed dissipation in UNCD resonators.
The effect of dissipative inhomogeneous medium on the statistics of the wave intensity
NASA Technical Reports Server (NTRS)
Saatchi, Sasan S.
1993-01-01
One of the main theoretical points in the theory of wave propagation in random medium is the derivation of closed form equations to describe the statistics of the propagating waves. In particular, in one dimensional problems, the closed form representation of the multiple scattering effects is important since it contributes in understanding such problems like wave localization, backscattering enhancement, and intensity fluctuations. In this the propagation of plane waves in a layer of one-dimensional dissipative random medium is considered. The medium is modeled by a complex permittivity whose real part is a constant representing the absorption. The one dimensional problem is mathematically equivalent to the analysis of a transmission line with randomly perturbed distributed parameters and a single mode lossy waveguide and the results can be used to study the propagation of radio waves through atmosphere and the remote sensing of geophysical media. It is assumed the scattering medium consists of an ensemble of one-dimensional point scatterers randomly positioned in a layer of thickness L with diffuse boundaries. A Poisson impulse process with density lambda is used to model the position of scatterers in the medium. By employing the Markov properties of this process an exact closed form equation of Kolmogorov-Feller type was obtained for the probability density of the reflection coefficient. This equation was solved by combining two limiting cases: (1) when the density of scatterers is small; and (2) when the medium is weakly dissipative. A two variable perturbation method for small lambda was used to obtain solutions valid for thick layers. These solutions are then asymptotically evaluated for small dissipation. To show the effect of dissipation, the mean and fluctuations of the reflected power are obtained. The results were compared with a lossy homogeneous medium and with a lossless inhomogeneous medium and the regions where the effect of absorption is not
Optimal estimators and asymptotic variances for nonequilibrium path-ensemble averages
NASA Astrophysics Data System (ADS)
Minh, David D. L.; Chodera, John D.
2009-10-01
Existing optimal estimators of nonequilibrium path-ensemble averages are shown to fall within the framework of extended bridge sampling. Using this framework, we derive a general minimal-variance estimator that can combine nonequilibrium trajectory data sampled from multiple path-ensembles to estimate arbitrary functions of nonequilibrium expectations. The framework is also applied to obtain asymptotic variance estimates, which are a useful measure of statistical uncertainty. In particular, we develop asymptotic variance estimates pertaining to Jarzynski's equality for free energies and the Hummer-Szabo expressions for the potential of mean force, calculated from uni- or bidirectional path samples. These estimators are demonstrated on a model single-molecule pulling experiment. In these simulations, the asymptotic variance expression is found to accurately characterize the confidence intervals around estimators when the bias is small. Hence, the confidence intervals are inaccurately described for unidirectional estimates with large bias, but for this model it largely reflects the true error in a bidirectional estimator derived by Minh and Adib.
Three dimensional Simulations of Self-Organization in a Driven Dissipative Plasma System
NASA Astrophysics Data System (ADS)
Shaikh, Dastgeer; Dasgupta, B.; Hu, Q.; Zank, G. P.
2009-11-01
We perform a fully self-consistent 3-D numerical simulation for a compressible, driven dissipative magneto-plasma driven by large-scale perturbations, that contain a fairly broader spectrum of characteristic modes, ranging from largest scales to intermediate scales and down to the smallest scales, where the energy of the system are dissipated by collisional (Ohmic) and viscous dissipations. Additionally, our simulation includes nonlinear interactions amongst a wide range of ?uctuations that are initialized with random spectral amplitudes, leading to the cascade of spectral energy in the inertial range spectrum, and takes into account large scale as well as small scale perturbation that may have been induced by the background plasma ?uctuations, also the non adiabatic exchange of energy leading to the migration of energy from the energy containing modes or randomly injected energy driven by perturbations and further dissipated by the smaller scales. Besides demonstrating the comparative decays of total energy and dissipation rate of energy, our results show the existence of a perpendicular component of current, thus clearly con?rming that the self-organized state is non-force free.
Roles of Energy Dissipation in a Liquid-Solid Transition of Out-of-Equilibrium Systems
NASA Astrophysics Data System (ADS)
Komatsu, Yuta; Tanaka, Hajime
2015-07-01
Self-organization of active matter as well as driven granular matter in nonequilibrium dynamical states has attracted considerable attention not only from the fundamental and application viewpoints but also as a model to understand the occurrence of such phenomena in nature. These systems share common features originating from their intrinsically out-of-equilibrium nature, and how energy dissipation affects the state selection in such nonequilibrium states remains elusive. As a simple model system, we consider a nonequilibrium stationary state maintained by continuous energy input, relevant to industrial processing of granular materials by vibration and/or flow. More specifically, we experimentally study roles of dissipation in self-organization of a driven granular particle monolayer. We find that the introduction of strong inelasticity entirely changes the nature of the liquid-solid transition from two-step (nearly) continuous transitions (liquid-hexatic-solid) to a strongly discontinuous first-order-like one (liquid-solid), where the two phases with different effective temperatures can coexist, unlike thermal systems, under a balance between energy input and dissipation. Our finding indicates a pivotal role of energy dissipation and suggests a novel principle in the self-organization of systems far from equilibrium. A similar principle may apply to active matter, which is another important class of out-of-equilibrium systems. On noting that interaction forces in active matter, and particularly in living systems, are often nonconservative and dissipative, our finding may also shed new light on the state selection in these systems.
Fine velocity structures collisional dissipation in plasmas
NASA Astrophysics Data System (ADS)
Pezzi, Oreste; Valentini, Francesco; Veltri, Pierluigi
2016-04-01
In a weakly collisional plasma, such as the solar wind, collisions are usually considered far too weak to produce any significant effect on the plasma dynamics [1]. However, the estimation of collisionality is often based on the restrictive assumption that the particle velocity distribution function (VDF) shape is close to Maxwellian [2]. On the other hand, in situ spacecraft measurements in the solar wind [3], as well as kinetic numerical experiments [4], indicate that marked non-Maxwellian features develop in the three-dimensional VDFs, (temperature anisotropies, generation of particle beams, ring-like modulations etc.) as a result of the kinetic turbulent cascade of energy towards short spatial scales. Therefore, since collisional effects are proportional to the velocity gradients of the VDF, the collisionless hypothesis may fail locally in velocity space. Here, the existence of several characteristic times during the collisional relaxation of fine velocity structures is investigated by means of Eulerian numerical simulations of a spatially homogeneous force-free weakly collisional plasma. The effect of smoothing out velocity gradients on the evolution of global quantities, such as temperature and entropy, is discussed, suggesting that plasma collisionality can increase locally due to the velocity space deformation of the particle velocity distribution. In particular, by means of Eulerian simulations of collisional relaxation of a spatially homogeneous force-free plasma, in which collisions among particles of the same species are modeled through the complete Landau operator, we show that the system entropy growth occurs over several time scales, inversely proportional to the steepness of the velocity gradients in the VDF. We report clear evidences that fine velocity structures are dissipated by collisions in a time much shorter than global non-Maxwellian features, like, for example, temperature anisotropies. Moreover we indicate that, if small-scale structures
Critical materials and dissipative losses: a screening study.
Zimmermann, Till; Gößling-Reisemann, Stefan
2013-09-01
This study deals with dissipative losses of critical materials between the life-cycle stages of manufacturing and end-of-life. Following the EU definition for critical materials, a screening of dissipative losses for the respective materials has been performed based on existing data and the most significant data gaps have been identified. Furthermore, a classification scheme for dissipative losses (dissipation into environment, dissipation into other material flows, dissipation to landfills) and for assessing their degree has been developed and a first qualitative assessment applying this classification scheme has been performed. In combination with existing criticality assessments, the results can be used to generate a map of metals indicating future research needs for analyzing metal dissipation in detail. The results include quantitative estimates of dissipative losses (where feasible) along the chosen life-cycle stages, and discuss research needs for analysis and avoidance of dissipative losses for improved resource efficiency.
Scattering theory without large-distance asymptotics
NASA Astrophysics Data System (ADS)
Liu, Tong; Li, Wen-Du; Dai, Wu-Sheng
2014-06-01
In conventional scattering theory, to obtain an explicit result, one imposes a precondition that the distance between target and observer is infinite. With the help of this precondition, one can asymptotically replace the Hankel function and the Bessel function with the sine functions so that one can achieve an explicit result. Nevertheless, after such a treatment, the information of the distance between target and observer is inevitably lost. In this paper, we show that such a precondition is not necessary: without losing any information of distance, one can still obtain an explicit result of a scattering rigorously. In other words, we give an rigorous explicit scattering result which contains the information of distance between target and observer. We show that at a finite distance, a modification factor — the Bessel polynomial — appears in the scattering amplitude, and, consequently, the cross section depends on the distance, the outgoing wave-front surface is no longer a sphere, and, besides the phase shift, there is an additional phase (the argument of the Bessel polynomial) appears in the scattering wave function.
Extended Analytic Device Optimization Employing Asymptotic Expansion
NASA Technical Reports Server (NTRS)
Mackey, Jonathan; Sehirlioglu, Alp; Dynsys, Fred
2013-01-01
Analytic optimization of a thermoelectric junction often introduces several simplifying assumptionsincluding constant material properties, fixed known hot and cold shoe temperatures, and thermallyinsulated leg sides. In fact all of these simplifications will have an effect on device performance,ranging from negligible to significant depending on conditions. Numerical methods, such as FiniteElement Analysis or iterative techniques, are often used to perform more detailed analysis andaccount for these simplifications. While numerical methods may stand as a suitable solution scheme,they are weak in gaining physical understanding and only serve to optimize through iterativesearching techniques. Analytic and asymptotic expansion techniques can be used to solve thegoverning system of thermoelectric differential equations with fewer or less severe assumptionsthan the classic case. Analytic methods can provide meaningful closed form solutions and generatebetter physical understanding of the conditions for when simplifying assumptions may be valid.In obtaining the analytic solutions a set of dimensionless parameters, which characterize allthermoelectric couples, is formulated and provide the limiting cases for validating assumptions.Presentation includes optimization of both classic rectangular couples as well as practically andtheoretically interesting cylindrical couples using optimization parameters physically meaningful toa cylindrical couple. Solutions incorporate the physical behavior for i) thermal resistance of hot andcold shoes, ii) variable material properties with temperature, and iii) lateral heat transfer through legsides.
Early Asymptotic Giant Branch: Theory and Observations
NASA Astrophysics Data System (ADS)
Frantsman, Ju.
1995-08-01
While on the asymptotic giant branch (AGB), a star passes through two evolutionary phases: an early stage (E-AGB), and thermally pulsing AGB (TP-AGB). The theory of two AGB stages was developed more than a decade ago but till now some authors do not take into account the E-AGB phase in spite of the fact that E-AGB phase lasts for some stars considerably longer than the TP-AGB phase. The typical outcomes of such ignoration are shown in the report (wrong conclusions about the evolution of Large Magellanic Cloud, the mistakes in the determination of the ages of Magellanic Cloud clusters). The results are obtained using the "population simultaion" technique. The origin of some types of chemically peculiar stars is investigated (S-stars, faint carbon stars, carbon stars bluer and somewhat brighter than in the mean N-Type stars in the Magellanic Clouds). A suggestion is proposed that these stars are on the E-AGB evolutionary stage. They develop chemical peculiarities in the process of mass transfer in close binaries. It was assumed that during the TP-AGB phase, the primary (more massive) component, when being the carbon star, transfered the carbon enriched material by Roche-lobe overflow to the secondary component, which becomes the star with carbon overabundance. During the subsequent evolution the former secondary (and now after mass transfer carbon enriched) component reaches the E-AGB phase. The results of calculations are discussed and compared with observations.
Asymptotic methods for internal transonic flows
NASA Technical Reports Server (NTRS)
Adamson, T. C., Jr.; Messiter, A. F.
1989-01-01
For many internal transonic flows of practical interest, some of the relevant nondimensional parameters typically are small enough that a perturbation scheme can be expected to give a useful level of numerical accuracy. A variety of steady and unsteady transonic channel and cascade flows is studied with the help of systematic perturbation methods which take advantage of this fact. Asymptotic representations are constructed for small changes in channel cross-section area, small flow deflection angles, small differences between the flow velocity and the sound speed, small amplitudes of imposed oscillations, and small reduced frequencies. Inside a channel the flow is nearly one-dimensional except in thin regions immediately downstream of a shock wave, at the channel entrance and exit, and near the channel throat. A study of two-dimensional cascade flow is extended to include a description of three-dimensional compressor-rotor flow which leads to analytical results except in thin edge regions which require numerical solution. For unsteady flow the qualitative nature of the shock-wave motion in a channel depends strongly on the orders of magnitude of the frequency and amplitude of impressed wall oscillations or fluctuations in back pressure. One example of supersonic flow is considered, for a channel with length large compared to its width, including the effect of separation bubbles and the possibility of self-sustained oscillations. The effect of viscosity on a weak shock wave in a channel is discussed.
Dynamic grasp planning of multifingered robot hands based on asymptotic stability.
Guo, G; Gruver, W A
1996-01-01
We describe an approach for planning grasps of multifingered robot hands based on a small vibration model. Using features of the grasp configuration, we analyze asymptotic stability, contact situations, and uniaxial fingertip force constraints for the combined planning of finger posture and finger position, and characterize the generalized mass, damping, and stiffness. Choosing the largest time constant of the vibration model as an optimization criterion for planning finger postures and positions, the original problem of dynamic grasp planning is formulated as a nonlinear program. Simulation examples for a three-fingered robot hand grasping a spherical object demonstrate the effectiveness of the approach.
Asymptotic Structure of Constrained Exponential Random Graph Models
NASA Astrophysics Data System (ADS)
Zhu, Lingjiong
2017-03-01
In this paper, we study exponential random graph models subject to certain constraints. We obtain some general results about the asymptotic structure of the model. We show that there exists non-trivial regions in the phase plane where the asymptotic structure is uniform and there also exists non-trivial regions in the phase plane where the asymptotic structure is non-uniform. We will get more refined results for the star model and in particular the two-star model for which a sharp transition from uniform to non-uniform structure, a stationary point and phase transitions will be obtained.
Coulomb string tension, asymptotic string tension, and the gluon chain
Greensite, Jeff; Szczepaniak, Adam P.
2015-02-01
We compute, via numerical simulations, the non-perturbative Coulomb potential and position-space ghost propagator in pure SU(3) gauge theory in Coulomb gauge. We find that that the Coulomb potential scales nicely in accordance with asymptotic freedom, that the Coulomb potential is linear in the infrared, and that the Coulomb string tension is about four times larger than the asymptotic string tension. We explain how it is possible that the asymptotic string tension can be lower than the Coulomb string tension by a factor of four.
Articular Contact Mechanics from an Asymptotic Modeling Perspective: A Review
Argatov, Ivan; Mishuris, Gennady
2016-01-01
In the present paper, we review the current state-of-the-art in asymptotic modeling of articular contact. Particular attention has been given to the knee joint contact mechanics with a special emphasis on implications drawn from the asymptotic models, including average characteristics for articular cartilage layer. By listing a number of complicating effects such as transverse anisotropy, non-homogeneity, variable thickness, nonlinear deformations, shear loading, and bone deformation, which may be accounted for by asymptotic modeling, some unsolved problems and directions for future research are also discussed. PMID:27847803
Asymptotic stability properties of linear Volterra integrodifferential equations.
NASA Technical Reports Server (NTRS)
Miller, R. K.
1971-01-01
The Liapunov stability properties of solution to a certain system of Volterra integrodifferential equations is studied. Various types of Liapunov stability are defined; the definitions are natural extensions of the corresponding notions for ordinary differential equations. Necessary and sufficient conditions, in general, for uniform stability and uniform asymptotic stability are obtained in the form of a theorem. Connections between the stability of the system studied and the stability properties of a related Volterra integrodifferential equation with infinite memory are examined. Sufficient conditions in order that the trivial solution to the system studied be stable, uniformly stable, asymptotically stable, or uniformly asymptotically stable are derived.
Uniform Asymptotic Expansion for the Incomplete Beta Function
NASA Astrophysics Data System (ADS)
Nemes, Gergő; Olde Daalhuis, Adri B.
2016-10-01
In [Temme N.M., Special functions. An introduction to the classical functions of mathematical physics, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1996, Section 11.3.3.1] a uniform asymptotic expansion for the incomplete beta function was derived. It was not obvious from those results that the expansion is actually an asymptotic expansion. We derive a remainder estimate that clearly shows that the result indeed has an asymptotic property, and we also give a recurrence relation for the coefficients.
Friction-based energy dissipation unit for circuit breaker
Kar, R.; Rainer, J.H.
1995-12-31
This paper describes a friction-based energy dissipation unit (EDU) that has been designed to introduce supplemental damping into a circuit breaker. The brittle porcelain insulator posts of a 330 kV SF6 breaker were thus subjected to reduced forces from a design earthquake specified to have a peak ground acceleration of 1.05 g. Pull and release tests were performed to determine the dynamic properties, i.e., natural frequency, damping ratio, and mode shapes. Calculations of response of the circuit breaker to the 1940 El Centro N-S component shows that the EDU reduces the bending moment at the base of the porcelain column by a factor of three.
Dynamic capillary wetting studied with dissipative particle dynamics
NASA Astrophysics Data System (ADS)
Cupelli, Claudio; Henrich, Björn; Glatzel, Thomas; Zengerle, Roland; Moseler, Michael; Santer, Mark
2008-04-01
We present a study on dynamic capillary wetting in the framework of dissipative particle dynamics (DPD) based on a novel wall model for wetting on solid boundaries. We consider capillary impregnation of a slit pore in two situations: (i) forced (piston-driven) steady state flow and (ii) capillarity driven imbibition out of a finite reservoir. The dynamic contact angle behavior under condition (i) is consistent with the hydrodynamic theories of Cox under partial wetting conditions and Eggers for complete wetting. The flow field near the contact line shows a region of apparent slip flow which provides a natural way of avoiding a stress singularity at the triple line. The dynamics of the capillary imbibition, i.e. condition (ii), is consistently described by the Lucas-Washburn equation augmented by expressions that account for inertia and the influence of the dynamic contact angle.
History-dependent dissipative vortex dynamics in superconducting arrays
Durkin, Malcolm; Mondragon-Shem, Ian; Eley, Serena Merteen; ...
2016-07-14
In this study, we perform current (I)-voltage (V) measurements on low resistance superconductor-normal-superconductor arrays in finite magnetic fields, focusing on the dilute vortex population regime. We observe significant deviations from predicted behavior, notably the absence of a differential resistance peak near the vortex depinning current, and a broad linear I-V region with an extrapolated I intercept equal to the depinning current. Comparing these results to an overdamped molecular vortex model, we find that this behavior can be explained by the presence of a history-dependent dissipative force. Lastly, this approach has not been considered previously, to our knowledge, yet it ismore » crucial for obtaining a correct description of the vortex dynamics in superconducting arrays.« less
Tidal dissipation in heterogeneous bodies: Maxwell vs Andrade rheology
NASA Astrophysics Data System (ADS)
Behounkova, M.; Cadek, O.
2014-04-01
The tremendous volcanism on Jupiter's moon Io as well as the huge activity at the south pole of Saturn's moon Enceladus show that tidal dissipation is a very strong source of energy for some bodies in the Solar System. Outside the Solar System, tidal heating in short-period exoplanets may cause Io-like volcanism, large-scale melting and even thermal runaways [1-4]. Here we further develop the method to compute tidal heating in heterogeneous bodies [5]. Especially, we concentrate on the Andrade rheology implementation. We study the impact of the improved model on bodies with large lateral viscosity variation such as Enceladus and tidally locked exoEarth with a large surface temperature contrast due to uneven insolation [6]. We discuss the influence of empirical parameters describing the Andrade rheology and compare the tidal heating and tidal stress obtained for the Andrade rheology with frequently used Maxwell models for different forcing frequencies.
History-dependent dissipative vortex dynamics in superconducting arrays
NASA Astrophysics Data System (ADS)
Durkin, Malcolm; Mondragon-Shem, Ian; Eley, Serena; Hughes, Taylor L.; Mason, Nadya
2016-07-01
We perform current (I )-voltage (V ) measurements on low resistance superconductor-normal-superconductor arrays in finite magnetic fields, focusing on the dilute vortex population regime. We observe significant deviations from predicted behavior, notably the absence of a differential resistance peak near the vortex depinning current, and a broad linear I -V region with an extrapolated I intercept equal to the depinning current. Comparing these results to an overdamped molecular vortex model, we find that this behavior can be explained by the presence of a history-dependent dissipative force. This approach has not been considered previously, to our knowledge, yet it is crucial for obtaining a correct description of the vortex dynamics in superconducting arrays.
Crossover from adiabatic to antiadiabatic quantum pumping with dissipation.
Pellegrini, Franco; Negri, C; Pistolesi, F; Manini, Nicola; Santoro, Giuseppe E; Tosatti, Erio
2011-08-05
Quantum pumping, in its different forms, is attracting attention from different fields, from fundamental quantum mechanics, to nanotechnology, to superconductivity. We investigate the crossover of quantum pumping from the adiabatic to the antiadiabatic regime in the presence of dissipation, and find general and explicit analytical expressions for the pumped current in a minimal model describing a system with the topology of a ring forced by a periodic modulation of frequency ω. The solution allows following in a transparent way the evolution of pumped dc current from much smaller to much larger ω values than the other relevant energy scale, the energy splitting introduced by the modulation. We find and characterize a temperature-dependent optimal value of the frequency for which the pumped current is maximal.
History-dependent dissipative vortex dynamics in superconducting arrays
Durkin, Malcolm; Mondragon-Shem, Ian; Eley, Serena Merteen; Hughes, Taylor L.; Mason, Nadya
2016-07-14
In this study, we perform current (I)-voltage (V) measurements on low resistance superconductor-normal-superconductor arrays in finite magnetic fields, focusing on the dilute vortex population regime. We observe significant deviations from predicted behavior, notably the absence of a differential resistance peak near the vortex depinning current, and a broad linear I-V region with an extrapolated I intercept equal to the depinning current. Comparing these results to an overdamped molecular vortex model, we find that this behavior can be explained by the presence of a history-dependent dissipative force. Lastly, this approach has not been considered previously, to our knowledge, yet it is crucial for obtaining a correct description of the vortex dynamics in superconducting arrays.
Lorentz-covariant dissipative Lagrangian systems
NASA Technical Reports Server (NTRS)
Kaufman, A. N.
1985-01-01
The concept of dissipative Hamiltonian system is converted to Lorentz-covariant form, with evolution generated jointly by two scalar functionals, the Lagrangian action and the global entropy. A bracket formulation yields the local covariant laws of energy-momentum conservation and of entropy production. The formalism is illustrated by a derivation of the covariant Landau kinetic equation.
Pederson Current Dissipation In Emerging Active Regions
NASA Astrophysics Data System (ADS)
Leake, James E.; Linton, M. G.
2011-05-01
Pederson current dissipation in emerging active regions. Certain regions of the solar atmosphere, such as the photosphere and chromosphere, as well as prominences, contain a significant amount of neutral atoms, and a complete description of the plasma requires including the effects of partial ionization. In the chromosphere the dissipation of Pederson currents is important for the evolution of emerging magnetic fields. Due to the relatively high number density in the chromosphere, the ion-neutral collision time-scale is much smaller than timescales associated with flux emergence. Hence we use a single-fluid approach to model the partially ionized plasma. Looking at both the emergence of large-scale sub-surface structures, and the emergence and reconnection of undulatory fields, we investigate the effect of Pederson current dissipation on the state of the emerging field, on magnetic reconnection and on dissipative heating of the atmosphere. Specifically we examine the effect of motions across fieldlines in the partially ionized regions, and how this can increase the free energy supplied to the corona by flux emergence. We also look at reconnection associated with flux emergence in the partially ionized atmosphere, and how this can account for observed small-scale brightenings (Ellerman Bombs).
Coherent interactions of dissipative spatial solitons.
Ultanir, Erdem A; Stegeman, George I; Lange, Christoph H; Lederer, Falk
2004-02-01
We report observation of the interaction between two coherent dissipative spatial solitons in a periodically patterned semiconductor optical amplifier with power levels of tens of milliwatts. The interactions are nonlocal and phase dependent and exhibit surprising features, such as soliton birth. The experimental results are in good agreement with the numerical simulations.
Fluctuation and dissipation in liquid crystal electroconvection
NASA Astrophysics Data System (ADS)
Goldburg, Walter I.; Goldschmidt, Yadin Y.; Kellay, Hamid
2002-11-01
The power dissipation P( t) was measured in a liquid crystal (MBBA) driven by an ac voltage into the chaotic electroconvective state. In that state, the power fluctuates about its mean value < P>. The quantity measured, and compared with the fluctuation theorem of Gallavotti and Cohen, is the dimensionless standard deviation of the fluctuations, σP/< P>.
Laminated insulators having heat dissipation means
Niemann, R.C.; Mataya, K.F.; Gonczy, J.D.
1980-04-24
A laminated body is provided with heat dissipation capabilities. The insulator body is formed by dielectric layers interleaved with heat conductive layers, and bonded by an adhesive to form a composite structure. The heat conductive layers include provision for connection to an external thermal circuit.
Herbicide dissipation from low density polyethylene mulch
Technology Transfer Automated Retrieval System (TEKTRAN)
Field and laboratory studies were conducted to examine herbicide dissipation when applied to low density polyethylene (LDPE) mulch for dry scenarios vs. washing off with water. In field studies, halosulfuron, paraquat, carfentrazone, glyphosate, and flumioxazin were applied to black 1.25-mil LDPE at...
Extrema Principles Of Dissipation In Fluids
NASA Technical Reports Server (NTRS)
Horne, W. Clifton; Karamcheti, Krishnamurty
1991-01-01
Report discusses application of principle of least action and other variational or extrema principles to dissipation of energy and production of entropy in fluids. Principle of least action applied successfully to dynamics of particles and to quantum mechanics, but not universally accepted that variational principles applicable to thermodynamics and hydrodynamics. Report argues for applicability of some extrema principles to some simple flows.
Galapon, Eric A; Martinez, Kay Marie L
2014-02-08
We obtain an exactification of the Poincaré asymptotic expansion (PAE) of the Hankel integral, [Formula: see text] as [Formula: see text], using the distributional approach of McClure & Wong. We find that, for half-integer orders of the Bessel function, the exactified asymptotic series terminates, so that it gives an exact finite sum representation of the Hankel integral. For other orders, the asymptotic series does not terminate and is generally divergent, but is amenable to superasymptotic summation, i.e. by optimal truncation. For specific examples, we compare the accuracy of the optimally truncated asymptotic series owing to the McClure-Wong distributional method with owing to the Mellin-Barnes integral method. We find that the former is spectacularly more accurate than the latter, by, in some cases, more than 70 orders of magnitude for the same moderate value of b. Moreover, the exactification can lead to a resummation of the PAE when it is exact, with the resummed Poincaré series exhibiting again the same spectacular accuracy. More importantly, the distributional method may yield meaningful resummations that involve scales that are not asymptotic sequences.
Heat dissipation in atomic-scale junctions.
Lee, Woochul; Kim, Kyeongtae; Jeong, Wonho; Zotti, Linda Angela; Pauly, Fabian; Cuevas, Juan Carlos; Reddy, Pramod
2013-06-13
Atomic and single-molecule junctions represent the ultimate limit to the miniaturization of electrical circuits. They are also ideal platforms for testing quantum transport theories that are required to describe charge and energy transfer in novel functional nanometre-scale devices. Recent work has successfully probed electric and thermoelectric phenomena in atomic-scale junctions. However, heat dissipation and transport in atomic-scale devices remain poorly characterized owing to experimental challenges. Here we use custom-fabricated scanning probes with integrated nanoscale thermocouples to investigate heat dissipation in the electrodes of single-molecule ('molecular') junctions. We find that if the junctions have transmission characteristics that are strongly energy dependent, this heat dissipation is asymmetric--that is, unequal between the electrodes--and also dependent on both the bias polarity and the identity of the majority charge carriers (electrons versus holes). In contrast, junctions consisting of only a few gold atoms ('atomic junctions') whose transmission characteristics show weak energy dependence do not exhibit appreciable asymmetry. Our results unambiguously relate the electronic transmission characteristics of atomic-scale junctions to their heat dissipation properties, establishing a framework for understanding heat dissipation in a range of mesoscopic systems where transport is elastic--that is, without exchange of energy in the contact region. We anticipate that the techniques established here will enable the study of Peltier effects at the atomic scale, a field that has been barely explored experimentally despite interesting theoretical predictions. Furthermore, the experimental advances described here are also expected to enable the study of heat transport in atomic and molecular junctions--an important and challenging scientific and technological goal that has remained elusive.
NASA Technical Reports Server (NTRS)
Kelkar, Atul G.; Joshi, Suresh M.
1994-01-01
Global asymptotic stability of a class of nonlinear multibody flexible space structures under dissipative compensation is established. Two cases are considered. The first case allows unlimited nonlinear motions of the entire system and uses quaternion feedback. The second case assumes that the central body motion is in the linear range although the other bodies can undergo unrestricted nonlinear motion. The stability is proved to be robust to the inherent modeling nonlinearities and uncertainties. Furthermore, for the second case, the stability is also shown to be robust to certain actuator and sensor nonlinearities. The stability proofs use the Lyapunov approach and exploit the inherent passivity of such systems. The results are applicable to a wide class of systems, including flexible space structures with articulated flexible appendages.
NASA Technical Reports Server (NTRS)
Kelkar, Atul G.; Joshi, Suresh M.
1994-01-01
Global asymptotic stability of a class of nonlinear multibody flexible space-stnuctures under dissipative compensation is established. Two cases are considered. The first case allows unlimited nonlinear motions of the entire system and uses quaternion feedback. The second case assumes that the central body motion is in the linear range although the other bodies can undergo unrestricted nonlinear motion. The stability is proved to be robust to the inherent modeling nonlinearities and uncertainties. Furthermore for the second case the stability is also shown to be robust to certain actuator and sensor nonlinearities. The stability proofs use the Lyapunov approach and exploit the inherent passivity of such systems. The results are applicable to a wide class of systems including flexible space-structures with articulated flexible appendages.
Asymptotically anti-de Sitter spacetimes in topologically massive gravity
Henneaux, Marc; Martinez, Cristian; Troncoso, Ricardo
2009-04-15
We consider asymptotically anti-de Sitter spacetimes in three-dimensional topologically massive gravity with a negative cosmological constant, for all values of the mass parameter {mu} ({mu}{ne}0). We provide consistent boundary conditions that accommodate the recent solutions considered in the literature, which may have a slower falloff than the one relevant for general relativity. These conditions are such that the asymptotic symmetry is in all cases the conformal group, in the sense that they are invariant under asymptotic conformal transformations and that the corresponding Virasoro generators are finite. It is found that, at the chiral point |{mu}l|=1 (where l is the anti-de Sitter radius), allowing for logarithmic terms (absent for general relativity) in the asymptotic behavior of the metric makes both sets of Virasoro generators nonzero even though one of the central charges vanishes.
Asymptotics of 6j and 10j symbols
NASA Astrophysics Data System (ADS)
Freidel, Laurent; Louapre, David
2003-04-01
It is well known that the building blocks for state sum models of quantum gravity are given by 6j and 10j symbols. In this work, we study the asymptotics of these symbols by using their expressions as group integrals. We carefully describe the measure involved in terms of invariant variables and develop new technics in order to study their asymptotics. Using these technics, we compute the asymptotics of the various Euclidean and Lorentzian 6j symbols. Finally, we compute the asymptotic expansion of the 10j symbol which is shown to be non-oscillating, in agreement with a recent result of Baez et al. We discuss the physical origin of this behaviour and a way to modify the Barrett-Crane model in order to cure this disease.
Asymptotic expansions of Feynman integrals of exponentials with polynomial exponent
NASA Astrophysics Data System (ADS)
Kravtseva, A. K.; Smolyanov, O. G.; Shavgulidze, E. T.
2016-10-01
In the paper, an asymptotic expansion of path integrals of functionals having exponential form with polynomials in the exponent is constructed. The definition of the path integral in the sense of analytic continuation is considered.
An asymptotic model in acoustics: acoustic drift equations.
Vladimirov, Vladimir A; Ilin, Konstantin
2013-11-01
A rigorous asymptotic procedure with the Mach number as a small parameter is used to derive the equations of mean flows which coexist and are affected by the background acoustic waves in the limit of very high Reynolds number.
Quick asymptotic expansion aided by a variational principle
Hameiri, Eliezer
2013-02-15
It is shown how expanding asymptotically a variational functional can yield the asymptotic expansion of its Euler equation. The procedure is simple but novel and requires taking the variation of the expanded functional with respect to the leading order of the originally unknown function, even though the leading order of this function has already been determined in a previous order. An example is worked out that of a large aspect ratio tokamak plasma equilibrium state with relatively strong flows and high plasma beta.
Asymptotic-induced numerical methods for conservation laws
NASA Technical Reports Server (NTRS)
Garbey, Marc; Scroggs, Jeffrey S.
1990-01-01
Asymptotic-induced methods are presented for the numerical solution of hyperbolic conservation laws with or without viscosity. The methods consist of multiple stages. The first stage is to obtain a first approximation by using a first-order method, such as the Godunov scheme. Subsequent stages of the method involve solving internal-layer problems identified by using techniques derived via asymptotics. Finally, a residual correction increases the accuracy of the scheme. The method is derived and justified with singular perturbation techniques.
Asymptotic relation between Bell-inequality violations and entanglement distillability
Kwon, Younghun
2010-11-15
We investigate the asymptotic relation between violations of the Mermin-Belinskii-Klyshko inequality and the entanglement distillability of multipartite entangled states, as the number of parties increases. We in particular consider noisy multiqubit GHZ and so-called Duer states in the Mermin-Belinskii-Klyshko inequality, and show that, in the asymptotic limit of the number of parties, the violation of the inequality implies the distillability in almost all bipartitions.
Asymptotic Expansion in Enzyme Reactions with High Enzyme Concentrations
NASA Astrophysics Data System (ADS)
Bersani, Alberto Maria; Dell'Acqua, Guido
2010-09-01
In this paper we find a new asymptotic expansion valid in enzymatic reactions where the total amount of enzyme exceeds greatly the total amount of substrate. In such case it is well known that the Michelis-Menten approximation is no longer valid; therefore our asymptotic expansion is a new tool to approximate in a closed form the concentrations of the reactants in presence of an enzyme excess.
Globally uniformly asymptotical stabilisation of time-delay nonlinear systems
NASA Astrophysics Data System (ADS)
Cai, Xiushan; Han, Zhengzhi; Zhang, Wei
2011-07-01
Globally uniformly asymptotical stabilisation of nonlinear systems in feedback form with a delay arbitrarily large in the input is dealt with based on the backstepping approach in this article. The design strategy depends on the construction of a Lyapunov-Krasovskii functional. A continuously differentiable control law is obtained to globally uniformly asymptotically stabilise the closed-loop system. The simulation shows the effectiveness of the method.
A smooth dissipative particle dynamics method for domains with arbitrary-geometry solid boundaries
NASA Astrophysics Data System (ADS)
Gatsonis, Nikolaos A.; Potami, Raffaele; Yang, Jun
2014-01-01
A smooth dissipative particle dynamics method with dynamic virtual particle allocation (SDPD-DV) for modeling and simulation of mesoscopic fluids in wall-bounded domains is presented. The physical domain in SDPD-DV may contain external and internal solid boundaries of arbitrary geometries, periodic inlets and outlets, and the fluid region. The SDPD-DV method is realized with fluid particles, boundary particles, and dynamically allocated virtual particles. The internal or external solid boundaries of the domain can be of arbitrary geometry and are discretized with a surface grid. These boundaries are represented by boundary particles with assigned properties. The fluid domain is discretized with fluid particles of constant mass and variable volume. Conservative and dissipative force models due to virtual particles exerted on a fluid particle in the proximity of a solid boundary supplement the original SDPD formulation. The dynamic virtual particle allocation approach provides the density and the forces due to virtual particles. The integration of the SDPD equations is accomplished with a velocity-Verlet algorithm for the momentum and a Runge-Kutta for the entropy equation. The velocity integrator is supplemented by a bounce-forward algorithm in cases where the virtual particle force model is not able to prevent particle penetration. For the incompressible isothermal systems considered in this work, the pressure of a fluid particle is obtained by an artificial compressibility formulation for liquids and the ideal gas law for gases. The self-diffusion coefficient is obtained by an implementation of the generalized Einstein and the Green-Kubo relations. Field properties are obtained by sampling SDPD-DV outputs on a post-processing grid that allows harnessing the particle information on desired spatiotemporal scales. The SDPD-DV method is verified and validated with simulations in bounded and periodic domains that cover the hydrodynamic and mesoscopic regimes for
Dissipation-Induced Coherent Structures in Bose-Einstein Condensates
Brazhnyi, Valeriy A.; Konotop, Vladimir V.; Perez-Garcia, Victor M.; Ott, Herwig
2009-04-10
We discuss how to engineer the phase and amplitude of a complex order parameter using localized dissipative perturbations. Our results are applied to generate and control various types of atomic nonlinear matter waves (solitons) by means of localized dissipative defects.
Goujon, Florent; Malfreyt, Patrice; Tildesley, Dominic J
2004-04-19
We have used the dissipative particle dynamics (DPD) method in the grand canonical ensemble to study the compression of grafted polymer brushes in good solvent conditions. The force-distance profiles calculated from DPD simulations in the grand canonical ensemble are in very good agreement with the self-consistent field (SCF) theoretical models and with experimental results for two polystyrene brush layers grafted onto mica surfaces in toluene.
NASA Astrophysics Data System (ADS)
Thieme, Horst R.
The concept of asymptotic proportionality and conditional asymptotic equality which is presented here aims at making global asymptotic stability statements for time-heterogeneous difference and differential equations. For such non-autonomous problems (apart from special cases) no prominent special solutions (equilibra, periodic solutions) exist which are natural candidates for the asymptotic behaviour of arbitrary solutions. One way out of this dilemma consists in looking for conditions under which any two solutions to the problem (with different initial conditions) behave in a similar or even the same way as time tends to infinity. We study a general sublinear difference equation in an ordered Banach space and, for illustration, time-heterogeneous versions of several well-known differential equations modelling the spread of gonorrhea in a heterogeneous population, the spread of a vector-borne infectious disease, and the dynamics of a logistically growing spatially diffusing population.
NASA Astrophysics Data System (ADS)
Storch, Natalia I.; Lai, Dong
2014-02-01
We study the possibility of tidal dissipation in the solid cores of giant planets and its implication for the formation of hot Jupiters through high-eccentricity migration. We present a general framework by which the tidal evolution of planetary systems can be computed for any form of tidal dissipation, characterized by the imaginary part of the complex tidal Love number, Im[{tilde{k}}_2(ω )], as a function of the forcing frequency ω. Using the simplest viscoelastic dissipation model (the Maxwell model) for the rocky core and including the effect of a non-dissipative fluid envelope, we show that with reasonable (but uncertain) physical parameters for the core (size, viscosity and shear modulus), tidal dissipation in the core can accommodate the tidal-Q constraint of the Solar system gas giants and at the same time allows exoplanetary hot Jupiters to form via tidal circularization in the high-e migration scenario. By contrast, the often-used weak friction theory of equilibrium tide would lead to a discrepancy between the Solar system constraint and the amount of dissipation necessary for high-e migration. We also show that tidal heating in the rocky core can lead to modest radius inflation of the planets, particularly when the planets are in the high-eccentricity phase (e ˜ 0.6) during their high-e migration. Finally, as an interesting by-product of our study, we note that for a generic tidal response function Im[{tilde{k}}_2(ω )], it is possible that spin equilibrium (zero torque) can be achieved for multiple spin frequencies (at a given e), and the actual pseudo-synchronized spin rate depends on the evolutionary history of the system.
Micro-power dissipation device described
NASA Astrophysics Data System (ADS)
Mao, X.; Zhou, L.; Zhou, J.
1985-11-01
The common-emitter current gain beta of a common two-pole transistor is generally below 250. They are referred to as high-beta or high gain transistors when the beta of such transistors exceeds 300. When the beta of a transistor is higher than 1,000, it is called a super-beta transistor (SBT) or supergain transistor. The micropower dissipation type has the widest applications among the high-beta. Micropower dissipation high-beta means that there is a high gain or a superhigh gain under a microcurrent. The device is widely used in small signal-detection systems and stereo audio equipment because of their characteristics of high gain, low frequency and low noise under small signals.
Mode-locking via dissipative Faraday instability
NASA Astrophysics Data System (ADS)
Tarasov, Nikita; Perego, Auro M.; Churkin, Dmitry V.; Staliunas, Kestutis; Turitsyn, Sergei K.
2016-08-01
Emergence of coherent structures and patterns at the nonlinear stage of modulation instability of a uniform state is an inherent feature of many biological, physical and engineering systems. There are several well-studied classical modulation instabilities, such as Benjamin-Feir, Turing and Faraday instability, which play a critical role in the self-organization of energy and matter in non-equilibrium physical, chemical and biological systems. Here we experimentally demonstrate the dissipative Faraday instability induced by spatially periodic zig-zag modulation of a dissipative parameter of the system--spectrally dependent losses--achieving generation of temporal patterns and high-harmonic mode-locking in a fibre laser. We demonstrate features of this instability that distinguish it from both the Benjamin-Feir and the purely dispersive Faraday instability. Our results open the possibilities for new designs of mode-locked lasers and can be extended to other fields of physics and engineering.
Magnetoacoustic shock waves in dissipative degenerate plasmas
Hussain, S.; Mahmood, S.
2011-11-15
Quantum magnetoacoustic shock waves are studied in homogenous, magnetized, dissipative dense electron-ion plasma by using two fluid quantum magneto-hydrodynamic (QMHD) model. The weak dissipation effects in the system are taken into account through kinematic viscosity of the ions. The reductive perturbation method is employed to derive Korteweg-de Vries Burgers (KdVB) equation for magnetoacoustic wave propagating in the perpendicular direction to the external magnetic field in dense plasmas. The strength of magnetoacoustic shock is investigated with the variations in plasma density, magnetic field intensity, and ion kinematic viscosity of dense plasma system. The necessary condition for the existence of monotonic and oscillatory shock waves is also discussed. The numerical results are presented for illustration by using the data of astrophysical dense plasma situations such as neutron stars exist in the literature.
Groundwater removal near heat dissipating waste packages
Manteufel, R.D.
1996-12-31
The thermohydrologic environment of heat-dissipating nuclear waste packages in a subsurface repository is affected by ventilation of the facility prior to permanent closure. Heat dissipated by the waste will raise the temperature of host rock and vaporize groundwater. Ventilation will remove some heat and water vapor from the subsurface, creating a desiccated region surrounding the waste packages. The resulting hot, dry environment will tend to favorably extend the containment time of the waste. This work evaluates the transient temperature field near emplacement drifts and predicts the extent of rock dryout and removal of groundwater. For two hypothetical ventilation schemes with 30-yr-old fuel and repository loading of 40 metric tons of uranium (MTU) per acre, about 4 to 5 m of rock surrounding the drifts are predicted to be dried during the preclosure period.
Pattern Generation by Dissipative Parametric Instability
NASA Astrophysics Data System (ADS)
Perego, A. M.; Tarasov, N.; Churkin, D. V.; Turitsyn, S. K.; Staliunas, K.
2016-01-01
Nonlinear instabilities are responsible for spontaneous pattern formation in a vast number of natural and engineered systems, ranging from biology to galaxy buildup. We propose a new instability mechanism leading to pattern formation in spatially extended nonlinear systems, which is based on a periodic antiphase modulation of spectrally dependent losses arranged in a zigzag way: an effective filtering is imposed at symmetrically located wave numbers k and -k in alternating order. The properties of the dissipative parametric instability differ from the features of both key classical concepts of modulation instabilities, i.e., the Benjamin-Feir instability and the Faraday instabiltyity. We demonstrate how the dissipative parametric instability can lead to the formation of stable patterns in one- and two-dimensional systems. The proposed instability mechanism is generic and can naturally occur or can be implemented in various physical systems.
Dissipative cryogenic filters with zero dc resistance.
Bluhm, Hendrik; Moler, Kathryn A
2008-01-01
The authors designed, implemented, and tested cryogenic rf filters with zero dc resistance, based on wires with a superconducting core inside a resistive sheath. The superconducting core allows low frequency currents to pass with negligible dissipation. Signals above the cutoff frequency are dissipated in the resistive part due to their small skin depth. The filters consist of twisted wire pairs shielded with copper tape. Above approximately 1 GHz, the attenuation is exponential in omega, as typical for skin depth based rf filters. By using additional capacitors of 10 nF per line, an attenuation of at least 45 dB above 10 MHz can be obtained. Thus, one single filter stage kept at mixing chamber temperature in a dilution refrigerator is sufficient to attenuate room temperature black body radiation to levels corresponding to 10 mK above about 10 MHz.
Blast Dynamics in a Dissipative Gas.
Barbier, M; Villamaina, D; Trizac, E
2015-11-20
The blast caused by an intense explosion has been extensively studied in conservative fluids, where the Taylor-von Neumann-Sedov hydrodynamic solution is a prototypical example of self-similarity driven by conservation laws. In dissipative media, however, energy conservation is violated, yet a distinctive self-similar solution appears. It hinges on the decoupling of random and coherent motion permitted by a broad class of dissipative mechanisms. This enforces a peculiar layered structure in the shock, for which we derive the full hydrodynamic solution, validated by a microscopic approach based on molecular dynamics simulations. We predict and evidence a succession of temporal regimes, as well as a long-time corrugation instability, also self-similar, which disrupts the blast boundary. These generic results may apply from astrophysical systems to granular gases, and invite further cross-fertilization between microscopic and hydrodynamic approaches of shock waves.
Dissipative solitons in pair-ion plasmas
Ghosh, Samiran; Adak, Ashish Khan, Manoranjan
2014-01-15
The effects of ion-neutral collisions on the dynamics of the nonlinear ion acoustic wave in pair-ion plasma are investigated. The standard perturbative approach leads to a Korteweg-de Vries equation with a linear damping term for the dynamics of the finite amplitude wave. The ion-neutral collision induced dissipation is responsible for the linear damping. The analytical solution and numerical simulation reveal that the nonlinear wave propagates in the form of a weakly dissipative compressive solitons. Furthermore, the width of the soliton is proportional to the amplitude of the wave for fixed soliton velocity. Results are discussed in the context of the fullerene pair-ion plasma experiment.
Fluctuation and Dissipation in Liquid Crystal Electroconvection
NASA Astrophysics Data System (ADS)
Goldburg, W. I.; Goldschmidt, Y. Y.
2001-11-01
Recently, Gallavotti and Cohen (GC) have generalized the fluctuation-dissipation theorem (FDT) to encompass systems that are in a steady state far from thermal equilibrium. We describe an experiment aimed at putting the GC theory to an experimental test [1]. The system is a liquid crystal (lc) across which an ac voltage \\cal V=√ 2V\\cos(ω t) is applied. We measure σ_P, the rms fluctuations of the power P(t) dissipated in the lc when V is large enough to generate chaotic or turbulent flow in the sample. To compare the experimental results with the GC theory, it is necessary to assign a dynamical temperature to the system by introducing a kinetic energy per quasi-particle generated by the chaotic flow. [1] W.I. Goldburg, Y. Y. Goldschmidt and Hamid Kellay, nlin.CD/0106015
Dissipative Cryogenic Filters with Zero DC Resistance
Bluhm, Hendrik; Moler, Kathryn A.; /Stanford U., Appl. Phys. Dept
2008-04-22
The authors designed, implemented and tested cryogenic RF filters with zero DC resistance, based on wires with a superconducting core inside a resistive sheath. The superconducting core allows low frequency currents to pass with negligible dissipation. Signals above the cutoff frequency are dissipated in the resistive part due to their small skin depth. The filters consist of twisted wire pairs shielded with copper tape. Above approximately 1 GHz, the attenuation is exponential in {radical}{omega}, as typical for skin depth based RF filters. By using additional capacitors of 10 nF per line, an attenuation of at least 45 dB above 10 MHz can be obtained. Thus, one single filter stage kept at mixing chamber temperature in a dilution refrigerator is sufficient to attenuate room temperature black body radiation to levels corresponding to 10 mK above about 10 MHz.
Astrophysical constraints on Planck scale dissipative phenomena.
Liberati, Stefano; Maccione, Luca
2014-04-18
The emergence of a classical spacetime from any quantum gravity model is still a subtle and only partially understood issue. If indeed spacetime is arising as some sort of large scale condensate of more fundamental objects, then it is natural to expect that matter, being a collective excitation of the spacetime constituents, will present modified kinematics at sufficiently high energies. We consider here the phenomenology of the dissipative effects necessarily arising in such a picture. Adopting dissipative hydrodynamics as a general framework for the description of the energy exchange between collective excitations and the spacetime fundamental degrees of freedom, we discuss how rates of energy loss for elementary particles can be derived from dispersion relations and used to provide strong constraints on the base of current astrophysical observations of high-energy particles.
Mode-locking via dissipative Faraday instability
Tarasov, Nikita; Perego, Auro M.; Churkin, Dmitry V.; Staliunas, Kestutis; Turitsyn, Sergei K.
2016-01-01
Emergence of coherent structures and patterns at the nonlinear stage of modulation instability of a uniform state is an inherent feature of many biological, physical and engineering systems. There are several well-studied classical modulation instabilities, such as Benjamin–Feir, Turing and Faraday instability, which play a critical role in the self-organization of energy and matter in non-equilibrium physical, chemical and biological systems. Here we experimentally demonstrate the dissipative Faraday instability induced by spatially periodic zig-zag modulation of a dissipative parameter of the system—spectrally dependent losses—achieving generation of temporal patterns and high-harmonic mode-locking in a fibre laser. We demonstrate features of this instability that distinguish it from both the Benjamin–Feir and the purely dispersive Faraday instability. Our results open the possibilities for new designs of mode-locked lasers and can be extended to other fields of physics and engineering. PMID:27503708
Dissipative cryogenic filters with zero dc resistance
NASA Astrophysics Data System (ADS)
Bluhm, Hendrik; Moler, Kathryn A.
2008-01-01
The authors designed, implemented, and tested cryogenic rf filters with zero dc resistance, based on wires with a superconducting core inside a resistive sheath. The superconducting core allows low frequency currents to pass with negligible dissipation. Signals above the cutoff frequency are dissipated in the resistive part due to their small skin depth. The filters consist of twisted wire pairs shielded with copper tape. Above approximately 1GHz, the attenuation is exponential in √ω , as typical for skin depth based rf filters. By using additional capacitors of 10nF per line, an attenuation of at least 45dB above 10MHz can be obtained. Thus, one single filter stage kept at mixing chamber temperature in a dilution refrigerator is sufficient to attenuate room temperature black body radiation to levels corresponding to 10mK above about 10MHz.
Mode-locking via dissipative Faraday instability.
Tarasov, Nikita; Perego, Auro M; Churkin, Dmitry V; Staliunas, Kestutis; Turitsyn, Sergei K
2016-08-09
Emergence of coherent structures and patterns at the nonlinear stage of modulation instability of a uniform state is an inherent feature of many biological, physical and engineering systems. There are several well-studied classical modulation instabilities, such as Benjamin-Feir, Turing and Faraday instability, which play a critical role in the self-organization of energy and matter in non-equilibrium physical, chemical and biological systems. Here we experimentally demonstrate the dissipative Faraday instability induced by spatially periodic zig-zag modulation of a dissipative parameter of the system-spectrally dependent losses-achieving generation of temporal patterns and high-harmonic mode-locking in a fibre laser. We demonstrate features of this instability that distinguish it from both the Benjamin-Feir and the purely dispersive Faraday instability. Our results open the possibilities for new designs of mode-locked lasers and can be extended to other fields of physics and engineering.
Astrophysical Constraints on Planck Scale Dissipative Phenomena
NASA Astrophysics Data System (ADS)
Liberati, Stefano; Maccione, Luca
2014-04-01
The emergence of a classical spacetime from any quantum gravity model is still a subtle and only partially understood issue. If indeed spacetime is arising as some sort of large scale condensate of more fundamental objects, then it is natural to expect that matter, being a collective excitation of the spacetime constituents, will present modified kinematics at sufficiently high energies. We consider here the phenomenology of the dissipative effects necessarily arising in such a picture. Adopting dissipative hydrodynamics as a general framework for the description of the energy exchange between collective excitations and the spacetime fundamental degrees of freedom, we discuss how rates of energy loss for elementary particles can be derived from dispersion relations and used to provide strong constraints on the base of current astrophysical observations of high-energy particles.
Introduction: Dissipative localized structures in extended systems
NASA Astrophysics Data System (ADS)
Tlidi, Mustapha; Taki, Majid; Kolokolnikov, Theodore
2007-09-01
Localized structures belong to the class of dissipative structures found far from equilibrium. Contributions from the most representative groups working on a various fields of natural science such as biology, chemistry, plant ecology, mathematics, optics, and laser physics are presented. The aim of this issue is to gather specialists from these fields towards a cross-fertilization among these active areas of research and thereby to present an overview of the state of art in the formation and the characterization of dissipative localized structures. Nonlinear optics and laser physics have an important part in this issue because of potential applications in information technology. In particular, localized structures could be used as "bits" for parallel information storage and processing.
Universality in dissipative Landau-Zener transitions
Orth, Peter P.; Le Hur, Karyn; Imambekov, Adilet
2010-09-15
We introduce a random-variable approach to investigate the dynamics of a dissipative two-state system. Based on an exact functional integral description, our method reformulates the problem as that of the time evolution of a quantum state vector subject to a Hamiltonian containing random noise fields. This numerically exact, nonperturbative formalism is particularly well suited in the context of time-dependent Hamiltonians, at both zero and finite temperature. As an important example, we consider the renowned Landau-Zener problem in the presence of an Ohmic environment with a large cutoff frequency at finite temperature. We investigate the ''scaling'' limit of the problem at intermediate times, where the decay of the upper-spin-state population is universal. Such a dissipative situation may be implemented using a cold-atom bosonic setup.
Structures of nonequilibrium fluctuations: dissipation and activity
NASA Astrophysics Data System (ADS)
Wynants, Bram
2010-11-01
We discuss research done in two important areas of nonequilibrium statistical mechanics: fluctuation dissipation relations and dynamical fluctuations. In equilibrium systems the fluctuation-dissipation theorem gives a simple relation between the response of observables to a perturation and correlation functions in the unperturbed system. Our contribution here is an investigation of the form of the response function for systems out of equilibrium. Furthermore, we use the theory of large deviations to examine dynamical fluctuations in systems out of equilibrium. In dynamical fluctuation theory we consider two kinds of observables: occupations (describing the fraction of time the system spends in each configuration) and currents (describing the changes of configuration the system makes). We explain how to compute the rate functions of the large deviations, and what the physical quantities are that govern their form.
INFLATING HOT JUPITERS WITH OHMIC DISSIPATION
Batygin, Konstantin; Stevenson, David J.
2010-05-10
We present a new, magnetohydrodynamic mechanism for inflation of close-in giant extrasolar planets. The idea behind the mechanism is that current, which is induced through interaction of atmospheric winds and the planetary magnetic field, results in significant Ohmic dissipation of energy in the interior. We develop an analytical model for computation of interior Ohmic dissipation, with a simplified treatment of the atmosphere. We apply our model to HD209458b, Tres-4b, and HD189733b. With conservative assumptions for wind speed and field strength, our model predicts a generated power that appears to be large enough to maintain the transit radii, opening an unexplored avenue toward solving a decade-old puzzle of extrasolar gas giant radius anomalies.
Dissipation effects in North Atlantic Ocean modeling
NASA Astrophysics Data System (ADS)
Dietrich, D. E.; Mehra, A.; Haney, R. L.; Bowman, M. J.; Tseng, Y. H.
2004-03-01
Numerical experiments varying lateral viscosity and diffusivity between 20 and 150 m2/s in a North Atlantic Ocean (NAO) model having 4th-order accurate numerics, in which the dense deep current system (DCS) from the northern seas and Arctic Ocean is simulated directly show that Gulf Stream (GS) separation is strongly affected by the dissipation of the DCS. This is true even though the separation is highly inertial with large Reynolds number for GS separation flow scales. We show that realistic NAO modeling requires less than 150 m2/s viscosity and diffusivity in order to maintain the DCS material current with enough intensity to get realistic GS separation near Cape Hatteras (CH). This also demands accurate, low dissipation numerics, because of the long transit time (1-10 years) of DCS material from its northern seas and Arctic Ocean source regions to the Cape Hatteras region and the small lateral and vertical scales of DCS.
Wave Dissipation and Balance - NOPP Wave Project
2014-09-30
processes that affect wind-generated ocean gravity waves. The various dissipative processes that contribute to the spectral wave evolution are isolated...over mature ocean surface wave spectra. J. Phys. Oceanogr., 34:3345–2358, 2004. K. Hasselmann. On the non-linear energy transfer in a gravity wave...P. Giovanangeli. Air flow structure over short- gravity breaking water waves. Boundary-Layer Meteorol., 126:477–705, 2008. doi: 10.1007/s10546-007
Wave Dissipation and Balance - NOPP Wave Project
2011-09-01
with a common structure , and now estimating the “cumulative term” with the breaking probabilities used for the main dissipation term. This has led to a...captured by the new parameterizations, but that will require the analysis of more detailed measurement campaigns Ardhuin et al. (2011b). These result have...much more flat bias as a function of wave height (figure 1). A detailed case study of the February 2011 storm Quirin, in the North Atlantic, has shown
NASA Astrophysics Data System (ADS)
Shamolin, M. V.
2016-12-01
Integrability in elementary functions is demonstrated for some classes of dynamic systems on tangent bundles of two- and three-dimensional spheres. The force fields possess the so-called variable dissipation with a zero mean and generalize those considered earlier.
Low Energy Dissipation Nano Device Research
NASA Astrophysics Data System (ADS)
Yu, Jenny
2015-03-01
The development of research on energy dissipation has been rapid in energy efficient area. Nano-material power FET is operated as an RF power amplifier, the transport is ballistic, noise is limited and power dissipation is minimized. The goal is Green-save energy by developing the Graphene and carbon nantube microwave and high performance devices. Higher performing RF amplifiers can have multiple impacts on broadly field, for example communication equipment, (such as mobile phone and RADAR); higher power density and lower power dissipation will improve spectral efficiency which translates into higher system level bandwidth and capacity for communications equipment. Thus, fundamental studies of power handling capabilities of new RF (nano)technologies can have broad, sweeping impact. Because it is critical to maximizing the power handling ability of grephene and carbon nanotube FET, the initial task focuses on measuring and understanding the mechanism of electrical breakdown. We aim specifically to determine how the breakdown voltage in graphene and nanotubes is related to the source-drain spacing, electrode material and thickness, and substrate, and thus develop reliable statistics on the breakdown mechanism and probability.
Estimation of turbulent kinetic energy dissipation
NASA Astrophysics Data System (ADS)
Chen, Huey-Long; Hondzo, Miki; Rao, A. Ramachandra
2001-06-01
The kinetic energy dissipation rate is one of the key intrinsic fluid flow parameters in environmental fluid dynamics. In an indirect method the kinetic energy dissipation rate is estimated from the Batchelor spectrum. Because the Batchelor spectrum has a significant difference between the highest and lowest spectral values, the spectral bias in the periodogram causes the lower spectral values at higher frequencies to increase. Consequently, the accuracy in fitting the Batchelor spectrum is affected. In this study, the multitaper spectral estimation method is compared to conventional methods in estimating the synthetic temperature gradient spectra. It is shown in the results that the multitaper spectra have less bias than the Hamming window smoothed spectra and the periodogram in estimating the synthetic temperature gradient spectra. The results of fitting the Batchelor spectrum based on four error functions are compared. When the theoretical noise spectrum is available and delineated at the intersection of the estimated spectrum, the fitting results of the kinetic energy dissipation rate corresponding to the four error functions do not have significant differences. However, when the noise spectrum is unknown and part of the Batchelor spectrum overlaps the region where the noise spectrum dominates, the weighted chi-square distributed error function has the best fitting results.
Nonlinear Landau damping and Alfven wave dissipation
NASA Technical Reports Server (NTRS)
Vinas, Adolfo F.; Miller, James A.
1995-01-01
Nonlinear Landau damping has been often suggested to be the cause of the dissipation of Alfven waves in the solar wind as well as the mechanism for ion heating and selective preacceleration in solar flares. We discuss the viability of these processes in light of our theoretical and numerical results. We present one-dimensional hybrid plasma simulations of the nonlinear Landau damping of parallel Alfven waves. In this scenario, two Alfven waves nonresonantly combine to create second-order magnetic field pressure gradients, which then drive density fluctuations, which in turn drive a second-order longitudinal electric field. Under certain conditions, this electric field strongly interacts with the ambient ions via the Landau resonance which leads to a rapid dissipation of the Alfven wave energy. While there is a net flux of energy from the waves to the ions, one of the Alfven waves will grow if both have the same polarization. We compare damping and growth rates from plasma simulations with those predicted by Lee and Volk (1973), and also discuss the evolution of the ambient ion distribution. We then consider this nonlinear interaction in the presence of a spectrum of Alfven waves, and discuss the spectrum's influence on the growth or damping of a single wave. We also discuss the implications for wave dissipation and ion heating in the solar wind.
Magnetotail energy dissipation during an auroral substorm.
Panov, E V; Baumjohann, W; Wolf, R A; Nakamura, R; Angelopoulos, V; Weygand, J M; Kubyshkina, M V
2016-12-01
Violent releases of space plasma energy from the Earth's magnetotail during substorms produce strong electric currents and bright aurora. But what modulates these currents and aurora and controls dissipation of the energy released in the ionosphere? Using data from the THEMIS fleet of satellites and ground-based imagers and magnetometers, we show that plasma energy dissipation is controlled by field-aligned currents (FACs) produced and modulated during magnetotail topology change and oscillatory braking of fast plasma jets at 10-14 Earth radii in the nightside magnetosphere. FACs appear in regions where plasma sheet pressure and flux tube volume gradients are non-collinear. Faster tailward expansion of magnetotail dipolarization and subsequent slower inner plasma sheet restretching during substorm expansion and recovery phases cause faster poleward then slower equatorward movement of the substorm aurora. Anharmonic radial plasma oscillations build up displaced current filaments and are responsible for discrete longitudinal auroral arcs that move equatorward at a velocity of about 1km/s. This observed auroral activity appears sufficient to dissipate the released energy.
Dissipative Continuous Spontaneous Localization (CSL) model
Smirne, Andrea; Bassi, Angelo
2015-01-01
Collapse models explain the absence of quantum superpositions at the macroscopic scale, while giving practically the same predictions as quantum mechanics for microscopic systems. The Continuous Spontaneous Localization (CSL) model is the most refined and studied among collapse models. A well-known problem of this model, and of similar ones, is the steady and unlimited increase of the energy induced by the collapse noise. Here we present the dissipative version of the CSL model, which guarantees a finite energy during the entire system’s evolution, thus making a crucial step toward a realistic energy-conserving collapse model. This is achieved by introducing a non-linear stochastic modification of the Schrödinger equation, which represents the action of a dissipative finite-temperature collapse noise. The possibility to introduce dissipation within collapse models in a consistent way will have relevant impact on the experimental investigations of the CSL model, and therefore also on the testability of the quantum superposition principle. PMID:26243034
Landing Energy Dissipation for Manned Reentry Vehicles
NASA Technical Reports Server (NTRS)
Fisher, Lloyd J., Jr.
1960-01-01
Analytical and experimental investigations have been made to determine the landing-energy-dissipation characteristics for several types of landing gear for manned reentry vehicles. The landing vehicles are considered in two categories: those having essentially vertical-descent paths, the parachute-supported vehicles, and those having essentially horizontal paths, the lifting vehicles. The energy-dissipation devices discussed are crushable materials such as foamed plastics and honeycomb for internal application in couch-support systems, yielding metal elements as part of the structure of capsules or as alternates for oleos in landing-gear struts, inflatable bags, braking rockets, and shaped surfaces for water impact. It appears feasible to readily evaluate landing-gear systems for internal or external application in hard-surface or water landings by using computational procedures and free-body landing techniques with dynamic models. The systems investigated have shown very interesting energy-dissipation characteristics over a considerable range of landing parameters. Acceptable gear can be developed along lines similar to those presented if stroke requirements and human-tolerance limits are considered.
Modeling open boundaries in dissipative MHD simulation
NASA Astrophysics Data System (ADS)
Meier, E. T.; Glasser, A. H.; Lukin, V. S.; Shumlak, U.
2012-04-01
The truncation of large physical domains to concentrate computational resources is necessary or desirable in simulating many natural and man-made plasma phenomena. Three open boundary condition (BC) methods for such domain truncation of dissipative magnetohydrodynamics (MHD) problems are described and compared here. A novel technique, lacuna-based open boundary conditions (LOBC), is presented for applying open BC to dissipative MHD and other hyperbolic and mixed hyperbolic-parabolic systems of partial differential equations. LOBC, based on manipulating Calderon-type near-boundary sources, essentially damp hyperbolic effects in an exterior region attached to the simulation domain and apply BC appropriate for the remaining parabolic effects (if present) at the exterior region boundary. Another technique, approximate Riemann BC (ARBC), is adapted from finite volume and discontinuous Galerkin methods. In ARBC, the value of incoming flux is specified using a local, characteristic-based method. A third commonly-used open BC, zero-normal derivative BC (ZND BC), is presented for comparison. These open BC are tested in several gas dynamics and dissipative MHD problems. LOBC are found to give stable, low-reflection solutions even in the presence of strong parabolic behavior, while ARBC are stable only when hyperbolic behavior is dominant. Pros and cons of the techniques are discussed and put into context within the body of open BC research to date.
Symmetry boundary condition in dissipative particle dynamics
NASA Astrophysics Data System (ADS)
Pal, Souvik; Lan, Chuanjin; Li, Zhen; Hirleman, E. Daniel; Ma, Yanbao
2015-07-01
Dissipative particle dynamics (DPD) is a coarse-grained particle method for modeling mesoscopic hydrodynamics. Most of the DPD simulations are carried out in 3D requiring remarkable computation time. For symmetric systems, this time can be reduced significantly by simulating only one half or one quarter of the systems. However, such simulations are not yet possible due to a lack of schemes to treat symmetric boundaries in DPD. In this study, we propose a numerical scheme for the implementation of the symmetric boundary condition (SBC) in both dissipative particle dynamics (DPD) and multibody dissipative particle dynamics (MDPD) using a combined ghost particles and specular reflection (CGPSR) method. We validate our scheme in four different configurations. The results demonstrate that our scheme can accurately reproduce the system properties, such as velocity, density and meniscus shapes of a full system with numerical simulations of a subsystem. Using a symmetric boundary condition for one half of the system, we demonstrate about 50% computation time saving in both DPD and MDPD. This approach for symmetric boundary treatment can be also applied to other coarse-grained particle methods such as Brownian and Langevin Dynamics to significantly reduce computation time.
Magnetotail energy dissipation during an auroral substorm
Panov, E.V.; Baumjohann, W.; Wolf, R.A.; Nakamura, R.; Angelopoulos, V.; Weygand, J. M.; Kubyshkina, M.V.
2016-01-01
Violent releases of space plasma energy from the Earth’s magnetotail during substorms produce strong electric currents and bright aurora. But what modulates these currents and aurora and controls dissipation of the energy released in the ionosphere? Using data from the THEMIS fleet of satellites and ground-based imagers and magnetometers, we show that plasma energy dissipation is controlled by field-aligned currents (FACs) produced and modulated during magnetotail topology change and oscillatory braking of fast plasma jets at 10-14 Earth radii in the nightside magnetosphere. FACs appear in regions where plasma sheet pressure and flux tube volume gradients are non-collinear. Faster tailward expansion of magnetotail dipolarization and subsequent slower inner plasma sheet restretching during substorm expansion and recovery phases cause faster poleward then slower equatorward movement of the substorm aurora. Anharmonic radial plasma oscillations build up displaced current filaments and are responsible for discrete longitudinal auroral arcs that move equatorward at a velocity of about 1km/s. This observed auroral activity appears sufficient to dissipate the released energy. PMID:27917231
Rings and boxes in dissipative environments
NASA Astrophysics Data System (ADS)
Horovitz, Baruch
2012-02-01
We study a particle on a ring in presence of a dissipative Caldeira-Leggett environment and derive its response to a DC field [1]. We find, through a 2-loop renormalization group analysis, that a large dissipation parameter η flows to a fixed point R̂=/2π. We also reexamine the mapping of this problem to that of the Coulomb box and show that the relaxation resistance, of recent interest, has a certain average that is quantized for η>R̂, leading to quantized noise. We propose a box experiment to detect this noise. When the particle carries a spin with spin-orbit interactions [2] we find that the spin correlations in the direction perpendicular to the ring are finite at long times, i.e. do not dephase, while the parallel components may decay as a power law at strong dissipation. [4pt] [1] Y. Etzioni, B. Horovitz and P. Le Doussal, Phys. Rev. Lett. 106, 166803 (2011). [0pt] [2] G. Zar'and, G. T. Zim'anyi and F. Wilhelm, Phys. Rev. B62, 8137 (2000).
Magnetotail energy dissipation during an auroral substorm
NASA Astrophysics Data System (ADS)
Panov, E. V.; Baumjohann, W.; Wolf, R. A.; Nakamura, R.; Angelopoulos, V.; Weygand, J. M.; Kubyshkina, M. V.
2016-12-01
Violent releases of space plasma energy from the Earth's magnetotail during substorms produce strong electric currents and bright aurora. But what modulates these currents and aurora and controls dissipation of the energy released in the ionosphere? Using data from the THEMIS fleet of satellites and ground-based imagers and magnetometers, we show that plasma energy dissipation is controlled by field-aligned currents (FACs) produced and modulated during magnetotail topology change and oscillatory braking of fast plasma jets at 10-14 Earth radii in the nightside magnetosphere. FACs appear in regions where plasma sheet pressure and flux tube volume gradients are non-collinear. Faster tailward expansion of magnetotail dipolarization and subsequent slower inner plasma sheet restretching during substorm expansion and recovery phases cause faster poleward then slower equatorward movement of the substorm aurora. Anharmonic radial plasma oscillations build up displaced current filaments and are responsible for discrete longitudinal auroral arcs that move equatorward at a velocity of about 1 km s-1. This observed auroral activity appears sufficient to dissipate the released energy.
Doubly transient chaos: generic form of chaos in autonomous dissipative systems.
Motter, Adilson E; Gruiz, Márton; Károlyi, György; Tél, Tamás
2013-11-08
Chaos is an inherently dynamical phenomenon traditionally studied for trajectories that are either permanently erratic or transiently influenced by permanently erratic ones lying on a set of measure zero. The latter gives rise to the final state sensitivity observed in connection with fractal basin boundaries in conservative scattering systems and driven dissipative systems. Here we focus on the most prevalent case of undriven dissipative systems, whose transient dynamics fall outside the scope of previous studies since no time-dependent solutions can exist for asymptotically long times. We show that such systems can exhibit positive finite-time Lyapunov exponents and fractal-like basin boundaries which nevertheless have codimension one. In sharp contrast to its driven and conservative counterparts, the settling rate to the (fixed-point) attractors grows exponentially in time, meaning that the fraction of trajectories away from the attractors decays superexponentially. While no invariant chaotic sets exist in such cases, the irregular behavior is governed by transient interactions with transient chaotic saddles, which act as effective, time-varying chaotic sets.
Doubly Transient Chaos: Generic Form of Chaos in Autonomous Dissipative Systems
NASA Astrophysics Data System (ADS)
Motter, Adilson E.; Gruiz, Márton; Károlyi, György; Tél, Tamás
2013-11-01
Chaos is an inherently dynamical phenomenon traditionally studied for trajectories that are either permanently erratic or transiently influenced by permanently erratic ones lying on a set of measure zero. The latter gives rise to the final state sensitivity observed in connection with fractal basin boundaries in conservative scattering systems and driven dissipative systems. Here we focus on the most prevalent case of undriven dissipative systems, whose transient dynamics fall outside the scope of previous studies since no time-dependent solutions can exist for asymptotically long times. We show that such systems can exhibit positive finite-time Lyapunov exponents and fractal-like basin boundaries which nevertheless have codimension one. In sharp contrast to its driven and conservative counterparts, the settling rate to the (fixed-point) attractors grows exponentially in time, meaning that the fraction of trajectories away from the attractors decays superexponentially. While no invariant chaotic sets exist in such cases, the irregular behavior is governed by transient interactions with transient chaotic saddles, which act as effective, time-varying chaotic sets.
Size Matters: Individual Variation in Ectotherm Growth and Asymptotic Size
King, Richard B.
2016-01-01
Body size, and, by extension, growth has impacts on physiology, survival, attainment of sexual maturity, fecundity, generation time, and population dynamics, especially in ectotherm animals that often exhibit extensive growth following attainment of sexual maturity. Frequently, growth is analyzed at the population level, providing useful population mean growth parameters but ignoring individual variation that is also of ecological and evolutionary significance. Our long-term study of Lake Erie Watersnakes, Nerodia sipedon insularum, provides data sufficient for a detailed analysis of population and individual growth. We describe population mean growth separately for males and females based on size of known age individuals (847 captures of 769 males, 748 captures of 684 females) and annual growth increments of individuals of unknown age (1,152 males, 730 females). We characterize individual variation in asymptotic size based on repeated measurements of 69 males and 71 females that were each captured in five to nine different years. The most striking result of our analyses is that asymptotic size varies dramatically among individuals, ranging from 631–820 mm snout-vent length in males and from 835–1125 mm in females. Because female fecundity increases with increasing body size, we explore the impact of individual variation in asymptotic size on lifetime reproductive success using a range of realistic estimates of annual survival. When all females commence reproduction at the same age, lifetime reproductive success is greatest for females with greater asymptotic size regardless of annual survival. But when reproduction is delayed in females with greater asymptotic size, lifetime reproductive success is greatest for females with lower asymptotic size when annual survival is low. Possible causes of individual variation in asymptotic size, including individual- and cohort-specific variation in size at birth and early growth, warrant further investigation. PMID
Size Matters: Individual Variation in Ectotherm Growth and Asymptotic Size.
King, Richard B; Stanford, Kristin M; Jones, Peter C; Bekker, Kent
2016-01-01
Body size, and, by extension, growth has impacts on physiology, survival, attainment of sexual maturity, fecundity, generation time, and population dynamics, especially in ectotherm animals that often exhibit extensive growth following attainment of sexual maturity. Frequently, growth is analyzed at the population level, providing useful population mean growth parameters but ignoring individual variation that is also of ecological and evolutionary significance. Our long-term study of Lake Erie Watersnakes, Nerodia sipedon insularum, provides data sufficient for a detailed analysis of population and individual growth. We describe population mean growth separately for males and females based on size of known age individuals (847 captures of 769 males, 748 captures of 684 females) and annual growth increments of individuals of unknown age (1,152 males, 730 females). We characterize individual variation in asymptotic size based on repeated measurements of 69 males and 71 females that were each captured in five to nine different years. The most striking result of our analyses is that asymptotic size varies dramatically among individuals, ranging from 631-820 mm snout-vent length in males and from 835-1125 mm in females. Because female fecundity increases with increasing body size, we explore the impact of individual variation in asymptotic size on lifetime reproductive success using a range of realistic estimates of annual survival. When all females commence reproduction at the same age, lifetime reproductive success is greatest for females with greater asymptotic size regardless of annual survival. But when reproduction is delayed in females with greater asymptotic size, lifetime reproductive success is greatest for females with lower asymptotic size when annual survival is low. Possible causes of individual variation in asymptotic size, including individual- and cohort-specific variation in size at birth and early growth, warrant further investigation.
Asymptotics of bivariate generating functions with algebraic singularities
NASA Astrophysics Data System (ADS)
Greenwood, Torin
Flajolet and Odlyzko (1990) derived asymptotic formulae the coefficients of a class of uni- variate generating functions with algebraic singularities. Gao and Richmond (1992) and Hwang (1996, 1998) extended these results to classes of multivariate generating functions, in both cases by reducing to the univariate case. Pemantle and Wilson (2013) outlined new multivariate ana- lytic techniques and used them to analyze the coefficients of rational generating functions. After overviewing these methods, we use them to find asymptotic formulae for the coefficients of a broad class of bivariate generating functions with algebraic singularities. Beginning with the Cauchy integral formula, we explicity deform the contour of integration so that it hugs a set of critical points. The asymptotic contribution to the integral comes from analyzing the integrand near these points, leading to explicit asymptotic formulae. Next, we use this formula to analyze an example from current research. In the following chapter, we apply multivariate analytic techniques to quan- tum walks. Bressler and Pemantle (2007) found a (d + 1)-dimensional rational generating function whose coefficients described the amplitude of a particle at a position in the integer lattice after n steps. Here, the minimal critical points form a curve on the (d + 1)-dimensional unit torus. We find asymptotic formulae for the amplitude of a particle in a given position, normalized by the number of steps n, as n approaches infinity. Each critical point contributes to the asymptotics for a specific normalized position. Using Groebner bases in Maple again, we compute the explicit locations of peak amplitudes. In a scaling window of size the square root of n near the peaks, each amplitude is asymptotic to an Airy function.
A statistical mechanical approach for the computation of the climatic response to general forcings
NASA Astrophysics Data System (ADS)
Lucarini, V.; Sarno, S.
2011-01-01
The climate belongs to the class of non-equilibrium forced and dissipative systems, for which most results of quasi-equilibrium statistical mechanics, including the fluctuation-dissipation theorem, do not apply. In this paper we show for the first time how the Ruelle linear response theory, developed for studying rigorously the impact of perturbations on general observables of non-equilibrium statistical mechanical systems, can be applied with great success to analyze the climatic response to general forcings. The crucial value of the Ruelle theory lies in the fact that it allows to compute the response of the system in terms of expectation values of explicit and computable functions of the phase space averaged over the invariant measure of the unperturbed state. We choose as test bed a classical version of the Lorenz 96 model, which, in spite of its simplicity, has a well-recognized prototypical value as it is a spatially extended one-dimensional model and presents the basic ingredients, such as dissipation, advection and the presence of an external forcing, of the actual atmosphere. We recapitulate the main aspects of the general response theory and propose some new general results. We then analyze the frequency dependence of the response of both local and global observables to perturbations having localized as well as global spatial patterns. We derive analytically several properties of the corresponding susceptibilities, such as asymptotic behavior, validity of Kramers-Kronig relations, and sum rules, whose main ingredient is the causality principle. We show that all the coefficients of the leading asymptotic expansions as well as the integral constraints can be written as linear function of parameters that describe the unperturbed properties of the system, such as its average energy. Some newly obtained empirical closure equations for such parameters allow to define such properties as an explicit function of the unperturbed forcing parameter alone for a
Oliveira, Diego F M; Leonel, Edson D
2012-06-01
Some dynamical properties for a time dependent Lorentz gas considering both the dissipative and non dissipative dynamics are studied. The model is described by using a four-dimensional nonlinear mapping. For the conservative dynamics, scaling laws are obtained for the behavior of the average velocity for an ensemble of non interacting particles and the unlimited energy growth is confirmed. For the dissipative case, four different kinds of damping forces are considered namely: (i) restitution coefficient which makes the particle experiences a loss of energy upon collisions; and in-flight dissipation given by (ii) F=-ηV(2); (iii) F=-ηV(μ) with μ≠1 and μ≠2 and; (iv) F=-ηV, where η is the dissipation parameter. Extensive numerical simulations were made and our results confirm that the unlimited energy growth, observed for the conservative dynamics, is suppressed for the dissipative case. The behaviour of the average velocity is described using scaling arguments and classes of universalities are defined.
Hybrid molecular-continuum simulations using smoothed dissipative particle dynamics.
Petsev, Nikolai D; Leal, L Gary; Shell, M Scott
2015-01-28
We present a new multiscale simulation methodology for coupling a region with atomistic detail simulated via molecular dynamics (MD) to a numerical solution of the fluctuating Navier-Stokes equations obtained from smoothed dissipative particle dynamics (SDPD). In this approach, chemical potential gradients emerge due to differences in resolution within the total system and are reduced by introducing a pairwise thermodynamic force inside the buffer region between the two domains where particles change from MD to SDPD types. When combined with a multi-resolution SDPD approach, such as the one proposed by Kulkarni et al. [J. Chem. Phys. 138, 234105 (2013)], this method makes it possible to systematically couple atomistic models to arbitrarily coarse continuum domains modeled as SDPD fluids with varying resolution. We test this technique by showing that it correctly reproduces thermodynamic properties across the entire simulation domain for a simple Lennard-Jones fluid. Furthermore, we demonstrate that this approach is also suitable for non-equilibrium problems by applying it to simulations of the start up of shear flow. The robustness of the method is illustrated with two different flow scenarios in which shear forces act in directions parallel and perpendicular to the interface separating the continuum and atomistic domains. In both cases, we obtain the correct transient velocity profile. We also perform a triple-scale shear flow simulation where we include two SDPD regions with different resolutions in addition to a MD domain, illustrating the feasibility of a three-scale coupling.
Hybrid molecular-continuum simulations using smoothed dissipative particle dynamics
Petsev, Nikolai D.; Leal, L. Gary; Shell, M. Scott
2015-01-28
We present a new multiscale simulation methodology for coupling a region with atomistic detail simulated via molecular dynamics (MD) to a numerical solution of the fluctuating Navier-Stokes equations obtained from smoothed dissipative particle dynamics (SDPD). In this approach, chemical potential gradients emerge due to differences in resolution within the total system and are reduced by introducing a pairwise thermodynamic force inside the buffer region between the two domains where particles change from MD to SDPD types. When combined with a multi-resolution SDPD approach, such as the one proposed by Kulkarni et al. [J. Chem. Phys. 138, 234105 (2013)], this method makes it possible to systematically couple atomistic models to arbitrarily coarse continuum domains modeled as SDPD fluids with varying resolution. We test this technique by showing that it correctly reproduces thermodynamic properties across the entire simulation domain for a simple Lennard-Jones fluid. Furthermore, we demonstrate that this approach is also suitable for non-equilibrium problems by applying it to simulations of the start up of shear flow. The robustness of the method is illustrated with two different flow scenarios in which shear forces act in directions parallel and perpendicular to the interface separating the continuum and atomistic domains. In both cases, we obtain the correct transient velocity profile. We also perform a triple-scale shear flow simulation where we include two SDPD regions with different resolutions in addition to a MD domain, illustrating the feasibility of a three-scale coupling.
Dissipative particle dynamics incorporating non-Markovian effect
NASA Astrophysics Data System (ADS)
Kinefuchi, Ikuya; Yoshimoto, Yuta; Takagi, Shu
2015-11-01
The coarse-graining methodology of molecular simulations is of great importance to analyze large-scale, complex hydrodynamic phenomena. In the present study, we derive the equation of motion for non-Markovian dissipative particle dynamics (NMDPD) by introducing the history effects on the time evolution of the system. Our formulation is based on the generalized Langevin equation, which describes the motions of the centers of mass of clusters comprising microscopic particles. The mean, friction, and fluctuating forces in the NMDPD model are directly constructed from an underlying MD system without any scaling procedure. For the validation of our formulation, we construct NMDPD models from high-density Lennard-Jones systems, in which the typical time scales of the coarse-grained particle motions and the fluctuating forces are not fully separable. The NMDPD models reproduce the temperatures, diffusion coefficients, and viscosities of the corresponding MD systems more accurately than the conventional DPD models based on a Markovian approximation. Our results suggest that the NMDPD method is a promising alternative for simulating mesoscale flows where a Markovian approximation is not valid.
Finite-size effects in dissipative particle dynamics simulations.
Velázquez, María Eugenia; Gama-Goicochea, Armando; González-Melchor, Minerva; Neria, Maricela; Alejandre, José
2006-02-28
We have performed dissipative particle dynamics (DPD) simulations to evaluate the effect that finite size of transversal area has on stress anisotropy and interfacial tension. The simulations were carried out in one phase and two phases in parallelepiped cells. In one-phase simulations there is no finite-size effect on stress anisotropy when the simulation is performed using repulsive forces. However, an oscillatory function of stress anisotropy is found for attractive-repulsive interactions. In the case of liquid-liquid interfaces with repulsive interaction between molecules, there is only a small effect of surface area on interfacial tension when the simulations are performed using the Monte Carlo method at constant temperature and normal pressure. An important but artificial finite-size effect of interfacial area on surface tension is found in simulations in the canonical ensemble. Reliable results of interfacial tension from DPD simulations can be obtained using small systems, less than 2000 particles, when they interact exclusively with repulsive forces.
Su, Hongling; Li, Shengtai
2016-02-03
In this study, we propose two new energy/dissipation-preserving Birkhoffian multi-symplectic methods (Birkhoffian and Birkhoffian box) for Maxwell's equations with dissipation terms. After investigating the non-autonomous and autonomous Birkhoffian formalism for Maxwell's equations with dissipation terms, we first apply a novel generating functional theory to the non-autonomous Birkhoffian formalism to propose our Birkhoffian scheme, and then implement a central box method to the autonomous Birkhoffian formalism to derive the Birkhoffian box scheme. We have obtained four formal local conservation laws and three formal energy global conservation laws. We have also proved that both of our derived schemes preserve the discrete versionmore » of the global/local conservation laws. Furthermore, the stability, dissipation and dispersion relations are also investigated for the schemes. Theoretical analysis shows that the schemes are unconditionally stable, dissipation-preserving for Maxwell's equations in a perfectly matched layer (PML) medium and have second order accuracy in both time and space. Numerical experiments for problems with exact theoretical results are given to demonstrate that the Birkhoffian multi-symplectic schemes are much more accurate in preserving energy than both the exponential finite-difference time-domain (FDTD) method and traditional Hamiltonian scheme. Finally, we also solve the electromagnetic pulse (EMP) propagation problem and the numerical results show that the Birkhoffian scheme recovers the magnitude of the current source and reaction history very well even after long time propagation.« less
Su, Hongling; Li, Shengtai
2016-02-03
In this study, we propose two new energy/dissipation-preserving Birkhoffian multi-symplectic methods (Birkhoffian and Birkhoffian box) for Maxwell's equations with dissipation terms. After investigating the non-autonomous and autonomous Birkhoffian formalism for Maxwell's equations with dissipation terms, we first apply a novel generating functional theory to the non-autonomous Birkhoffian formalism to propose our Birkhoffian scheme, and then implement a central box method to the autonomous Birkhoffian formalism to derive the Birkhoffian box scheme. We have obtained four formal local conservation laws and three formal energy global conservation laws. We have also proved that both of our derived schemes preserve the discrete version of the global/local conservation laws. Furthermore, the stability, dissipation and dispersion relations are also investigated for the schemes. Theoretical analysis shows that the schemes are unconditionally stable, dissipation-preserving for Maxwell's equations in a perfectly matched layer (PML) medium and have second order accuracy in both time and space. Numerical experiments for problems with exact theoretical results are given to demonstrate that the Birkhoffian multi-symplectic schemes are much more accurate in preserving energy than both the exponential finite-difference time-domain (FDTD) method and traditional Hamiltonian scheme. Finally, we also solve the electromagnetic pulse (EMP) propagation problem and the numerical results show that the Birkhoffian scheme recovers the magnitude of the current source and reaction history very well even after long time propagation.
Analysing half-lives for pesticide dissipation in plants.
Jacobsen, R E; Fantke, P; Trapp, S
2015-01-01
Overall dissipation of pesticides from plants is frequently measured, but the contribution of individual loss processes is largely unknown. We use a pesticide fate model for the quantification of dissipation by processes other than degradation. The model was parameterised using field studies. Scenarios were established for Copenhagen/Denmark and Shanghai/PR China, and calibrated with measured results. The simulated dissipation rates of 42 pesticides were then compared with measured overall dissipation from field studies using tomato and wheat. The difference between measured overall dissipation and calculated dissipation by non-degradative processes should ideally be contributable to degradation in plants. In 11% of the cases, calculated dissipation was above the measured dissipation. For the remaining cases, the non-explained dissipation ranged from 30% to 83%, depending on crop type, plant part and scenario. Accordingly, degradation is the most relevant dissipation process for these 42 pesticides, followed by growth dilution. Volatilisation was less relevant, which can be explained by the design of plant protection agents. Uptake of active compound from soil into plants leads to a negative dissipation process (i.e. a gain) that is difficult to quantify because it depends largely on interception, precipitation and plant stage. This process is particularly relevant for soluble compounds.
Coupling mantle convection and tidal dissipation: applications to Enceladus and Earth-like planets
NASA Astrophysics Data System (ADS)
Behounkova, Marie; Tobie, Gabriel; Choblet, Gael; Cadek, Ondrej
2010-05-01
Anelastic dissipation of tidal forces is often proposed to significantly contribute to the thermal budget of several satellites of giant planets and Earth-like planets closely orbiting other stars. In order to address how tidal heating influences the thermal evolution of such bodies, we develop a new numerical tool that solves simultaneously mantle convection and tidal dissipation in a three-dimensional spherical geometry. Since both processes occur at different time scales, we propose a model where tidal dissipation averaged over a forcing period is included as a volumetric heat source for mantle dynamics. In the case of the long-term flow, a purely viscous material is considered. Numerical approach employing a grid-based method Choblet et al. (2007) efficiently solving viscous flow with large lateral viscosity variations is used. For tidal visco-elastic deformations, a Maxwell-like formalism where effective viscosity is introduced in order to reproduce observed dissipation function is employed. This problem is treated in the time domain and uses a combined spectral and grid-based spatial discretization (Tobie et al. 2008). Since both mechanisms are associated to strongly temperature dependent rheological properties, the coupling is achieved via the temperature field. We apply this model to two examples: Enceladus and an Earth-like planet. In both cases, the tidal dissipation focuses in the polar regions owing to the presence of a liquid layer at the base of the mantle. As a consequence, hot upwellings tend to concentrate at high latitudes whereas cold downwellings are mostly located in the equatorial region. In the case of Enceladus, we demonstrate that tidal stresses calculated with our new 3D method are strongly reduced in hot upwellings when compared with classical methods based on radially layered interior models. As a consequence, the classical methods could overestimate tidal dissipation locally by a factor of 2 which can lead to a final difference of more
Black hole thermodynamics from a variational principle: asymptotically conical backgrounds
An, Ok Song; Cvetič, Mirjam; Papadimitriou, Ioannis
2016-03-14
The variational problem of gravity theories is directly related to black hole thermodynamics. For asymptotically locally AdS backgrounds it is known that holographic renormalization results in a variational principle in terms of equivalence classes of boundary data under the local asymptotic symmetries of the theory, which automatically leads to finite conserved charges satisfying the first law of thermodynamics. We show that this connection holds well beyond asymptotically AdS black holes. In particular, we formulate the variational problem for N = 2 STU supergravity in four dimensions with boundary conditions corresponding to those obeyed by the so called ‘subtracted geometries’. Wemore » show that such boundary conditions can be imposed covariantly in terms of a set of asymptotic second class constraints, and we derive the appropriate boundary terms that render the variational problem well posed in two different duality frames of the STU model. This allows us to define finite conserved charges associated with any asymptotic Killing vector and to demonstrate that these charges satisfy the Smarr formula and the first law of thermodynamics. Moreover, by uplifting the theory to five dimensions and then reducing on a 2-sphere, we provide a precise map between the thermodynamic observables of the subtracted geometries and those of the BTZ black hole. Finally, surface terms play a crucial role in this identification.« less
Black hole thermodynamics from a variational principle: asymptotically conical backgrounds
An, Ok Song; Cvetič, Mirjam; Papadimitriou, Ioannis
2016-03-14
The variational problem of gravity theories is directly related to black hole thermodynamics. For asymptotically locally AdS backgrounds it is known that holographic renormalization results in a variational principle in terms of equivalence classes of boundary data under the local asymptotic symmetries of the theory, which automatically leads to finite conserved charges satisfying the first law of thermodynamics. We show that this connection holds well beyond asymptotically AdS black holes. In particular, we formulate the variational problem for N = 2 STU supergravity in four dimensions with boundary conditions corresponding to those obeyed by the so called ‘subtracted geometries’. We show that such boundary conditions can be imposed covariantly in terms of a set of asymptotic second class constraints, and we derive the appropriate boundary terms that render the variational problem well posed in two different duality frames of the STU model. This allows us to define finite conserved charges associated with any asymptotic Killing vector and to demonstrate that these charges satisfy the Smarr formula and the first law of thermodynamics. Moreover, by uplifting the theory to five dimensions and then reducing on a 2-sphere, we provide a precise map between the thermodynamic observables of the subtracted geometries and those of the BTZ black hole. Finally, surface terms play a crucial role in this identification.
Conserved Charges in Asymptotically (Locally) AdS Spacetimes
NASA Astrophysics Data System (ADS)
Marolf, Donald; Kelly, William; Fischetti, Sebastian
When a physical system is complicated and nonlinear, global symmetries and the associated conserved quantities provide some of the most powerful analytic tools to understand its behavior. This is as true in theories with a dynamical spacetime metric as for systems defined on a fixed spacetime background. Chapter 17, 10.1007/978-3-642-41992-8_17 has already discussed the so-called Arnowitt-Deser-Misner (ADM) conserved quantities for asymptotically flat dynamical spacetimes, exploring in detail certain subtleties related to diffeomorphism invariance. In particular, it showed that the correct notion of global symmetry is given by the so-called asymptotic symmetries; equivalence classes of diffeomorphisms with the same asymptotic behavior at infinity. It was also noted that the notion of asymptotic symmetry depends critically on the choice of boundary conditions. Indeed, it is the imposition of boundary conditions that causes the true gauge symmetries to be only a subset of the full diffeomorphism group and thus allows the existence of nontrivial asymptotic symmetries at all.
Preheating in an asymptotically safe quantum field theory
NASA Astrophysics Data System (ADS)
Svendsen, Ole; Moghaddam, Hossein Bazrafshan; Brandenberger, Robert
2016-10-01
We consider reheating in a class of asymptotically safe quantum field theories recently studied in [D. F. Litim and F. Sannino, Asymptotic safety guaranteed, J. High Energy Phys. 12 (2014) 178; D. F. Litim, M. Mojaza, and F. Sannino, Vacuum stability of asymptotically safe gauge-Yukawa theories, J. High Energy Phys. 01 (2016) 081]. These theories allow for an inflationary phase in the very early universe. Inflation ends with a period of reheating. Since the models contain many scalar fields which are intrinsically coupled to the inflaton there is the possibility of parametric resonance instability in the production of these fields, and the danger that the induced curvature fluctuations will become too large. Here we show that the parametric instability indeed arises, and that hence the energy transfer from the inflaton condensate to fluctuating fields is rapid. Demanding that the curvature fluctuations induced by the parametrically amplified entropy modes do not exceed the upper observational bounds puts a lower bound on the number of fields which the model followed in [D. F. Litim and F. Sannino, Asymptotic safety guaranteed, J. High Energy Phys. 12 (2014) 178; D. F. Litim, M. Mojaza, and F. Sannino, Vacuum stability of asymptotically safe gauge-Yukawa theories, J. High Energy Phys. 01 (2016) 081] must contain. This bound also depends on the total number of e -foldings of the inflationary phase.
Estimation of the kinetic energy dissipation in fall-arrest system and manikin during fall impact.
Wu, John Z; Powers, John R; Harris, James R; Pan, Christopher S
2011-04-01
Fall-arrest systems (FASs) have been widely applied to provide a safe stop during fall incidents for occupational activities. The mechanical interaction and kinetic energy exchange between the human body and the fall-arrest system during fall impact is one of the most important factors in FAS ergonomic design. In the current study, we developed a systematic approach to evaluate the energy dissipated in the energy absorbing lanyard (EAL) and in the harness/manikin during fall impact. The kinematics of the manikin and EAL during the impact were derived using the arrest-force time histories that were measured experimentally. We applied the proposed method to analyse the experimental data of drop tests at heights of 1.83 and 3.35 m. Our preliminary results indicate that approximately 84-92% of the kinetic energy is dissipated in the EAL system and the remainder is dissipated in the harness/manikin during fall impact. The proposed approach would be useful for the ergonomic design and performance evaluation of an FAS. STATEMENT OF RELEVANCE: Mechanical interaction, especially kinetic energy exchange, between the human body and the fall-arrest system during fall impact is one of the most important factors in the ergonomic design of a fall-arrest system. In the current study, we propose an approach to quantify the kinetic energy dissipated in the energy absorbing lanyard and in the harness/body system during fall impact.
Magnetic Prandtl number dependence of the kinetic-to-magnetic dissipation ratio
Brandenburg, Axel
2014-08-10
Using direct numerical simulations of three-dimensional hydromagnetic turbulence, either with helical or non-helical forcing, we show that the kinetic-to-magnetic energy dissipation ratio always increases with the magnetic Prandtl number, i.e., the ratio of kinematic viscosity to magnetic diffusivity. This dependence can always be approximated by a power law, but the exponent is not the same in all cases. For non-helical turbulence, the exponent is around 1/3, while for helical turbulence it is between 0.6 and 2/3. In the statistically steady state, the rate of energy conversion from kinetic into magnetic by the dynamo must be equal to the Joule dissipation rate. We emphasize that for both small-scale and large-scale dynamos, the efficiency of the energy conversion depends sensitively on the magnetic Prandtl number, and thus on the microphysical dissipation process. To understand this behavior, we also study shell models of turbulence and one-dimensional passive and active scalar models. We conclude that the magnetic Prandtl number dependence is qualitatively best reproduced in the one-dimensional model as a result of dissipation via localized Alfvén kinks.
Yeow, C H; Lee, P V S; Goh, J C H
2009-08-25
Lack of the necessary magnitude of energy dissipation by lower extremity joint muscles may be implicated in elevated impact stresses present during landing from greater heights. These increased stresses are experienced by supporting tissues like cartilage, ligaments and bones, thus aggravating injury risk. This study sought to investigate frontal plane kinematics, kinetics and energetics of lower extremity joints during landing from different heights. Eighteen male recreational athletes were instructed to perform drop-landing tasks from 0.3- to 0.6-m heights. Force plates and motion-capture system were used to capture ground reaction force and kinematics data, respectively. Joint moment was calculated using inverse dynamics. Joint power was computed as a product of joint moment and angular velocity. Work was defined as joint power integrated over time. Hip and knee joints delivered significantly greater joint power and eccentric work (p<0.05) than the ankle joint at both landing heights. Substantial increase (p<0.05) in eccentric work was noted at the hip joint in response to increasing landing height. Knee and hip joints acted as key contributors to total energy dissipation in the frontal plane with increase in peak ground reaction force (GRF). The hip joint was the top contributor to energy absorption, which indicated a hip-dominant strategy in the frontal plane in response to peak GRF during landing. Future studies should investigate joint motions that can maximize energy dissipation or reduce the need for energy dissipation in the frontal plane at the various joints, and to evaluate their effects on the attenuation of lower extremity injury risk during landing.
Holography of 3D asymptotically flat black holes
NASA Astrophysics Data System (ADS)
Fareghbal, Reza; Hosseini, Seyed Morteza
2015-04-01
We study the asymptotically flat rotating hairy black hole solution of a three-dimensional gravity theory which is given by taking the flat-space limit (zero cosmological constant limit) of new massive gravity. We propose that the dual field theory of the flat-space limit of new massive gravity can be described by a contracted conformal field theory which is invariant under the action of the BMS3 group. Using the flat/contracted conformal field theory correspondence, we construct a stress tensor which yields the conserved charges of the asymptotically flat black hole solution. We check that our expressions of the mass and angular momentum fit with the first law of black hole thermodynamics. Furthermore, by taking the appropriate limit of the Cardy formula in the parent conformal field theory, we find a Cardy-like formula which reproduces the Wald's entropy of the 3D asymptotically flat black hole.
Asymptotically Jλ -statistical equivalent sequences of weight g
NASA Astrophysics Data System (ADS)
Savaş, Ekrem
2016-08-01
This paper presents the following definition which is a natural combination of the definition for asymptotically equivalent of weight g, J -statistically limit, and λ - statistical convergence, where g :ℕ →[0 , ∞ ) is a function satisfying g (n) → ∞ and g(n) ↛ 0. The two nonnegative sequences x = (xk) and y = (yk) are said to be asymptotically Jg -statistical equivalent of weight g to multiple L provided that for every ɛ > 0, and δ > 0, {n ∈ℕ : 1/g (λn) |{k ∈In:|x/k yk -L | ≥ɛ }| ≥δ }∈J , (denoted by x ˜SλL(I) g y ) and simply asymptotically Jg -statistical equivalent of weight g if L = 1. In addition, we shall also present some inclusion theorems.
Revisiting r > g-The asymptotic dynamics of wealth inequality
NASA Astrophysics Data System (ADS)
Berman, Yonatan; Shapira, Yoash
2017-02-01
Studying the underlying mechanisms of wealth inequality dynamics is essential for its understanding and for policy aiming to regulate its level. We apply a heterogeneous non-interacting agent-based modeling approach, solved using iterated maps to model the dynamics of wealth inequality based on 3 parameters-the economic output growth rate g, the capital value change rate a and the personal savings rate s and show that for a < g the wealth distribution reaches an asymptotic shape and becomes close to the income distribution. If a > g, the wealth distribution constantly becomes more and more inegalitarian. We also show that when a < g, wealth is asymptotically accumulated at the same rate as the economic output, which also implies that the wealth-disposable income ratio asymptotically converges to s /(g - a) .
A new class of asymptotically non-chaotic vacuum singularities
Klinger, Paul
2015-12-15
The BKL conjecture, stated in the 1960s and early 1970s by Belinski, Khalatnikov and Lifschitz, proposes a detailed description of the generic asymptotic dynamics of spacetimes as they approach a spacelike singularity. It predicts complicated chaotic behaviour in the generic case, but simpler non-chaotic one in cases with symmetry assumptions or certain kinds of matter fields. Here we construct a new class of four-dimensional vacuum spacetimes containing spacelike singularities which show non-chaotic behaviour. In contrast with previous constructions, no symmetry assumptions are made. Rather, the metric is decomposed in Iwasawa variables and conditions on the asymptotic evolution of some of them are imposed. The constructed solutions contain five free functions of all space coordinates, two of which are constrained by inequalities. We investigate continuous and discrete isometries and compare the solutions to previous constructions. Finally, we give the asymptotic behaviour of the metric components and curvature.
Asymptotically free scaling solutions in non-Abelian Higgs models
NASA Astrophysics Data System (ADS)
Gies, Holger; Zambelli, Luca
2015-07-01
We construct asymptotically free renormalization group trajectories for the generic non-Abelian Higgs model in four-dimensional spacetime. These ultraviolet-complete trajectories become visible by generalizing the renormalization/boundary conditions in the definition of the correlation functions of the theory. Though they are accessible in a controlled weak-coupling analysis, these trajectories originate from threshold phenomena which are missed in a conventional perturbative analysis relying on the deep Euclidean region. We identify a candidate three-parameter family of renormalization group trajectories interconnecting the asymptotically free ultraviolet regime with a Higgs phase in the low-energy limit. We provide estimates of their low-energy properties in the light of a possible application to the standard model Higgs sector. Finally, we find a two-parameter subclass of asymptotically free Coleman-Weinberg-type trajectories that do not suffer from a naturalness problem.
Fracture Strength of Disordered Media: Universality, Interactions, and Tail Asymptotics
NASA Astrophysics Data System (ADS)
Manzato, Claudio; Shekhawat, Ashivni; Nukala, Phani K. V. V.; Alava, Mikko J.; Sethna, James P.; Zapperi, Stefano
2012-02-01
We study the asymptotic properties of fracture strength distributions of disordered elastic media by a combination of renormalization group, extreme value theory, and numerical simulation. We investigate the validity of the “weakest-link hypothesis” in the presence of realistic long-ranged interactions in the random fuse model. Numerical simulations indicate that the fracture strength is well-described by the Duxbury-Leath-Beale (DLB) distribution which is shown to flow asymptotically to the Gumbel distribution. We explore the relation between the extreme value distributions and the DLB-type asymptotic distributions and show that the universal extreme value forms may not be appropriate to describe the nonuniversal low-strength tail.
Stable parabolic Higgs bundles as asymptotically stable decorated swamps
NASA Astrophysics Data System (ADS)
Beck, Nikolai
2016-06-01
Parabolic Higgs bundles can be described in terms of decorated swamps, which we studied in a recent paper. This description induces a notion of stability of parabolic Higgs bundles depending on a parameter, and we construct their moduli space inside the moduli space of decorated swamps. We then introduce asymptotic stability of decorated swamps in order to study the behaviour of the stability condition as one parameter approaches infinity. The main result is the existence of a constant, such that stability with respect to parameters greater than this constant is equivalent to asymptotic stability. This implies boundedness of all decorated swamps which are semistable with respect to some parameter. Finally, we recover the usual stability condition of parabolic Higgs bundles as asymptotic stability.
NASA Astrophysics Data System (ADS)
Yamauchi, Hiroyuki; Akamatsu, Hironori; Fujita, Tsutomu
1995-04-01
An asymptotically zero power charge recycling bus (CRB) architecture, featuring virtual stacking of the individual bus-capacitance into a series configuration between supply voltage and ground, has been proposed. This CRB architecture makes it possible to reduce not only each bus-swing but also a total equivalent bus-capacitance of the ultramultibit buses running in parallel. The voltage swing of each bus is given by the recycled charge-supplying from the upper adjacent bus capacitance, instead of the power line. The dramatical power reduction was verified by the simulated and measured data. According to these data, the ultrahigh data rate of 25.6 Gb/s can be achieved while maintaining the power dissipation to be less than 100 mW, which corresponds to less than 10% that of the previously reported 0.9 V suppressed bus-swing scheme, at V(sub cc) = 3.6 V for the bus width of 512 b with the bus-capacitance of 14 pF per bit operating at 50 MHz.
NASA Astrophysics Data System (ADS)
Fleury, R. M. N.; Hills, D. A.; Ramesh, R.; Barber, J. R.
2017-02-01
We develop a method for the solution of partial slip contact problems suffering complex loading cycles where, generally, the normal load, shear force and, potentially, differential bulk tensions are all functions of time, using an edge-asymptote approach. The size of the slip zone and local shear traction distribution are revealed as functions of time. The results are then re-worked in asymptotic form, so that they do not hinge on inherent symmetry and anti-symmetry conditions for the contact overall, and are of general applicability. The multipliers on the local solutions (generalised stress intensity factors) are also appropriate as a means of taking laboratory tests quantifying fretting fatigue and employing them to wholly different prototypical problems.
Asymptotic sideslip angle and yaw rate decoupling control in four-wheel steering vehicles
NASA Astrophysics Data System (ADS)
Marino, Riccardo; Scalzi, Stefano
2010-09-01
This paper shows that, for a four-wheel steering vehicle, a proportional-integral (PI) active front steering control and a PI active rear steering control from the yaw rate error together with an additive feedforward reference signal for the vehicle sideslip angle can asymptotically decouple the lateral velocity and the yaw rate dynamics; that is the control can set arbitrary steady state values for lateral speed and yaw rate at any longitudinal speed. Moreover, the PI controls can suppress oscillatory behaviours by assigning real stable eigenvalues to a widely used linearised model of the vehicle steering dynamics for any value of longitudinal speed in understeering vehicles. In particular, the four PI control parameters are explicitly expressed in terms of the three real eigenvalues to be assigned. No lateral acceleration and no lateral speed measurements are required. The controlled system maintains the well-known advantages of both front and rear active steering controls: higher controllability, enlarged bandwidth for the yaw rate dynamics, suppressed resonances, new stable cornering manoeuvres and improved manoeuvrability. In particular, zero lateral speed may be asymptotically achieved while controlling the yaw rate: in this case comfort is improved since the phase lag between lateral acceleration and yaw rate is reduced. Also zero yaw rate can be asymptotically achieved: in this case additional stable manoeuvres are obtained in obstacle avoidance. Several simulations, including step references and moose tests, are carried out on a standard small SUV CarSim model to explore the robustness with respect to unmodelled effects such as combined lateral and longitudinal tyre forces, pitch, roll and driver dynamics. The simulations confirm the decoupling between the lateral velocity and the yaw rate and show the advantages obtained by the proposed control: reduced lateral speed or reduced yaw rate, suppressed oscillations and new stable manoeuvres.
Josephson vortex motion as a source for dissipation of superflow of e-h pairs in bilayers.
Fil, D V; Shevchenko, S I
2009-05-27
It is shown that in a bilayer excitonic superconductor dissipative losses emerge under transmission of the current from the source to the load. These losses are proportional to the square of the interlayer tunneling amplitude and are independent of the value of the input current. The case of a quantum Hall bilayer is considered. The bilayer may work as a transmission line if the input current exceeds a certain critical value. An input current higher than the critical one induces Josephson vortices in the bilayer. The difference in electrochemical potentials is required to feed the load and it forces Josephson vortices to move. The state becomes non-stationary which leads to dissipation.
Chacón, Ricardo
2008-12-01
Optimal energy amplification via autoresonance in dissipative systems subjected to separatrix crossings is discussed through the universal model of a damped driven pendulum. Analytical expressions of the autoresonance responses and forces as well as the associated adiabatic invariants for the phase space regions separated by the underlying separatrix are derived from the energy-based theory of autoresonance. Additionally, applications to a single Josephson junction, topological solitons in Frenkel-Kontorova chains, as well as to the three-wave problem in dissipative media are discussed in detail from the autoresonance analysis.
Asymptotic Robustness Study of the Polychoric Correlation Estimation.
Jin, Shaobo; Yang-Wallentin, Fan
2017-03-01
Asymptotic robustness against misspecification of the underlying distribution for the polychoric correlation estimation is studied. The asymptotic normality of the pseudo-maximum likelihood estimator is derived using the two-step estimation procedure. The t distribution assumption and the skew-normal distribution assumption are used as alternatives to the normal distribution assumption in a numerical study. The numerical results show that the underlying normal distribution can be substantially biased, even though skewness and kurtosis are not large. The skew-normal assumption generally produces a lower bias than the normal assumption. Thus, it is worth using a non-normal distributional assumption if the normal assumption is dubious.
Asymptotic teleportation scheme as a universal programmable quantum processor.
Ishizaka, Satoshi; Hiroshima, Tohya
2008-12-12
We consider a scheme of quantum teleportation where a receiver has multiple (N) output ports and obtains the teleported state by merely selecting one of the N ports according to the outcome of the sender's measurement. We demonstrate that such teleportation is possible by showing an explicit protocol where N pairs of maximally entangled qubits are employed. The optimal measurement performed by a sender is the square-root measurement, and a perfect teleportation fidelity is asymptotically achieved for a large N limit. Such asymptotic teleportation can be utilized as a universal programmable processor.
Asymptotic entanglement transformation between W and GHZ states
Vrana, Péter; Christandl, Matthias
2015-02-15
We investigate entanglement transformations with stochastic local operations and classical communication in an asymptotic setting using the concepts of degeneration and border rank of tensors from algebraic complexity theory. Results well-known in that field imply that GHZ states can be transformed into W states at rate 1 for any number of parties. As a generalization, we find that the asymptotic conversion rate from GHZ states to Dicke states is bounded as the number of subsystems increases and the number of excitations is fixed. By generalizing constructions of Coppersmith and Winograd and by using monotones introduced by Strassen, we also compute the conversion rate from W to GHZ states.
Asymptotic traveling wave solution for a credit rating migration problem
NASA Astrophysics Data System (ADS)
Liang, Jin; Wu, Yuan; Hu, Bei
2016-07-01
In this paper, an asymptotic traveling wave solution of a free boundary model for pricing a corporate bond with credit rating migration risk is studied. This is the first study to associate the asymptotic traveling wave solution to the credit rating migration problem. The pricing problem with credit rating migration risk is modeled by a free boundary problem. The existence, uniqueness and regularity of the solution are obtained. Under some condition, we proved that the solution of our credit rating problem is convergent to a traveling wave solution, which has an explicit form. Furthermore, numerical examples are presented.
On the asymptotic distribution of block-modified random matrices
Arizmendi, Octavio; Nechita, Ion; Vargas, Carlos
2016-01-15
We study random matrices acting on tensor product spaces which have been transformed by a linear block operation. Using operator-valued free probability theory, under some mild assumptions on the linear map acting on the blocks, we compute the asymptotic eigenvalue distribution of the modified matrices in terms of the initial asymptotic distribution. Moreover, using recent results on operator-valued subordination, we present an algorithm that computes, numerically but in full generality, the limiting eigenvalue distribution of the modified matrices. Our analytical results cover many cases of interest in quantum information theory: we unify some known results and we obtain new distributions and various generalizations.
Uniform Asymptotics of Orthogonal Polynomials Arising from Coherent States
NASA Astrophysics Data System (ADS)
Dai, Dan; Hu, Weiying; Wang, Xiang-Sheng
2015-08-01
In this paper, we study a family of orthogonal polynomials {φ_n(z)} arising from nonlinear coherent states in quantum optics. Based on the three-term recurrence relation only, we obtain a uniform asymptotic expansion of φ_n(z) as the polynomial degree n tends to infinity. Our asymptotic results suggest that the weight function associated with the polynomials has an unusual singularity, which has never appeared for orthogonal polynomials in the Askey scheme. Our main technique is the Wang and Wong's difference equation method. In addition, the limiting zero distribution of the polynomials φ_n(z) is provided.
Asymptotic treatment of the Elenbaas-Heller equation
NASA Astrophysics Data System (ADS)
Kuiken, H. K.
1991-04-01
When the maximum temperatures within a high-pressure gas discharge arc are lower than the ionization temperature of the gas molecules by an order of magnitude, an asymptotic treatment of the temperature equation is possible. This is illustrated by means of the Elenbaas-Heller equation [e.g., M. F. Hoyaux, Arc Physics (Springer, Berlin, 1968), p. 36] for a nonradiating wall-stabilized arc. The asymptotics lead to a closed-form expression for the relationship between the arc current and the axis temperature. An expression for the heat loss per unit length is also given.
Asymptotic/numerical analysis of supersonic propeller noise
NASA Technical Reports Server (NTRS)
Myers, M. K.; Wydeven, R.
1989-01-01
An asymptotic analysis based on the Mach surface structure of the field of a supersonic helical source distribution is applied to predict thickness and loading noise radiated by high speed propeller blades. The theory utilizes an integral representation of the Ffowcs-Williams Hawkings equation in a fully linearized form. The asymptotic results are used for chordwise strips of the blade, while required spanwise integrations are performed numerically. The form of the analysis enables predicted waveforms to be interpreted in terms of Mach surface propagation. A computer code developed to implement the theory is described and found to yield results in close agreement with more exact computations.
Asymptotic falloff of local waveform measurements in numerical relativity
Pollney, Denis; Reisswig, Christian; Dorband, Nils; Schnetter, Erik; Diener, Peter
2009-12-15
We examine current numerical relativity computations of gravitational waves, which typically determine the asymptotic waves at infinity by extrapolation from finite (small) radii. Using simulations of a black hole binary with accurate wave extraction at r=1000M, we show that extrapolations from the near zone are self-consistent in approximating measurements at this radius, although with a somewhat reduced accuracy. We verify that {psi}{sub 4} is the dominant asymptotic contribution to the gravitational energy (as required by the peeling theorem) but point out that gauge effects may complicate the interpretation of the other Weyl components.
Current results on the asymptotics of dynamo models
NASA Astrophysics Data System (ADS)
Popova, H. P.
2016-06-01
Magnetic field generation and evolution models that are capable of describing a large body of observational material are currently available for different celestial bodies. Despite recent decades of great success in numerical magnetic hydrodynamics and in detailed research into some specific problems, asymptotic methods still have to be used to clarify the magnetic field generation mechanism in dynamo theory. In this review, current asymptotic methods are presented together with the results of their application to the simulation of solar, stellar, and galactic magnetic activities.
Asymptotic approach to special relativity compatible with a relativistic principle
Carmona, J. M.; Cortes, J. L.; Mazon, D.
2010-10-15
We propose a general framework to describe Planckian deviations from special relativity compatible with a relativistic principle. They are introduced as the leading corrections in an asymptotic approach to special relativity going beyond the energy power expansion of effective field theories. We discuss the conditions in which these Planckian effects might be experimentally observable in the near future, together with the nontrivial limits of applicability of this asymptotic approach that such a situation would produce, both at the very high (ultraviolet) and the very low (infrared) energy regimes.
Counting spanning trees on fractal graphs and their asymptotic complexity
NASA Astrophysics Data System (ADS)
Anema, Jason A.; Tsougkas, Konstantinos
2016-09-01
Using the method of spectral decimation and a modified version of Kirchhoff's matrix-tree theorem, a closed form solution to the number of spanning trees on approximating graphs to a fully symmetric self-similar structure on a finitely ramified fractal is given in theorem 3.4. We show how spectral decimation implies the existence of the asymptotic complexity constant and obtain some bounds for it. Examples calculated include the Sierpiński gasket, a non-post critically finite analog of the Sierpiński gasket, the Diamond fractal, and the hexagasket. For each example, the asymptotic complexity constant is found.
Vacuum energy in asymptotically flat 2 + 1 gravity
NASA Astrophysics Data System (ADS)
Miskovic, Olivera; Olea, Rodrigo; Roy, Debraj
2017-04-01
We compute the vacuum energy of three-dimensional asymptotically flat space based on a Chern-Simons formulation for the Poincaré group. The equivalent action is nothing but the Einstein-Hilbert term in the bulk plus half of the Gibbons-Hawking term at the boundary. The derivation is based on the evaluation of the Noether charges in the vacuum. We obtain that the vacuum energy of this space has the same value as the one of the asymptotically flat limit of three-dimensional anti-de Sitter space.
On the Asymptotics of Bessel Functions in the Fresnel Regime
2014-07-10
between the solutions u, v of (1) and the corresponding phase function is given by the formula α′(z) = W u2(z) + v2(z) , (8) with W the (constant...We introduce a version of the asymptotic expansions for Bessel functions Jν(z), Yν(z) that is valid whenever |z| > ν (which is deep in the Fresnel... function , and uses classical formulas to obtain an asymptotic expansion for this function ; this in turn leads to both an analytical tool and a nu
Homothetic motion in radiating and dissipative spheres
NASA Astrophysics Data System (ADS)
Barreto, W.; Castillo, L.
1995-10-01
A method used to study the evolution of radiating dissipative fluid spheres is applied to the case in which the space-time admits a homothetic motion. We obtain a system of equations at the surface of the distribution which is integrated numerically. Considering that the shear viscosity induces anisotropy, we obtain a model derived from the static solution by Herrera, Jiménez, Leal, Esculpi, Ponce de León, and Galina [J. Math. Phys. 25, 3274 (1984)] for homothetic fluids but which includes dynamic variables. Therefore, the profiles of the physical variables at the surface are calculated and discussed in the light of one astrophysical scenario.
Dissipation and tunneling in quantum Hall bilayers.
Jack, Robert L; Lee, Derek K K; Cooper, Nigel R
2004-09-17
We discuss the interplay between transport and intrinsic dissipation in quantum Hall bilayers, within the framework of a simple thought experiment. We compute, for the first time, quantum corrections to the semiclassical dynamics of this system. This allows us to reinterpret tunneling measurements on these systems. We find a strong peak in the zero-temperature tunneling current that arises from the decay of Josephson-like oscillations into incoherent charge fluctuations. In the presence of an in-plane field, resonances in the tunneling current develop an asymmetric line shape.
Floating hydrometer with energy dissipating baffle
Kownurko, W.A.
1987-11-24
This patent describes a floating hydrometer employable for purposes of obtaining measurements of the presence of suspended solids in a fluid substance contained in a receptacle comprising: a. a probe portion operative as an instrument-bearing housing; b. an elongated tubular element having a hollow interior and at least one open end so as to enable the flow into the hollow interior of the elongated tubular element through the open end; and c. energy dissipating baffle means having a first mode of action and a second mode of action and including a member having a hollow interior.
Growth and dissipation in biological tissues
NASA Astrophysics Data System (ADS)
Ambrosi, D.; Guillou, A.
2007-10-01
This paper provides a unified mathematical framework so as to study the growth of biological tissues on an energetic basis. All the contributions to growth of solute chemicals and nutrients are here resumed in one scalar descriptor, the biochemical energy of the system. The free energy of the system accounts for both strain and biochemical storage. The exploitation of a dissipation inequality by standard means provides admissible couplings between growth, tension and energy. Specific admissible constitutive equations lead back, in some cases, to classical models.
Dissipative Structures At Laser-Solid Interactions
NASA Astrophysics Data System (ADS)
Nanai, Laszlo
1989-05-01
The questions which are discussed in this lecture refer to one of sections of laser-solid interactions, namely: to formation of different dissipative structures on the surface of metals and semiconductors when they are irradiated by intensive laser light in chemically active media (f.e.air). Some particular examples of the development at different spatial and time instabilities, periodic and stochastic structures, auto-wave processes are present-ed using testing materials vanadium metal and semiconducting V205 single crystals and light sources: cw and pulsed CO2 and YAG lasers.
Dissipative universe-inflation with soft singularity
NASA Astrophysics Data System (ADS)
Brevik, Iver; Timoshkin, Alexander V.
We investigate the early-time accelerated universe after the Big Bang. We pay attention to the dissipative properties of the inflationary universe in the presence of a soft type singularity, making use of the parameters of the generalized equation of state of the fluid. Flat Friedmann-Robertson-Walker metric is being used. We consider cosmological models leading to the so-called type IV singular inflation. Our obtained theoretical results are compared with observational data from the Planck satellite. The theoretical predictions for the spectral index turn out to be in agreement with the data, while for the scalar-to-tensor ratio, there are minor deviations.
Numerical and Laboratory Investigation of Turbulence Dissipation in the Swash Zone
NASA Astrophysics Data System (ADS)
Pintado-Patino, J. C.; Torres-Freyermuth, A.; Puleo, J. A.
2014-12-01
An integrated study of turbulence dissipation in the swash zone was conducted in the Large Wave Flume (Großer Wellenkanall, GWK) in Hannover in July 2013. The experiments were focused on the collection of high spatial/temporal resolution data inside the swash zone, consisting of simultaneous measurements of free surface and wave run up from 45 across-shore ultrasonic distance meters (UDM), near bed velocity profiles from 2 Vectrino II acoustic Doppler profiling velocimeters, and direct bed shear stresses from 3 shear plates. This data set is employed to validate a 2D Reynolds-Averaged Navier-Stokes model with VOF-tracking scheme and a k-ɛ turbulence closure. The numerical model is compared with measurements under different forcing conditions (H=0.6 m to 1.0 m and T=8 s to 14 s) over both rough and smooth steep (1/6) beach slopes. The depth and phase resolving model simulations are used to further investigate the cross-shore variability of turbulence dissipation and shear stress at the tip of the swash lens. Furthermore, this work will explore the dependency of the turbulence dissipation on the forcing and bed roughness conditions. Funded by NSF.
Plate Tectonics as a Far-From-Equilibrium Self-Organized Dissipative System
NASA Astrophysics Data System (ADS)
Anderson, D. L.
2001-12-01
A fluid above the critical Rayleigh number is far from equilibrium and spontaneously organizes itself into patterns involving the collective motion of large numbers of molecules which are resisted by the viscosity of the fluid. No external template is involved in forming the pattern. In 1928 Pearson showed that Bénard's experiments were driven by variations in surface tension at the top of the fluid and the surface motions drove convection in the fluid. In this case, the surface organized itself AND the underlying fluid. Both internal buoyancy driven flow and flow driven by surface forces can be far-from-equilibrium self-organized open systems that receive energy and matter from the environment. In the Earth, the cold thermal boundary layer at the surface drives plate tectonics and introduces temperature, shear and pressure gradients into the mantle that drive mantle convection. The mantle provides energy and material but may not provide the template. Plate tectonics is therefore a candidate for a far-from-equilibrium dissipative self-organizing system. Alternatively, one could view mantle convection as the self-organized system and the plates as simply the surface manifestation. Lithospheric architecture also imposes lateral temperature gradients onto the mantle which can drive and organize flow. Far-from-equilibrium self-organization requires; an open system, interacting parts, nonlinearities or feedbacks, an outside steady source of energy or matter, multiple possible states and a source of dissipation. In uniform fluids viscosity is the source of dissipation. Sources of dissipation in the plate system include bending, breaking, folding, shearing, tearing, collision and basal drag. These can change rapidly, in contrast to plate driving forces, and introduce the sort of fluctuations that can reorganize far-from-equilibrium systems. Global plate reorganizations can alternatively be thought of as convective overturns of the mantle, or thermal weakening of plates
System analysis of force feedback microscopy
Rodrigues, Mario S.; Chevrier, Joël; Comin, Fabio
2014-02-07
It was shown recently that the Force Feedback Microscope (FFM) can avoid the jump-to-contact in Atomic force Microscopy even when the cantilevers used are very soft, thus increasing force resolution. In this letter, we explore theoretical aspects of the associated real time control of the tip position. We take into account lever parameters such as the lever characteristics in its environment, spring constant, mass, dissipation coefficient, and the operating conditions such as controller gains and interaction force. We show how the controller parameters are determined so that the FFM functions at its best and estimate the bandwidth of the system under these conditions.
NASA Astrophysics Data System (ADS)
Grifoni, Milena; Paladino, Elisabetta
2008-11-01
Quantum dissipation has been the object of study within the physics and chemistry communities for many years. Despite this, the field is in constant evolution, largely due to the fact that novel systems where the understanding of dissipation and dephasing processes is of crucial importance have become experimentally accessible in recent years. Among the ongoing research themes, we mention the defeat of decoherence in solid state-based quantum bits (qubits) (e.g. superconducting qubits or quantum dot based qubits), or dissipation due to non-equilibrium Fermi reservoirs, as is the case for quantum transport through meso- and nanoscale structures. A close inspection of dissipation in such systems reveals that one has to deal with 'unconventional' environments, where common assumptions of, for example, linearity of the bath and/or equilibrium reservoir have to be abandoned. Even for linear baths at equilibrium it might occur that the bath presents some internal structure, due, for example, to the presence of localized bath modes. A large part of this focus issue is devoted to topics related to the rapidly developing fields of quantum computation and information with solid state nanodevices. In these implementations, single and two-qubit gates as well as quantum information transmission takes place in the presence of broadband noise that is typically non-Markovian and nonlinear. On both the experimental and theory side, understanding and defeating such noise sources has become a crucial step towards the implementation of efficient nanodevices. On a more fundamental level, electron and spin transport through quantum dot nanostructures may suffer from 'unconventional' dissipation mechanisms such as the simultaneous presence of spin relaxation and fermionic dissipation, or may represent themselves out of equilibrium baths for nearby mesoscopic systems. Finally, although not expected from the outset, the present collection of articles has revealed that different
Bhaumik, Himangsu; Santra, S B
2016-12-01
A dissipative stochastic sandpile model is constructed and studied on small-world networks in one and two dimensions with different shortcut densities ϕ, where ϕ=0 represents regular lattice and ϕ=1 represents random network. The effect of dimension, network topology, and specific dissipation mode (bulk or boundary) on the the steady-state critical properties of nondissipative and dissipative avalanches along with all avalanches are analyzed. Though the distributions of all avalanches and nondissipative avalanches display stochastic scaling at ϕ=0 and mean-field scaling at ϕ=1, the dissipative avalanches display nontrivial critical properties at ϕ=0 and 1 in both one and two dimensions. In the small-world regime (2^{-12}≤ϕ≤0.1), the size distributions of different types of avalanches are found to exhibit more than one power-law scaling with different scaling exponents around a crossover toppling size s_{c}. Stochastic scaling is found to occur for s
NASA Astrophysics Data System (ADS)
Bhaumik, Himangsu; Santra, S. B.
2016-12-01
A dissipative stochastic sandpile model is constructed and studied on small-world networks in one and two dimensions with different shortcut densities ϕ , where ϕ =0 represents regular lattice and ϕ =1 represents random network. The effect of dimension, network topology, and specific dissipation mode (bulk or boundary) on the the steady-state critical properties of nondissipative and dissipative avalanches along with all avalanches are analyzed. Though the distributions of all avalanches and nondissipative avalanches display stochastic scaling at ϕ =0 and mean-field scaling at ϕ =1 , the dissipative avalanches display nontrivial critical properties at ϕ =0 and 1 in both one and two dimensions. In the small-world regime (2-12≤ϕ ≤0.1 ) , the size distributions of different types of avalanches are found to exhibit more than one power-law scaling with different scaling exponents around a crossover toppling size sc. Stochastic scaling is found to occur for s
A three-dimensional map of tidal dissipation over abyssal hills
NASA Astrophysics Data System (ADS)
Lefauve, Adrien; Muller, Caroline; Melet, Angélique
2015-07-01
The breaking of internal tides is believed to provide a large part of the power needed to mix the abyssal ocean and sustain the meridional overturning circulation. Both the fraction of internal tide energy that is dissipated locally and the resulting vertical mixing distribution are crucial for the ocean state, but remain poorly quantified. Here we present a first worldwide estimate of mixing due to internal tides generated at small-scale abyssal hills. Our estimate is based on linear wave theory, a nonlinear parameterization for wave breaking and uses quasi-global small-scale abyssal hill bathymetry, stratification, and tidal data. We show that a large fraction of abyssal-hill generated internal tide energy is locally dissipated over mid-ocean ridges in the Southern Hemisphere. Significant dissipation occurs above ridge crests, and, upon rescaling by the local stratification, follows a monotonic exponential decay with height off the bottom, with a nonuniform decay scale. We however show that a substantial part of the dissipation occurs over the smoother flanks of mid-ocean ridges, and exhibits a middepth maximum due to the interplay of wave amplitude with stratification. We link the three-dimensional map of dissipation to abyssal hills characteristics, ocean stratification, and tidal forcing, and discuss its potential implementation in time-evolving parameterizations for global climate models. Current tidal parameterizations only account for waves generated at large-scale satellite-resolved bathymetry. Our results suggest that the presence of small-scale, mostly unresolved abyssal hills could significantly enhance the spatial inhomogeneity of tidal mixing, particularly above mid-ocean ridges in the Southern Hemisphere.
Dissipative time-dependent quantum transport theory.
Zhang, Yu; Yam, Chi Yung; Chen, GuanHua
2013-04-28
A dissipative time-dependent quantum transport theory is developed to treat the transient current through molecular or nanoscopic devices in presence of electron-phonon interaction. The dissipation via phonon is taken into account by introducing a self-energy for the electron-phonon coupling in addition to the self-energy caused by the electrodes. Based on this, a numerical method is proposed. For practical implementation, the lowest order expansion is employed for the weak electron-phonon coupling case and the wide-band limit approximation is adopted for device and electrodes coupling. The corresponding hierarchical equation of motion is derived, which leads to an efficient and accurate time-dependent treatment of inelastic effect on transport for the weak electron-phonon interaction. The resulting method is applied to a one-level model system and a gold wire described by tight-binding model to demonstrate its validity and the importance of electron-phonon interaction for the quantum transport. As it is based on the effective single-electron model, the method can be readily extended to time-dependent density functional theory.
Engineering dissipation with phononic spectral hole burning.
Behunin, R O; Kharel, P; Renninger, W H; Rakich, P T
2017-03-01
Optomechanics, nano-electromechanics, and integrated photonics have brought about a renaissance in phononic device physics and technology. Central to this advance are devices and materials supporting ultra-long-lived photonic and phononic excitations that enable novel regimes of classical and quantum dynamics based on tailorable photon-phonon coupling. Silica-based devices have been at the forefront of such innovations for their ability to support optical excitations persisting for nearly 1 billion cycles, and for their low optical nonlinearity. While acoustic phonon modes can persist for a similar number of cycles in crystalline solids at cryogenic temperatures, it has not been possible to achieve such performance in silica, as silica becomes acoustically opaque at low temperatures. We demonstrate that these intrinsic forms of phonon dissipation are greatly reduced (by >90%) by nonlinear saturation using continuous drive fields of disparate frequencies. The result is a form of steady-state phononic spectral hole burning that produces a wideband transparency window with optically generated phonon fields of modest (nW) powers. We developed a simple model that explains both dissipative and dispersive changes produced by phononic saturation. Our studies, conducted in a microscale device, represent an important step towards engineerable phonon dynamics on demand and the use of glasses as low-loss phononic media.
The dissipative Bose-Hubbard model
NASA Astrophysics Data System (ADS)
Kordas, G.; Witthaut, D.; Buonsante, P.; Vezzani, A.; Burioni, R.; Karanikas, A. I.; Wimberger, S.
2015-11-01
Open many-body quantum systems have attracted renewed interest in the context of quantum information science and quantum transport with biological clusters and ultracold atomic gases. The physical relevance in many-particle bosonic systems lies in the realization of counter-intuitive transport phenomena and the stochastic preparation of highly stable and entangled many-body states due to engineered dissipation. We review a variety of approaches to describe an open system of interacting ultracold bosons which can be modeled by a tight-binding Hubbard approximation. Going along with the presentation of theoretical and numerical techniques, we present a series of results in diverse setups, based on a master equation description of the dissipative dynamics of ultracold bosons in a one-dimensional lattice. Next to by now standard numerical methods such as the exact unravelling of the master equation by quantum jumps for small systems and beyond mean-field expansions for larger ones, we present a coherent-state path integral formalism based on Feynman-Vernon theory applied to a many-body context.
Wetlands as energy-dissipating systems.
Pokorný, Jan; Květ, Jan; Rejšková, Alžběta; Brom, Jakub
2010-12-01
Since wetlands are ecosystems that have an ample supply of water, they play an important role in the energy budgets of their respective landscapes due to their capacity to shift energy fluxes in favor of latent heat. Rates of evapotranspiration in wetlands are commonly as high as 6-15 mm day⁻¹, testifying to the large amount of energy that is dissipated through this process. Emergent or semi-emergent wetland macrophytes substantially influence the solar energy distribution due to their high capacity for transpiration. Wetland ecosystems in eutrophic habitats show a high primary production of biomass because of the highly efficient use of solar energy in photosynthesis. In wetlands associated with the slow decomposition of dead organic matter, such as oligotrophic marshes or fens and bogs, the accumulation of biomass is also high, in spite of the rather low primary production of biomass. Most of the energy exchange in water-saturated wetlands is, however, linked with heat balance, whereby the largest proportion of the incoming energy is dissipated during the process of evapotranspiration. An example is shown of energy fluxes during the course of a day in the wetland ecosystem of Mokré Louky (Wet Meadows) near Třeboň. The negative consequences of the loss of wetlands for the local and regional climate are discussed.
Dissipative processes in superfluid neutron stars
Mannarelli, Massimo; Colucci, Giuseppe; Manuel, Cristina
2011-05-23
We present some results about a novel damping mechanism of r-mode oscillations in neutron stars due to processes that change the number of protons, neutrons and electrons. Deviations from equilibrium of the number densities of the various species lead to the appearance in the Euler equations of the system of a dissipative mechanism, the so-called rocket effect. The evolution of the r-mode oscillations of a rotating neutron star are influenced by the rocket effect and we present estimates of the corresponding damping timescales. In the description of the system we employ a two-fluid model, with one fluid consisting of all the charged components locked together by the electromagnetic interaction, while the second fluid consists of superfluid neutrons. Both components can oscillate however the rocket effect can only efficiently damp the countermoving r-mode oscillations, with the two fluids oscillating out of phase. In our analysis we include the mutual friction dissipative process between the neutron superfluid and the charged component. We neglect the interaction between the two r-mode oscillations as well as effects related with the crust of the star. Moreover, we use a simplified model of neutron star assuming a uniform mass distribution.
Mechanochemistry for shock wave energy dissipation
NASA Astrophysics Data System (ADS)
Shaw, William L.; Ren, Yi; Moore, Jeffrey S.; Dlott, Dana D.
2017-01-01
Using a laser-driven flyer-plate apparatus to launch 75 μm thick Al flyers up to 2.8 km/s, we developed a technique for detecting the attenuation of shock waves by mechanically-driven chemical reactions. The attenuating sample was spread on an ultrathin Au mirror deposited onto a glass window having a known Hugoniot. As shock energy exited the sample and passed through the mirror, into the glass, photonic Doppler velocimetry monitored the velocity profile of the ultrathin mirror. Knowing the window Hugoniot, the velocity profile could be quantitatively converted into a shock energy flux or fluence. The flux gave the temporal profile of the shock front, and showed how the shock front was reshaped by passing through the dissipative medium. The fluence, the time-integrated flux, showed how much shock energy was transmitted through the sample. Samples consisted of microgram quantities of carefully engineered organic compounds selected for their potential to undergo negative-volume chemistry. Post mortem analytical methods were used to confirm that shock dissipation was associated with shock-induced chemical reactions.
Dissipation in ferrofluids: mesoscopic versus hydrodynamic theory.
Müller, H W; Engel, A
1999-12-01
Part of the field dependent dissipation in ferrofluids occurs due to the rotational motion of the ferromagnetic grains relative to the viscous flow of the carrier fluid. The classical theoretical description due to Shliomis (Zh. Eksp. Teor. Fiz. 61, 2411 (1971) [Sov. Phy JETP 34, 1291 (1972)]) uses a mesoscopic treatment of the particle motion to derive a relaxation equation for the nonequilibrium part of the magnetization. Complementary, the hydrodynamic approach of Liu [Phys. Rev. Lett. 70, 3580 (1993)] involves only macroscopic quantities and results in dissipative Maxwell equations for the magnetic fields in the ferrofluid. Different stress tensors and constitutive equations lead to deviating theoretical predictions in those situations, where the magnetic relaxation processes cannot be considered instantaneous on the hydrodynamic time scale. We quantify these differences for two situations of experimental relevance, namely, a resting fluid in an oscillating oblique field and the damping of parametrically excited surface waves. The possibilities of an experimental differentiation between the two theoretical approaches is discussed.
Engineering dissipation with phononic spectral hole burning
NASA Astrophysics Data System (ADS)
Behunin, R. O.; Kharel, P.; Renninger, W. H.; Rakich, P. T.
2016-12-01
Optomechanics, nano-electromechanics, and integrated photonics have brought about a renaissance in phononic device physics and technology. Central to this advance are devices and materials supporting ultra-long-lived photonic and phononic excitations that enable novel regimes of classical and quantum dynamics based on tailorable photon-phonon coupling. Silica-based devices have been at the forefront of such innovations for their ability to support optical excitations persisting for nearly 1 billion cycles, and for their low optical nonlinearity. While acoustic phonon modes can persist for a similar number of cycles in crystalline solids at cryogenic temperatures, it has not been possible to achieve such performance in silica, as silica becomes acoustically opaque at low temperatures. We demonstrate that these intrinsic forms of phonon dissipation are greatly reduced (by >90%) by nonlinear saturation using continuous drive fields of disparate frequencies. The result is a form of steady-state phononic spectral hole burning that produces a wideband transparency window with optically generated phonon fields of modest (nW) powers. We developed a simple model that explains both dissipative and dispersive changes produced by phononic saturation. Our studies, conducted in a microscale device, represent an important step towards engineerable phonon dynamics on demand and the use of glasses as low-loss phononic media.
Asymptotically solvable model for a solitonic vortex in a compressible superfluid
NASA Astrophysics Data System (ADS)
Toikka, L. A.; Brand, J.
2017-02-01
Vortex motion is a complex problem due to the interplay between the short-range physics at the vortex core level and the long-range hydrodynamical effects. Here we show that the hydrodynamic equations of vortex motion in a compressible superfluid can be solved asymptotically in a model ‘slab’ geometry. Starting from an exact solution for an incompressible fluid, the hydrodynamic equations are solved with a series expansion in a small tunable parameter provided by the ratio of the healing length, characterising the vortex cores, to the slab width. The key dynamical properties of the vortex, the inertial and physical masses, are well defined and renormalizable. They are calculated at leading order beyond the logarithmic accuracy that has limited previous approaches. Subtracting the asymptotic solutions of the universal hydrodynamic problem from experimental observations of vortex motion exposes the physics of the vortex core and provides a window into interesting many-body phenomena that are currently poorly understood including the role of quantum pressure. Our results provide a solid framework for further detailed study of the vortex mass and vortex forces in strongly correlated and exotic superfluids.
Dissipation Element Analysis of Reacting- and Non-Reacting Flows
NASA Astrophysics Data System (ADS)
Denker, Dominik; Boschung, Jonas; Hennig, Fabian; Pitsch, Heinz
2016-11-01
Dissipation element analysis is a tried and tested method for analyzing scalar field in turbulent flows. Dissipation elements are defined as an ensemble of grid point whose gradient trajectories reach the same extremal points. Therefore, the scalar field can be compartmentalized in monotonous space filling regions. Dissipation elements can be described by two parameters, namely the Euclidean distance between their extremal points and their scalar difference in these points. The joint probability density function of these two parameters is expected to suffice for a statistical reconstruction of the scalar field. In addition, normalized dissipation element statistics show a remarkable invariance towards changes in Reynolds numbers. Dissipation element statistics of the passive scalar and the turbulent kinetic energy are compared for different flow configurations including reacting and non-reacting turbulent flows. Furthermore, the Reynolds number scaling of the dissipation element parameters is investigated.
Mesoscopic simulation of a thinning liquid bridge using the dissipative particle dynamics method
NASA Astrophysics Data System (ADS)
Mo, Chao-jie; Yang, Li-jun; Zhao, Fei; Cui, Kun-da
2015-08-01
In this research, the dissipative particle dynamics method was used to investigate the problem of thinning and breakup in a liquid bridge. It was found that both the inertial-force-dominated thinning process and the thermal-fluctuation-dominated thinning process can be reproduced with the dissipative particle dynamics (DPD) method by varying the simulation parameters. A highly suspect viscous thinning regime was also found, but the conclusion is not irrefutable because of the complication of the shear viscosity of DPD fluid. We show in this article that the DPD method can serve as a good candidate to elucidate crossover problem in liquid bridge thinning from being hydrodynamics dominated to being thermal fluctuation dominated.
CONSTRAINING TIDAL DISSIPATION IN STARS FROM THE DESTRUCTION RATES OF EXOPLANETS
Penev, Kaloyan; Jackson, Brian; Spada, Federico; Thom, Nicole
2012-06-01
We use the distribution of extrasolar planets in circular orbits around stars with surface convective zones detected by ground-based transit searches to constrain how efficiently tides raised by the planet are dissipated on the parent star. We parameterize this efficiency as a tidal quality factor (Q{sub *}). We conclude that the population of currently known planets is inconsistent with Q{sub *} < 10{sup 7} at the 99% level. Previous studies show that values of Q{sub *} between 10{sup 5} and 10{sup 7} are required in order to explain the orbital circularization of main-sequence low-mass binary stars in clusters, suggesting that different dissipation mechanisms might be acting in the two cases, most likely due to the very different tidal forcing frequencies relative to the stellar rotation frequency occurring for star-star versus planet-star systems.
Diamagnetic effect on the Casimir force
Inui, Norio
2011-03-15
The Casimir force between a diamagnetic plate and a magnetodielectric plate at finite temperature is considered. Under the condition that the permittivity of the magnetodielectric plate is sufficiently small, we show that the diamagnetic property dominantly determines the asymptotic behavior of the repulsive Casimir force for large separations. On the basis of this simple property, we present numerical results showing that if an effective permeability of a superconductor is much less than one, its diamagnetic response can be indirectly detected by measuring the Casimir force.
Quantum analysis applied to thermo field dynamics on dissipative systems
Hashizume, Yoichiro; Okamura, Soichiro; Suzuki, Masuo
2015-03-10
Thermo field dynamics is one of formulations useful to treat statistical mechanics in the scheme of field theory. In the present study, we discuss dissipative thermo field dynamics of quantum damped harmonic oscillators. To treat the effective renormalization of quantum dissipation, we use the Suzuki-Takano approximation. Finally, we derive a dissipative von Neumann equation in the Lindbrad form. In the present treatment, we can easily obtain the initial damping shown previously by Kubo.
If there is dissipation the particle can gain energy
NASA Astrophysics Data System (ADS)
Egydio de Carvalho, R.
2015-10-01
In this work, we summarize two different mechanisms to gain energy from the presence of dissipation in a time-dependent non-linear system. The particles can gain energy, in the average, from two different scenarios: i) for very week dissipation with the creation of an attractor with high velocity, and ii) in the opposite limit, for very strong dissipation, the particles can also gain energy from a boundary crisis. From the thermodynamic viewpoint both results are totally acceptable.
Asymptotic Learning of Alphanumeric Coding in Autobiographical Memory
ERIC Educational Resources Information Center
Martin, Maryanne; Jones, Gregory V.
2007-01-01
Studies of autobiographical memory have shown that observed levels of incidental learning are often relatively low. Do low levels of retention result simply from a low learning rate, or is learning also asymptotic? To address this question, it is necessary to trace performance over a large number of learning opportunities, and this was carried out…
Asymptotic Spectra Of Banded Quasi-Toeplitz Matrices
NASA Technical Reports Server (NTRS)
Beam, Richard; Warming, Robert
1995-01-01
Paper presents theoretical and numerical study of asymptotic spectra of eigenvalues of banded Toeplitz and quasi-Toeplitz matrices. Emphasis in study on non-normal banded Toeplitz and quasi-Toeplitz matrices of arbitrarily large order and relatively small bandwidth.
The Asymptotic Distribution of the Renyi Maximal Correlation
1990-10-01
functions of U and W with finite second moments. In this paper we derive the asymptotic distribution of the estimate of the Renyi correlation ... coefficient based on a sample of independent observations under the assumption that (U,W) are independent and assume only a finite number of values. (kr)
Asymptotic Analysis of Fiber-Reinforced Composites of Hexagonal Structure
NASA Astrophysics Data System (ADS)
Kalamkarov, Alexander L.; Andrianov, Igor V.; Pacheco, Pedro M. C. L.; Savi, Marcelo A.; Starushenko, Galina A.
2016-08-01
The fiber-reinforced composite materials with periodic cylindrical inclusions of a circular cross-section arranged in a hexagonal array are analyzed. The governing analytical relations of the thermal conductivity problem for such composites are obtained using the asymptotic homogenization method. The lubrication theory is applied for the asymptotic solution of the unit cell problems in the cases of inclusions of large and close to limit diameters, and for inclusions with high conductivity. The lubrication method is further generalized to the cases of finite values of the physical properties of inclusions, as well as for the cases of medium-sized inclusions. The analytical formulas for the effective coefficient of thermal conductivity of the fiber-reinforced composite materials of a hexagonal structure are derived in the cases of small conductivity of inclusions, as well as in the cases of extremely low conductivity of inclusions. The three-phase composite model (TPhM) is applied for solving the unit cell problems in the cases of the inclusions with small diameters, and the asymptotic analysis of the obtained solutions is performed for inclusions of small sizes. The obtained results are analyzed and illustrated graphically, and the limits of their applicability are evaluated. They are compared with the known numerical and asymptotic data in some particular cases, and very good agreement is demonstrated.
Asymptotics of surface-plasmon redshift saturation at subnanometric separations
NASA Astrophysics Data System (ADS)
Schnitzer, Ory; Giannini, Vincenzo; Craster, Richard V.; Maier, Stefan A.
2016-01-01
Many promising nanophotonics endeavors hinge upon the unique plasmonic properties of nanometallic structures with narrow nonmetallic gaps, which support superconcentrated bonding modes that singularly redshift with decreasing separations. In this Rapid Communication, we present a descriptive physical picture, complemented by elementary asymptotic formulas, of a nonlocal mechanism for plasmon redshift saturation at subnanometric gap widths. Thus, by considering the electron-charge and field distributions in the close vicinity of the metal-vacuum interface, we show that nonlocality is asymptotically manifested as an effective potential discontinuity. For bonding modes in the near-contact limit, the latter discontinuity is shown to be effectively equivalent to a widening of the gap. As a consequence, the resonance-frequency near-contact asymptotics are a renormalization of the corresponding local ones. Specifically, the renormalization furnishes an asymptotic plasmon-frequency lower bound that scales with the 1 /4 power of the Fermi wavelength. We demonstrate these remarkable features in the prototypical cases of nanowire and nanosphere dimers, showing agreement between our elementary expressions and previously reported numerical computations.
Cosmological attractors and asymptotic freedom of the inflaton field
Kallosh, Renata; Linde, Andrei
2016-06-28
We show that the inflaton coupling to all other fields is exponentially suppressed during inflation in the cosmological α-attractor models. In the context of supergravity, this feature is a consequence of the underlying hyperbolic geometry of the moduli space which has a flat direction corresponding to the inflaton field. A combination of these factors protects the asymptotic flatness of the inflaton potential.