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.
Dissipation of acoustic-gravity waves: an asymptotic approach.
Godin, Oleg A
2014-12-01
Acoustic-gravity waves in the middle and upper atmosphere and long-range propagation of infrasound are strongly affected by air viscosity and thermal conductivity. To characterize the wave dissipation, it is typical to consider idealized environments, which admit plane-wave solutions. Here, an asymptotic approach is developed that relies instead on the assumption that spatial variations of environmental parameters are gradual. It is found that realistic assumptions about the atmosphere lead to rather different predictions for wave damping than do the plane-wave solutions. A modification to the Sutherland-Bass model of infrasound absorption is proposed. PMID:25480091
Dissipation of acoustic-gravity waves: an asymptotic approach.
Godin, Oleg A
2014-12-01
Acoustic-gravity waves in the middle and upper atmosphere and long-range propagation of infrasound are strongly affected by air viscosity and thermal conductivity. To characterize the wave dissipation, it is typical to consider idealized environments, which admit plane-wave solutions. Here, an asymptotic approach is developed that relies instead on the assumption that spatial variations of environmental parameters are gradual. It is found that realistic assumptions about the atmosphere lead to rather different predictions for wave damping than do the plane-wave solutions. A modification to the Sutherland-Bass model of infrasound absorption is proposed.
Energy dissipation in multifrequency atomic force microscopy.
Pukhova, Valentina; Banfi, Francesco; Ferrini, Gabriele
2014-01-01
The instantaneous displacement, velocity and acceleration of a cantilever tip impacting onto a graphite surface are reconstructed. The total dissipated energy and the dissipated energy per cycle of each excited flexural mode during the tip interaction is retrieved. The tip dynamics evolution is studied by wavelet analysis techniques that have general relevance for multi-mode atomic force microscopy, in a regime where few cantilever oscillation cycles characterize the tip-sample interaction. PMID:24778976
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.
Energy transfer and dissipation in forced isotropic turbulence.
McComb, W D; Berera, A; Yoffe, S R; Linkmann, M F
2015-04-01
A model for the Reynolds-number dependence of the dimensionless dissipation rate C(ɛ) was derived from the dimensionless Kármán-Howarth equation, resulting in C(ɛ)=C(ɛ,∞)+C/R(L)+O(1/R(L)(2)), where R(L) is the integral scale Reynolds number. The coefficients C and C(ɛ,∞) arise from asymptotic expansions of the dimensionless second- and third-order structure functions. This theoretical work was supplemented by direct numerical simulations (DNSs) of forced isotropic turbulence for integral scale Reynolds numbers up to R(L)=5875 (R(λ)=435), which were used to establish that the decay of dimensionless dissipation with increasing Reynolds number took the form of a power law R(L)(n) with exponent value n=-1.000±0.009 and that this decay of C(ɛ) was actually due to the increase in the Taylor surrogate U(3)/L. The model equation was fitted to data from the DNS, which resulted in the value C=18.9±1.3 and in an asymptotic value for C(ɛ) in the infinite Reynolds-number limit of C(ɛ,∞)=0.468±0.006. PMID:25974586
Energy transfer and dissipation in forced isotropic turbulence.
McComb, W D; Berera, A; Yoffe, S R; Linkmann, M F
2015-04-01
A model for the Reynolds-number dependence of the dimensionless dissipation rate C(ɛ) was derived from the dimensionless Kármán-Howarth equation, resulting in C(ɛ)=C(ɛ,∞)+C/R(L)+O(1/R(L)(2)), where R(L) is the integral scale Reynolds number. The coefficients C and C(ɛ,∞) arise from asymptotic expansions of the dimensionless second- and third-order structure functions. This theoretical work was supplemented by direct numerical simulations (DNSs) of forced isotropic turbulence for integral scale Reynolds numbers up to R(L)=5875 (R(λ)=435), which were used to establish that the decay of dimensionless dissipation with increasing Reynolds number took the form of a power law R(L)(n) with exponent value n=-1.000±0.009 and that this decay of C(ɛ) was actually due to the increase in the Taylor surrogate U(3)/L. The model equation was fitted to data from the DNS, which resulted in the value C=18.9±1.3 and in an asymptotic value for C(ɛ) in the infinite Reynolds-number limit of C(ɛ,∞)=0.468±0.006.
NASA Technical Reports Server (NTRS)
Kelkar, Atul G.; Joshi, Suresh M.; Alberts, Thomas E.
1993-01-01
The stability characteristics of dynamic dissipative compensators are investigated for multibody flexible space structures having nonlinear dynamics. The problem addressed is that of proving asymptotic stability of dynamic dissipative compensators. The stability proof uses the Liapunov approach and exploits the inherent passivity of such systems. For such systems these compensators are shown to be robust to parametric uncertainties and unmodeled dynamics. The results are applicable to a large class of structures such as flexible space structures with articulated flexible appendages.
Identification of nanoscale dissipation processes by dynamic atomic force microscopy.
Garcia, R; Gómez, C J; Martinez, N F; Patil, S; Dietz, C; Magerle, R
2006-07-01
Identification of energy-dissipation processes at the nanoscale is demonstrated by using amplitude-modulation atomic force microscopy. The variation of the energy dissipated on a surface by a vibrating tip as a function of its oscillation amplitude has a shape that singles out the dissipative process occurring at the surface. The method is illustrated by calculating the energy-dissipation curves for surface energy hysteresis, long-range interfacial interactions and viscoelasticity. The method remains valid with independency of the amount of dissipated energy per cycle, from 0.1 to 50 eV. The agreement obtained between theory and experiments performed on silicon and polystyrene validates the method.
Intrinsic dissipation in atomic force microscopy cantilevers.
Zypman, Fredy
2011-07-01
In this paper we build a practical modification to the standard Euler-Bernoulli equation for flexural modes of cantilever vibrations most relevant for operation of AFM in high vacuum conditions. This is done by the study of a new internal dissipation term into the Euler-Bernoulli equation. This term remains valid in ultra-high vacuum, and becomes particularly relevant when viscous dissipation with the fluid environment becomes negligible. We derive a compact explicit equation for the quality factor versus pressure for all the flexural modes. This expression is used to compare with corresponding extant high vacuum experiments. We demonstrate that a single internal dissipation parameter and a single viscosity parameter provide enough information to reproduce the first three experimental flexural resonances at all pressures. The new term introduced here has a mesoscopic origin in the relative motion between adjacent layers in the cantilever. PMID:21741914
Iliev, Stanimir; Pesheva, Nina; Iliev, Dimitar
2010-01-01
The relaxation of straight contact lines is considered in the context of the Wilhelmy-plate experiment: a homogeneous solid plate is moving vertically at constant velocity in a tank of liquid in the partial wetting regime. We apply the contact line dissipation approach to describe the quasistatic relaxation of the contact line toward the stationary state (below the entrainment transition). Asymptotic solutions are derived from the differential equations describing the capillary rise height and the contact angle relaxation for small initial deviations of the height from the final stationary value in the model considering the friction dissipation at the moving contact line, in the model considering the viscous flow dissipation in the wedge, and in the combined model taking into account both channels of dissipation. We find that for all models the time relaxation of the height and the cosine of the contact angle are given by sums of exponential functions up to a second order in the expansion of the small parameter. We analyze the implications which follow when only one dissipation channel is taken into account and compare them to the case when both dissipation channels are included. The asymptotic solutions are compared with experimental results and with numerically obtained solutions which are based on hydrodynamic approach in lubrication approximation with and without a correction factor for finite contact angles. The best description of the experimental data, based on multicriteria testing, is obtained with the combined contact line dissipation model which takes into account both channels of dissipation. PMID:20365384
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.
Power dissipation and magnetic forces and MAGLEV rebars
Zahn, M.
1997-03-01
Concrete guideways for proposed MAGLEV vehicles may be reinforced with electrically conducting and magnetizable steel rebars. Transient magnetic fields due to passing MAGLEV vehicles will then induce transient currents in the rebars leading to power dissipation and temperature rise as well as Lorentz and magnetization forces on the rebars. In order to evaluate if this heating and force on the rebars affects concrete life and performance, analysis is presented for an infinitely long conducting and magnetizable cylinder in imposed uniform axial or transverse magnetic fields. Exact and approximate solutions are presented for sinusoidal steady state and step transient magnetic fields inside and outside the cylinder, the induced current density, the vector potential for transverse magnetic fields, the time average dissipated power in the sinusoidal steady state, and the total energy dissipated for step transients. Forces are approximately calculated for imposed magnetic fields` with a weak spatial gradient. The analysis is applied to representative rebar materials.
An asymptotic symmetry of the rapidly forced pendulum
Chang, Yi-Hua . Applied Mathematics Program State Univ. of New York, Buffalo, NY . Dept. of Mathematics); Segur, H. . Applied Mathematics Program)
1990-09-01
The inhomogeneous differential equation (x{double prime} + sin x = {delta} sin (t + t{sub 0}){var epsilon}) describes the motion of a sinusoidally forced pendulum. The orbits that connect the two saddle points of the unforced ({delta} = 0) pendulum, (x = {pi}) and (x = {minus}{pi}), are called separatrices. If {var epsilon} {Omicron}(1), then one can use Melnikov's method to show that these separatrices can split for weak forcing ({delta} {much lt} 1), and that the perturbed motion is chaotic. If {var epsilon} 1, Melnikov's method fails because the perturbation term is not analytic in {var epsilon} at {var epsilon} = 0. In this paper we show that for {delta} {much lt} 1 and {var epsilon} {much lt} 1, the solution of the perturbed problem exhibits a symmetry to all orders in an asymptotic expansion. From the asymptotic expansion it follows that the separatrices split by an amount that is at most transcendentally small. This proof differs from that of Holmes, Marsden and Scheurle. 16 refs.
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.
Quantification of dissipation and deformation in ambient atomic force microscopy
NASA Astrophysics Data System (ADS)
Santos, Sergio; Gadelrab, Karim R.; Barcons, Victor; Stefancich, Marco; Chiesa, Matteo
2012-07-01
A formalism to extract and quantify unknown quantities such as sample deformation, the viscosity of the sample and surface energy hysteresis in amplitude modulation atomic force microscopy is presented. Recovering the unknowns only requires the cantilever to be accurately calibrated and the dissipative processes occurring during sample deformation to be well modeled. The theory is validated by comparison with numerical simulations and shown to be able to provide, in principle, values of sample deformation with picometer resolution.
de Beer, Sissi; van den Ende, Dirk; Mugele, Frieder
2010-08-13
We determine conservative and dissipative tip-sample interaction forces from the amplitude and phase response of acoustically driven atomic force microscope (AFM) cantilevers using a non-polar model fluid (octamethylcyclotetrasiloxane, which displays strong molecular layering) and atomically flat surfaces of highly ordered pyrolytic graphite. Taking into account the base motion and the frequency-dependent added mass and hydrodynamic damping on the AFM cantilever, we develop a reliable force inversion procedure that allows for extracting tip-sample interaction forces for a wide range of drive frequencies. We systematically eliminate the effect of finite drive amplitudes. Dissipative tip-sample forces are consistent with the bulk viscosity down to a thickness of 2-3 nm. Dissipation measurements far below resonance, which we argue to be the most reliable, indicate the presence of peaks in the damping, corresponding to an enhanced 'effective' viscosity, upon expelling the last and second-last molecular layer. PMID:20639584
Renormalized dissipation in the nonconservatively forced Burgers equation
Krommes, J.A.
2000-01-19
A previous calculation of the renormalized dissipation in the nonconservatively forced one-dimensional Burgers equation, which encountered a catastrophic long-wavelength divergence approximately [k min]-3, is reconsidered. In the absence of velocity shear, analysis of the eddy-damped quasi-normal Markovian closure predicts only a benign logarithmic dependence on kmin. The original divergence is traced to an inconsistent resonance-broadening type of diffusive approximation, which fails in the present problem. Ballistic scaling of renormalized pulses is retained, but such scaling does not, by itself, imply a paradigm of self-organized criticality. An improved scaling formula for a model with velocity shear is also given.
Stochastic friction force mechanism of energy dissipation in noncontact atomic force microscopy
NASA Astrophysics Data System (ADS)
Kantorovich, L. N.
2001-12-01
The tip-surface interaction in noncontact atomic force microscopy (NC-AFM) leads to energy dissipation, which has been used as another imaging mechanism of surface topography with atomic resolution. In this paper, using a rigorous approach based on the coarse graining method of (classical) nonequilibrium statistical mechanics, we derive the Fokker-Planck equation for the tip distribution function and then the Langevin equation (equation of motion) for the tip. We show that the latter equation contains a friction force leading to the energy dissipation. The friction force is related to the correlation function of the fluctuating tip-surface force in agreement with earlier treatments by other methods. Using a simple model of a plane surface in which only one surface atom interacts directly with the tip (it, however, interacts with other surface atoms), we calculate the friction coefficient and the corresponding dissipation energy as a function of the tip position. In our model all surface atoms are allowed to relax. Nevertheless, our calculations qualitatively agree with a previous much simpler treatment by Gauthier and Tsukada [Phys. Rev. B 60, 11 716 (1999)] that, at least for the plain terraces, the calculated dissipation energies appear to be much smaller than observed in experiments. We also demonstrate the validity of the Markovian approximation in studying the NC-AFM system.
One-Dimensional Relativistic Dissipative System with Constant Force and its Quantization
NASA Astrophysics Data System (ADS)
López, G.; López, X. E.; Hernández, H.
2006-04-01
For a relativistic particle under a constant force and a linear velocity dissipation force, a constant of motion is found. Problems are shown for getting the Hamiltonian of this system. Thus, the quantization of this system is carried out through the constant of motion and using the quantization on the velocity variable. The dissipative relativistic quantum bouncer is outlined within this quantization approach.
Casimir-Lifshitz Force Out of Thermal Equilibrium and Asymptotic Nonadditivity
Antezza, Mauro; Stringari, Sandro; Pitaevskii, Lev P.; Svetovoy, Vitaly B.
2006-12-01
We investigate the force acting between two parallel plates held at different temperatures. The force reproduces, as limiting cases, the well-known Casimir-Lifshitz surface-surface force at thermal equilibrium and the surface-atom force out of thermal equilibrium recently derived by M. Antezza et al., Phys. Rev. Lett. 95, 113202 (2005). The asymptotic behavior of the force at large distances is explicitly discussed. In particular when one of the two bodies is a rarefied gas the force is not additive, being proportional to the square root of the density. Nontrivial crossover regions at large distances are also identified.
On the asymptotic behaviour for an electromagnetic system with a dissipative boundary condition
NASA Astrophysics Data System (ADS)
Amendola, Giovambattista
2005-04-01
In this work we study some properties of solutions for the system describing a three-dimensional non-homogeneous non-conducting dielectric with a general boundary condition with memory. We first show the existence of the inverse of this boundary condition, which allows us to introduce a boundary free energy, similar to the one considered by Fabrizio & Morro (1996, Arch. Rat. Mech. Anal., 136, 359-381). Then, we prove existence and uniqueness theorems for weak and strong solutions of the evolutive problem in a finite time interval. Moreover, following Rivera & Olivera (1997, Boll. U.M.I., 11-A, 115-127), we examine some dissipative properties of the boundary condition and of its inverse and we give a useful energy estimate. Finally, when there is no memory in the boundary condition the exponential decay of the solution is proved.
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.
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.
Accurate formula for dissipative interaction in frequency modulation atomic force microscopy
NASA Astrophysics Data System (ADS)
Suzuki, Kazuhiro; Kobayashi, Kei; Labuda, Aleksander; Matsushige, Kazumi; Yamada, Hirofumi
2014-12-01
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.
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.
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. PMID:27420398
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.
Computational model for noncontact atomic force microscopy: energy dissipation of cantilever
NASA Astrophysics Data System (ADS)
Senda, Yasuhiro; Blomqvist, Janne; Nieminen, Risto M.
2016-09-01
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
Pulsatile blood flow, shear force, energy dissipation and Murray's Law
Painter, Page R; Edén, Patrik; Bengtsson, Hans-Uno
2006-01-01
Background Murray's Law states that, when a parent blood vessel branches into daughter vessels, the cube of the radius of the parent vessel is equal to the sum of the cubes of the radii of daughter blood vessels. Murray derived this law by defining a cost function that is the sum of the energy cost of the blood in a vessel and the energy cost of pumping blood through the vessel. The cost is minimized when vessel radii are consistent with Murray's Law. This law has also been derived from the hypothesis that the shear force of moving blood on the inner walls of vessels is constant throughout the vascular system. However, this derivation, like Murray's earlier derivation, is based on the assumption of constant blood flow. Methods To determine the implications of the constant shear force hypothesis and to extend Murray's energy cost minimization to the pulsatile arterial system, a model of pulsatile flow in an elastic tube is analyzed. A new and exact solution for flow velocity, blood flow rate and shear force is derived. Results For medium and small arteries with pulsatile flow, Murray's energy minimization leads to Murray's Law. Furthermore, the hypothesis that the maximum shear force during the cycle of pulsatile flow is constant throughout the arterial system implies that Murray's Law is approximately true. The approximation is good for all but the largest vessels (aorta and its major branches) of the arterial system. Conclusion A cellular mechanism that senses shear force at the inner wall of a blood vessel and triggers remodeling that increases the circumference of the wall when a shear force threshold is exceeded would result in the observed scaling of vessel radii described by Murray's Law. PMID:16923189
Measuring phase shifts and energy dissipation with amplitude modulation atomic force microscopy.
Martínez, Nicolás F; García, Ricardo
2006-04-14
By recording the phase angle difference between the excitation force and the tip response in amplitude modulation AFM it is possible to image compositional variations in heterogeneous samples. In this contribution we address some of the experimental issues relevant to perform phase contrast imaging measurements. Specifically, we study the dependence of the phase shift on the tip-surface separation, interaction regime, cantilever parameters, free amplitude and tip-surface dissipative processes. We show that phase shift measurements can be converted into energy dissipation values. Energy dissipation curves show a maximum (∼10 eV/cycle) with the amplitude ratio. Furthermore, energy dissipation maps provide a robust method to image material properties because they do not depend directly on the tip-surface interaction regime. Compositional contrast images are illustrated by imaging conjugated molecular islands deposited on silicon surfaces. PMID:21727409
Measuring phase shifts and energy dissipation with amplitude modulation atomic force microscopy.
Martínez, Nicolás F; García, Ricardo
2006-04-14
By recording the phase angle difference between the excitation force and the tip response in amplitude modulation AFM it is possible to image compositional variations in heterogeneous samples. In this contribution we address some of the experimental issues relevant to perform phase contrast imaging measurements. Specifically, we study the dependence of the phase shift on the tip-surface separation, interaction regime, cantilever parameters, free amplitude and tip-surface dissipative processes. We show that phase shift measurements can be converted into energy dissipation values. Energy dissipation curves show a maximum (∼10 eV/cycle) with the amplitude ratio. Furthermore, energy dissipation maps provide a robust method to image material properties because they do not depend directly on the tip-surface interaction regime. Compositional contrast images are illustrated by imaging conjugated molecular islands deposited on silicon surfaces.
Sensing dispersive and dissipative forces by an optomechanical cavity
NASA Astrophysics Data System (ADS)
Suchoi, Oren; Buks, Eyal
2016-07-01
We experimentally study an optomechanical cavity that is formed between a mechanical resonator, which serves as a movable mirror, and a stationary on-fiber dielectric mirror. A significant change in the behavior of the system is observed when the distance between the fiber's tip and the mechanical resonator is made smaller than about 1 μ \\text{m} . The combined influence of Casimir force, Coulomb interaction due to trapped charges, and optomechanical coupling is theoretically analyzed. The comparison between experimental results and theory yields a partial agreement.
NASA Astrophysics Data System (ADS)
Hughes, Scott; Flanagan, Eanna; Hinderer, Tanja; Ruangsri, Uchupol
2015-04-01
We describe how we have modified a frequency-domain Teukolsky-equation solver, previously used for computing orbit-averaged dissipation, in order to compute the dissipative piece of the gravitational self force on orbits of Kerr black holes. This calculation involves summing over a large number of harmonics. Each harmonic is independent of all others, so it is well suited to parallel computation. We show preliminary results for equatorial eccentric orbits and circular inclined orbits, demonstrating convergence of the harmonic expansion, as well as interesting phenomenology of the self force's behavior in the strong field. We conclude by discussing plans for using this force to study generic orbits, with a focus on the behavior of orbital resonances.
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. PMID:27653475
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.
A simple non-equilibrium theory of non-contact dissipation force microscopy
NASA Astrophysics Data System (ADS)
Kantorovich, L. N.
2001-02-01
The tip-surface interaction in the non-contact atomic force microscopy (NC-AFM) leads to energy dissipation. Recently, this effect has been harnessed to obtain images with atomic resolution. In an important paper Gauthier and Tsukada (GT) (1999 Phys. Rev. B 60 11716) suggested a theory of this, so-called non-contact dissipation force microscopy (NC-DFM) using a stochastic approach within a simple one-atomic representation of the surface. In this paper we elaborate on this model further, stressing the importance of a consistent non-equilibrium consideration. Then, using a more general model, we offer an alternative derivation based on a rather simple approach to non-equilibrium phenomenon used by Kirkwood for the Brownian motion. We show that our method leads to the final result similar to that obtained in the GT paper. We also discuss some other models for the energy dissipation in NC-AFM. In particular, we emphasise that the `stick and slip' (or adhesion hysteresis) model of energy dissipation, although containing a specific element which requires additional features to be incorporated in our model, is to be considered using non-equilibrium methods.
Dynamics of the coiled-coil unfolding transition of myosin rod probed by dissipation force spectrum.
Taniguchi, Yukinori; Khatri, Bhavin S; Brockwell, David J; Paci, Emanuele; Kawakami, Masaru
2010-07-01
The motor protein myosin II plays a crucial role in muscle contraction. The mechanical properties of its coiled-coil region, the myosin rod, are important for effective force transduction during muscle function. Previous studies have investigated the static elastic response of the myosin rod. However, analogous to the study of macroscopic complex fluids, how myosin will respond to physiological time-dependent loads can only be understood from its viscoelastic response. Here, we apply atomic force microscopy using a magnetically driven oscillating cantilever to measure the dissipative properties of single myosin rods that provide unique dynamical information about the coiled-coil structure as a function of force. We find that the friction constant of the single myosin rod has a highly nontrivial variation with force; in particular, the single-molecule friction constant is reduced dramatically and increases again as it passes through the coiled-uncoiled transition. This is a direct indication of a large free-energy barrier to uncoiling, which may be related to a fine-tuned dynamic mechanosignaling response to large and unexpected physiological loads. Further, from the critical force at which the minimum in friction occurs we determine the asymmetry of the bistable landscape that controls uncoiling of the coiled coil. This work highlights the sensitivity of the dissipative signal in force unfolding to dynamic molecular structure that is hidden to the elastic signal. PMID:20655854
NASA Astrophysics Data System (ADS)
Cerino, L.; Puglisi, A.
2015-08-01
In macroscopic systems, velocity-dependent phenomenological forces F(v) are used to model friction, feedback devices or self-propulsion. Such forces usually include a dissipative component which conceals the fast energy exchanges with a thermostat at the environment temperature T, ruled by a microscopic Hamiltonian H. The mapping (H,T) \\to F(v) —even if effective for many purposes— may lead to applications of stochastic thermodynamics where an incomplete fluctuating entropy production (FEP) is derived. An enlighting example is offered by recent macroscopic experiments where dissipation is dominated by solid-on-solid friction, typically modelled through a deterministic Coulomb force F(v). Through an adaptation of the microscopic Prandtl-Tomlinson model for friction, we show how the FEP is dominated by the heat released to the T-thermostat, ignored by the macroscopic Coulomb model. This problem, which haunts several studies in the literature, cannot be cured by weighing the time-reversed trajectories with a different auxiliary dynamics: it is only solved by a more accurate stochastic modelling of the thermostat underlying dissipation.
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.
Dynamics of dissipative self-assembly of particles interacting through oscillatory forces.
Tagliazucchi, M; Szleifer, I
2016-01-01
Dissipative self-assembly is the formation of ordered structures far from equilibrium, which continuously uptake energy and dissipate it into the environment. Due to its dynamical nature, dissipative self-assembly can lead to new phenomena and possibilities of self-organization that are unavailable to equilibrium systems. Understanding the dynamics of dissipative self-assembly is required in order to direct the assembly to structures of interest. In the present work, Brownian dynamics simulations and analytical theory were used to study the dynamics of self-assembly of a mixture of particles coated with weak acids and bases under continuous oscillations of the pH. The pH of the system modulates the charge of the particles and, therefore, the interparticle forces oscillate in time. This system produces a variety of self-assembled structures, including colloidal molecules, fibers and different types of crystalline lattices. The most important conclusions of our study are: (i) in the limit of fast oscillations, the whole dynamics (and not only those at the non-equilibrium steady state) of a system of particles interacting through time-oscillating interparticle forces can be described by an effective potential that is the time average of the time-dependent potential over one oscillation period; (ii) the oscillation period is critical to determine the order of the system. In some cases the order is favored by very fast oscillations while in others small oscillation frequencies increase the order. In the latter case, it is shown that slow oscillations remove kinetic traps and, thus, allow the system to evolve towards the most stable non-equilibrium steady state.
Martínez, Nicolas F; Kamiński, Wojciech; Gómez, Carlos J; Albonetti, Cristiano; Biscarini, Fabio; Pérez, Rubén; García, Ricardo
2009-10-28
We perform a combined experimental and theoretical approach to establish the atomistic origin of energy dissipation occurring while imaging a molecular surface with an amplitude modulation atomic force microscope. We show that the energy transferred by a single nano-asperity to a sexithiophene monolayer is about 0.15 eV/cycle. The configuration space sampled by the tip depends on whether it approaches or withdraws from the surface. The asymmetry arises because of the presence of energy barriers among different deformations of the molecular geometry. This is the source of the material contrast provided by the phase-shift images. PMID:19801766
Martínez, Nicolas F; Kamiński, Wojciech; Gómez, Carlos J; Albonetti, Cristiano; Biscarini, Fabio; Pérez, Rubén; García, Ricardo
2009-10-28
We perform a combined experimental and theoretical approach to establish the atomistic origin of energy dissipation occurring while imaging a molecular surface with an amplitude modulation atomic force microscope. We show that the energy transferred by a single nano-asperity to a sexithiophene monolayer is about 0.15 eV/cycle. The configuration space sampled by the tip depends on whether it approaches or withdraws from the surface. The asymmetry arises because of the presence of energy barriers among different deformations of the molecular geometry. This is the source of the material contrast provided by the phase-shift images.
A many-body dissipative particle dynamics study of forced water-oil displacement in capillary.
Chen, Chen; Zhuang, Lin; Li, Xuefeng; Dong, Jinfeng; Lu, Juntao
2012-01-17
The forced water-oil displacement in capillary is a model that has important applications such as the groundwater remediation and the oil recovery. Whereas it is difficult for experimental studies to observe the displacement process in a capillary at nanoscale, the computational simulation is a unique approach in this regard. In the present work, the many-body dissipative particle dynamics (MDPD) method is employed to simulate the process of water-oil displacement in capillary with external force applied by a piston. As the property of all interfaces involved in this system can be manipulated independently, the dynamic displacement process is studied systematically under various conditions of distinct wettability of water in capillary and miscibility between water and oil as well as of different external forces. By analyzing the dependence of the starting force on the properties of water/capillary and water/oil interfaces, we find that there exist two different modes of the water-oil displacement. In the case of stronger water-oil interaction, the water particles cannot displace those oil particles sticking to the capillary wall, leaving a low oil recovery efficiency. To minimize the residual oil content in capillary, enhancing the wettability of water and reducing the external force will be beneficial. This simulation study provides microscopic insights into the water-oil displacement process in capillary and guiding information for relevant applications.
Turbulent dissipation in the Rhine ROFI forced by tidal flow and wind stress
NASA Astrophysics Data System (ADS)
Fisher, N. R.; Simpson, J. H.; Howarth, M. J.
2002-12-01
The Rhine ROFI (Region Of Freshwater Influence), which extends northwards along the Dutch coast from the estuary source, exhibits strong cross-shore salinity gradients which interact with straining by the tidal flow and stirring, by tides and wind stress, to produce a semi-diurnal cycle of stratification. Here we report new time-series observations of the rate of turbulent kinetic energy dissipation ɛ from the FLY Profiler, which were made in parallel with measurements of density structure and horizontal flow using moored instruments and bottom-mounted Acoustic Doppler Current Profilers. Under light wind conditions, ɛ in the lower half of the water column follows a predominantly M 4 cycle although with higher values during north-eastward flow associated with the residual flow in that direction. Following the strong peak in dissipation near the bed, enhanced dissipation is apparent extending up the water column. The time delay of the maximum in ɛ increases with height above the bed and peak values increase up to the highest level, 15 mab (metres above bed), at which measurements were possible. At this level, ɛ shows a predominantly M 2 variation with the maximum occurring at a time when vertical stability is negligible and the effect of tidal straining is to create instability in the water column as the cross-shore shear forces higher salinity water over fresher. The inference is that potential energy released by straining is responsible for convective motions and, hence, the enhanced turbulent activity observed. Under conditions of substantial wind stress (τ w ˜0.2 N m -2), turbulent activity in the upper layers is considerably increased with values up to 0.1 W m -3 at 15 mab which is enough to obscure the influence of convection. Near the bed, dissipation is still dominated by the M 4 cycle with asymmetry due to the residual flow. The cycle of dissipation in the Rhine ROFI is compared with that previously reported for Liverpool Bay. It is suggested that
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.
NASA Astrophysics Data System (ADS)
Mo, M. Y.; Kantorovich, L.
2001-02-01
We apply the non-equilibrium statistical operator method to non-contact atomic force microscopy, considering explicitly the statistical effects of (classical) vibrations of surface atoms and associated energy transfer from the tip to the surface. We derive several, physically and mathematically equivalent, forms of the equation of motion for the tip, each containing a friction term due to the so-called intrinsic mechanism of energy dissipation first suggested by Gauthier and Tsukada. Our exact treatment supports the results of some earlier work which were all approximate. We also demonstrate, using the same theory, that the distribution function of the tip in the coordinate-momentum phase subspace is governed by the Fokker-Planck equation and should be considered as strongly peaked around the exact values t and t of the momentum and the position of the tip, respectively.
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.
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.
Ferguson-Pell, Martin; Ferguson-Pell, Grace; Mohammadi, Farhood; Call, Evan
2015-01-01
Results from applying the International Organization for Standardization (ISO) 16840-2 test method for determining the impact damping characteristics of 35 wheelchair cushions plus a high resilience (HR70) polyurethane reference foam sample are reported. The generation of impact forces when a wheelchair user either transfers onto a cushion or the wheelchair encounters rough terrain or bumps down a step can endanger the viability of tissues, especially if these forces occur repeatedly. The results demonstrate significant differences in the impact force dissipation characteristics of different cushion products but do not reliably identify differences in performance that can be attributed to descriptive information about cushion composition alone. Instead, these results demonstrate that the materials, proprietary design, and construction features of wheelchair cushions in combination dictate impact force dissipation properties. The results of a cluster analysis are used to generate a model that can be used to compare the impact damping properties obtained from the ISO 16840-2 test method with those of a range of cushions and the reference cushion. Manufacturers will therefore be able to provide users and clinicians with information about the impact force dissipation properties of the cushions that will enable them to make more informed product choices for achieving improved comfort and to protect skin integrity. PMID:26230038
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.
NASA Technical Reports Server (NTRS)
Mitchell, K. E.; Dutton, J. A.
1981-01-01
The considered investigation is concerned with periodic solutions in the context of a forced, dissipative, barotropic spectral model truncated to three complex coefficients with constant forcing on only the intermediate scale. It is found that determining a periodic solution of this three-coefficient model also reduces to finding the algebraic roots of a real polynomial. In the derivation of this polynomial, a class of hydrodynamic spectral systems is described for which a periodic solution might be similarly specified. The existence of periodic solutions of the three-coefficient model is controlled by the roots of the stability polynomial of the basic stationary solution, which represents the simplest response to the constant forcing. When the forcing exceeds a critical value, the basic solution becomes unstable. Owing to the nature of the roots of the stability polynomial at critical forcing, bifurcation theory guarantees the existence of a periodic solution.
New Asymptotic Behavior of the Surface-Atom Force out of Thermal Equilibrium
Antezza, Mauro; Pitaevskii, Lev P.; Stringari, Sandro
2005-09-09
The Casimir-Polder-Lifshitz force felt by an atom near the surface of a substrate is calculated out of thermal equilibrium in terms of the dielectric function of the material and of the atomic polarizability. The new force decays like 1/z{sup 3} at large distances (i.e., slower than at equilibrium), exhibits a sizable temperature dependence, and is attractive or repulsive depending on whether the temperature of the substrate is higher or smaller than the one of the environment. Our predictions can be relevant for experiments with ultracold atomic gases. Both dielectric and metal substrates are considered.
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”).
NASA Technical Reports Server (NTRS)
Parker, E. N.
1990-01-01
Direct integration of the force-free field equation del x B = alpha B, in the simple case of the local deformation of a laminar field, produces field configurations containing tangential discontinuities (current sheets). Whereas continuous solutions allow only restricted field topologies, the discontinuities provide the necessary release from those restrictions in more general topologies. Magnetic fields in nature are strongly deformed by convection, so as to contain significant internal discontinuities. The bipolar magnetic fields containing the active X-ray corona of the sun are a case in point. It appears that the dissipation caused by the discontinuities may be the primary heat source producing the X-ray corona.
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…
Hickey, M.P. )
1988-05-01
The theory of Walterscheid et al. (1987) to explain internal gravity wave induced oscillations in the emission intensity I and rotational temperature T of the OH nightglow was modified by Hickey (1988) to include the effects of eddy dissipation and Coriolis force. In the theory of Walterscheid et al. (1987) the ratio {eta} = ({delta}I/I{sub 0})/({delta}T/T{sub 0}) ({delta} refers to a perturbation quantity, and a zero subscript refers to an average) was found to be independent of horizontal wavelength at long periods, while in the extended theory of Hickey (1988) some such dependence was inferred. In the present paper the horizontal wavelength dependence of {eta} is examined. It is found that values of {eta} will be dependent on both wave period and horizontal wavelength, meaning that in order to compare measurement with theory, horizontal wavelengths will need to be measured in conjunction with the OH nightglow measurements. At long periods the modifications to {eta} by the inclusion of eddy dissipation are much larger for the shorter horizontal wavelength waves, although such modifications may be more observable for some of the longer horizontal wavelength waves. The Coriolis force is important only for waves of very large horizontal wavelength.
Lin, Shueei Muh
2007-01-01
In a common environment of atomic force microscopy (AFM), a damping force occurs between a tip and a sample. The influence of damping on the dynamic response of a cantilever must be significant. Moreover, accurate theory is very helpful for the interpretation of a sample's topography and properties. In this study, the effects of damping and nonlinear interatomic tip-sample forces on the dynamic response of an amplitude-formulation AFM are investigated. The damping force is simulated by using the conventional Kelvin-Voigt damping model. The interatomic tip-sample force is the attractive van der Waals force. For consistance with real measurement of a cantilever, the mathematical equations of the beam theory of an AM-AFM are built and its analytical solution is derived. Moreover, an AFM system is also simplified into a mass-spring-damper model. Its exact solution is simple and intuitive. Several relations among the damping ratio, the response ratio, the frequency shift, the energy dissipation and the Q-factor are revealed. It is found that the resonant frequencies and the phase angles determined by the two models are almost same. Significant differences in the resonant quality factors and the response ratios determined by using the two models are also found. Finally, the influences of the variations of several parameters on the error of measuring a sample's topography are investigated. PMID:16982149
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.
Trément, Sébastien; Rousseau, Bernard; Schnell, Benoît; Petitjean, Laurent; Couty, Marc
2014-04-07
We apply operational procedures available in the literature to the construction of coarse-grained conservative and friction forces for use in dissipative particle dynamics (DPD) simulations. The full procedure rely on a bottom-up approach: large molecular dynamics trajectories of n-pentane and n-decane modeled with an anisotropic united atom model serve as input for the force field generation. As a consequence, the coarse-grained model is expected to reproduce at least semi-quantitatively structural and dynamical properties of the underlying atomistic model. Two different coarse-graining levels are studied, corresponding to five and ten carbon atoms per DPD bead. The influence of the coarse-graining level on the generated force fields contributions, namely, the conservative and the friction part, is discussed. It is shown that the coarse-grained model of n-pentane correctly reproduces self-diffusion and viscosity coefficients of real n-pentane, while the fully coarse-grained model for n-decane at ambient temperature over-predicts diffusion by a factor of 2. However, when the n-pentane coarse-grained model is used as a building block for larger molecule (e.g., n-decane as a two blobs model), a much better agreement with experimental data is obtained, suggesting that the force field constructed is transferable to large macro-molecular systems.
NASA Astrophysics Data System (ADS)
Trément, Sébastien; Schnell, Benoît.; Petitjean, Laurent; Couty, Marc; Rousseau, Bernard
2014-04-01
We apply operational procedures available in the literature to the construction of coarse-grained conservative and friction forces for use in dissipative particle dynamics (DPD) simulations. The full procedure rely on a bottom-up approach: large molecular dynamics trajectories of n-pentane and n-decane modeled with an anisotropic united atom model serve as input for the force field generation. As a consequence, the coarse-grained model is expected to reproduce at least semi-quantitatively structural and dynamical properties of the underlying atomistic model. Two different coarse-graining levels are studied, corresponding to five and ten carbon atoms per DPD bead. The influence of the coarse-graining level on the generated force fields contributions, namely, the conservative and the friction part, is discussed. It is shown that the coarse-grained model of n-pentane correctly reproduces self-diffusion and viscosity coefficients of real n-pentane, while the fully coarse-grained model for n-decane at ambient temperature over-predicts diffusion by a factor of 2. However, when the n-pentane coarse-grained model is used as a building block for larger molecule (e.g., n-decane as a two blobs model), a much better agreement with experimental data is obtained, suggesting that the force field constructed is transferable to large macro-molecular systems.
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.
Nisin dissipates the proton motive force of the obligate anaerobe Clostridium sporogenes PA 3679.
Okereke, A; Montville, T J
1992-01-01
The influence of nisin on the proton motive force (delta p) generated by glucose-energized cells of the obligate putrefactive anaerobe Clostridium sporogenes PA 3679 was determined. The components of delta p, the transmembrane potential (delta psi) and the pH gradient (delta pH), were determined from the distributions of the lipophilic cation [3H]TPP+ ([3H]tetraphenylphosphonium bromide) and [14C]salicylic acid, respectively. The cells maintained a constant delta p of -111 mV, consisting of a delta pH of 0.4 to 1.0 pH units at an external pH of 5 to 7 and a delta psi of -60 to -88 mV. Nisin, carbonyl cyanide m-chlorophenylhydrazone (CCCP), and N,N'-dicyclohexylcarbodiimide (DCCD) at pH 6.0 elicited the complete release of preaccumulated [3H]tetraphenylphosphonium bromide and [14C]salicylic acid, with a concomitant depletion of delta psi and delta pH. Nisin and DCCD caused rapid drops in intracellular ATP levels from 1.2 to 0.01 and 0.06 nmol/mg of cells (dry weight), respectively. Cells exposed to nisin and DCCD lost the ability to form colonies, thus suggesting that delta psi and delta pH are necessary for cell viability. The data suggest that depletion of delta p and exhaustion of cellular ATP reserves are the basis for nisin inhibition of C. sporogenes PA 3679. PMID:1325140
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.
Localized chaotic patterns in weakly dissipative systems
NASA Astrophysics Data System (ADS)
Urzagasti, D.; Laroze, D.; Pleiner, H.
2014-01-01
A generalized parametrically driven damped nonlinear Schrödinger equation is used to describe, close to the resonance, the dynamics of weakly dissipative systems, like a harmonically coupled pendula chain or an easy-plane magnetic wire. The combined effects of parametric forcing, spatial coupling, and dissipation allows for the existence of stable non-trivial uniform states as well as homogeneous pattern states. The latter can be regular or chaotic. A new family of localized states that connect asymptotically a non-trivial uniform state with a spatio-temporal chaotic pattern is numerically found. We discuss the parameter range, where these localized structures exist. This article is dedicated to Prof. Helmut R. Brand on the occasion of his 60th birthday.
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)
Sharma, S.; Narayan, A.
2001-06-01
The non-linear oscillation of inter-connected satellites system about its equilibrium position in the neighabourhood of main resonance ??=3D 1, under the combined effects of the solar radiation pressure and the dissipative forces of general nature has been discussed. It is found that the oscillation of the system gets disturbed when the frequency of the natural oscillation approaches the resonance frequency.
Drell, S.D.
1980-09-15
The concept of asymptotic freedom in quantum chromodynamics (QCD) is reviewed. Analogies are drawn to quantum electrodynamics and non-relativistic quantum mechanics. Asymptotic freedom is seen as the effect of anti-shielding due to the quantums of QCD, the gluons, carrying the color charge. Beginning with the Hamiltonian for the color gauge field plus fixed sources of color charge, the interaction energy between two fixed charges is derived. Both the interaction energy and the running coupling constant are seen to decrease with decreasing distance.
Asymptotic Behavior of an Elastic Satellite with Internal Friction
NASA Astrophysics Data System (ADS)
Haus, E.; Bambusi, D.
2015-12-01
We study the dynamics of an elastic body whose shape and position evolve due to the gravitational forces exerted by a pointlike planet. The main result is that, if all the deformations of the satellite dissipate some energy, then under a suitable nondegeneracy condition there are only three possible outcomes for the dynamics: (i) the orbit of the satellite is unbounded, (ii) the satellite falls on the planet, (iii) the satellite is captured in synchronous resonance i.e. its orbit is asymptotic to a motion in which the barycenter moves on a circular orbit, and the satellite moves rigidly, always showing the same face to the planet. The result is obtained by making use of LaSalle's invariance principle and by a careful kinematic analysis showing that energy stops dissipating only on synchronous orbits. We also use in quite an extensive way the fact that conservative elastodynamics is a Hamiltonian system invariant under the action of the rotation group.
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.
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.
Dissipative nonlinear dynamics in holography
NASA Astrophysics Data System (ADS)
Basu, Pallab; Ghosh, Archisman
2014-02-01
We look at the response of a nonlinearly coupled scalar field in an asymptotically AdS black brane geometry and find a behavior very similar to that of known dissipative nonlinear systems like the chaotic pendulum. Transition to chaos proceeds through a series of period-doubling bifurcations. The presence of dissipation, crucial to this behavior, arises naturally in a black hole background from the ingoing conditions imposed at the horizon. AdS/CFT translates our solution to a chaotic response of O, the operator dual to the scalar field. Our setup can also be used to study quenchlike behavior in strongly coupled nonlinear systems.
NASA Astrophysics Data System (ADS)
Zheng, Quanan; Zhu, Benlu; Li, Junyi; Sun, Zhenyu; Xu, Ying; Hu, Jianyu
2015-08-01
This study aims to gain insight into the sea level response to typhoon in the northern South China Sea using typhoon records from 1978 to 1997, simultaneous tidal gauge records and satellite altimeter along-track sea level data. We find that the ocean sea level response signatures in the deep water agree well with a single sea level soliton, of which the average soliton amplitude is (34 ± 6) cm and the average characteristic half width is (115 ± 12) km. Evolution of the single soliton as propagating across a shoaling bottom topography obeys solutions of the perturbed Korteweg and de Vries equation. The solutions reveal that forced by the hyperbolic-tangent-shaped topography, the single soliton evolves to a solitary wave packet consisting of a large leading soliton and smaller following waves in an oscillatory tail as approaching the shallow water. This phenomenon is verified by observed sea level signatures of 19 storm surges. The correlation coefficient between theoretical solution and observations is as high as 0.91. Meanwhile, the soliton amplitude grows with a soliton amplitude growth ratio (SAGR), which depends on the deep water and shallow water depths. However, without consideration of viscous effects, the SAGR model overestimates the soliton amplitude growth. Thus the vorticity equation for viscous fluid is adopted to solve this issue. The results indicate that turbulent viscosities are responsible to soliton amplitude decay concurring with the growth and causes dependence of the storm surge amplitude on the typhoon incident angle.
NASA Astrophysics Data System (ADS)
Zheng, Quanan; Zhu, Benlu; Li, Junyi; Sun, Zhenyu; Xu, Ying; Hu, Jianyu
2014-09-01
This study aims to gain insight into the sea level response to typhoon in the northern South China Sea using typhoon records from 1978 to 1997, simultaneous tidal gauge records and satellite altimeter along-track sea level data. We find that the ocean sea level response signatures in the deep water agree well with a single sea level soliton, of which the average soliton amplitude is (34 ± 6) cm and the average characteristic half width is (115 ± 12) km. Evolution of the single soliton as propagating across a shoaling bottom topography obeys solutions of the perturbed Korteweg and de Vries equation. The solutions reveal that forced by the hyperbolic-tangent-shaped topography, the single soliton evolves to a solitary wave packet consisting of a large leading soliton and smaller following waves in an oscillatory tail as approaching the shallow water. This phenomenon is verified by observed sea level signatures of 19 storm surges. The correlation coefficient between theoretical solution and observations is as high as 0.91. Meanwhile, the soliton amplitude grows with a soliton amplitude growth ratio (SAGR), which depends on the deep water and shallow water depths. However, without consideration of viscous effects, the SAGR model overestimates the soliton amplitude growth. Thus the vorticity equation for viscous fluid is adopted to solve this issue. The results indicate that turbulent viscosities are responsible to soliton amplitude decay concurring with the growth and causes dependence of the storm surge amplitude on the typhoon incident angle.
Asymptotic stability of Riemann waves for conservation laws
NASA Astrophysics Data System (ADS)
Chen, G.-Q.; Frid, H.; Marta
We are concerned with the asymptotic behavior of entropy solutions of conservation laws. A new notion about the asymptotic stability of Riemann solutions is introduced, and corresponding analytical frameworks are developed. The correlation between the asymptotic problem and many important topics in conservation laws and nonlinear analysis is recognized and analyzed, such as zero dissipation limits, uniqueness of entropy solutions, entropy analysis, and divergence-measure fields in L∞ . Then this theory is applied to understanding the asymptotic behavior of entropy solutions for many important systems of conservation laws.
NASA Astrophysics Data System (ADS)
Evesque, Pierre
2013-06-01
A 1d Boltzmann equation is introduced to describe the speed distribution function in granular gas system with local collision dissipation. It leads to introduce a new term, equivalent to an acceleration This term was always assumed to be 0, but it is not zero in general, even when the system is steady (i.e. when local mean flow equals 0). This shows that the flow (+ boundary) exerts a force on any extra steady particle (or plane) that drives it to the center. This result is analyzed, compared and interpreted using the Lagrangian & Eulerian view points of the mechanics; it demonstrates that classic view point of hydrodynamics does not hold anymore. The paper investigates different cases and gives experimental evidences of the features: it explains while local speed distribution f(v,r) of granular gas in a box subjected to vibration is non symmetric in the direction of vibration, while the system is stationary (mean local speed equals 0). Papers giving local experimental or simulated distributions are quoted, where two local pressures P± = Σv>0,orv<0 (mv2) in +Ox and -Ox direction are different. It implies also introducing two local temperatures T± in the ±Ox vibration direction. These points are confirmed using 2d and 3d granular gas simulation. It should apply likely to get deeper understanding of different effects as the "granular Leidenfrost effect", the stoppage of vibrated-hourglass, some turbulent flow, and the granular-Maxwell-demon.
Zhou, Cheng; Friedt, Jean-Michel; Angelova, Angelina; Choi, Kang-Hoon; Laureyn, Wim; Frederix, Filip; Francis, Laurent A; Campitelli, Andrew; Engelborghs, Yves; Borghs, Gustaaf
2004-07-01
Time-resolved adsorption behavior of a human immunoglobin G (hIgG) protein on a hydrophobized gold surface is investigated using multitechniques: quartz crystal microbalance/dissipation (QCM-D) technique; combined surface plasmon resonance (SPR) and Love mode surface acoustic wave (SAW) technique; combined QCM-D and atomic force microscopy (AFM) technique. The adsorbed hIgG forms interfacial structures varying in organization from a submonolayer to a multilayer. An "end-on" IgG orientation in the monolayer film, associated with the surface coverage results, does not corroborate with the effective protein thickness determined from SPR/SAW measurements. This inconsistence is interpreted by a deformation effect induced by conformation change. This conformation change is confirmed by QCM-D measurement. Combined SPR/SAW measurements suggest that the adsorbed protein barely contains water after extended contact with the hydrophobic surface. This limited interfacial hydration also contributed to a continuous conformation change in the adsorbed protein layer. The viscoelastic variation associated with interfacial conformation changes induces about 1.5 times overestimation of the mass uptake in the QCM-D measurements. The merit of combined multitechnique measurements is demonstrated.
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.
Spatial Localization in Dissipative Systems
NASA Astrophysics Data System (ADS)
Knobloch, E.
2015-03-01
Spatial localization is a common feature of physical systems, occurring in both conservative and dissipative systems. This article reviews the theoretical foundations of our understanding of spatial localization in forced dissipative systems, from both a mathematical point of view and a physics perspective. It explains the origin of the large multiplicity of simultaneously stable spatially localized states present in a parameter region called the pinning region and its relation to the notion of homoclinic snaking. The localized states are described as bound states of fronts, and the notions of front pinning, self-pinning, and depinning are emphasized. Both one-dimensional and two-dimensional systems are discussed, and the reasons behind the differences in behavior between dissipative systems with conserved and nonconserved dynamics are explained. The insights gained are specific to forced dissipative systems and are illustrated here using examples drawn from fluid mechanics (convection and shear flows) and a simple model of crystallization.
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.
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.
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)
Dissipative superfluid dynamics from gravity
NASA Astrophysics Data System (ADS)
Bhattacharya, Jyotirmoy; Bhattacharyya, Sayantani; Minwalla, Shiraz
2011-04-01
Charged asymptotically AdS 5 black branes are sometimes unstable to the condensation of charged scalar fields. For fields of infinite charge and squared mass -4 Herzog was able to analytically determine the phase transition temperature and compute the endpoint of this instability in the neighborhood of the phase transition. We generalize Herzog's construction by perturbing away from infinite charge in an expansion in inverse charge and use the solutions so obtained as input for the fluid gravity map. Our tube wise construction of patched up locally hairy black brane solutions yields a one to one map from the space of solutions of superfluid dynamics to the long wavelength solutions of the Einstein Maxwell system. We obtain explicit expressions for the metric, gauge field and scalar field dual to an arbitrary superfluid flow at first order in the derivative expansion. Our construction allows us to read off the the leading dissipative corrections to the perfect superfluid stress tensor, current and Josephson equations. A general framework for dissipative superfluid dynamics was worked out by Landau and Lifshitz for zero superfluid velocity and generalized to nonzero fluid velocity by Clark and Putterman. Our gravitational results do not fit into the 13 parameter Clark-Putterman framework. Purely within fluid dynamics we present a consistent new generalization of Clark and Putterman's equations to a set of superfluid equations parameterized by 14 dissipative parameters. The results of our gravitational calculation fit perfectly into this enlarged framework. In particular we compute all the dissipative constants for the gravitational superfluid.
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.
Melting of Io by tidal dissipation
NASA Technical Reports Server (NTRS)
Peale, S. J.; Cassen, P.; Reynolds, R. T.
1979-01-01
The resonant structure of Io leads to forced eccentricities that are considerably larger than the free values. Although still modest by all standards, these forced eccentricities coupled with the enormous tides induced by Jupiter lead to magnitudes of tidal dissipation that are large enough to completely dominate the thermal history of Io. In the present paper, the forced eccentricities are calculated and then substituted into an expression for the total tidal dissipation. The results point to the possibility that the dissipation of tidal energy in Io may have melted a major fraction of Io's mass.
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.
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. PMID:24032805
Dissipative effects on quantum sticking.
Zhang, Yanting; Clougherty, Dennis P
2012-04-27
Using variational mean-field theory, many-body dissipative effects on the threshold law for quantum sticking and reflection of neutral and charged particles are examined. For the case of an Ohmic bosonic bath, we study the effects of the infrared divergence on the probability of sticking and obtain a nonperturbative expression for the sticking rate. We find that for weak dissipative coupling α, the low-energy threshold laws for quantum sticking are modified by an infrared singularity in the bath. The sticking probability for a neutral particle with incident energy E→0 behaves asymptotically as s~E((1+α)/2(1-α)); for a charged particle, we obtain s~E(α/2(1-α)). Thus, "quantum mirrors"-surfaces that become perfectly reflective to particles with incident energies asymptotically approaching zero-can also exist for charged particles. We provide a numerical example of the effects for electrons sticking to porous silicon via the emission of a Rayleigh phonon. PMID:22680861
Dissipative Effects on Quantum Sticking
NASA Astrophysics Data System (ADS)
Zhang, Yanting; Clougherty, Dennis P.
2012-04-01
Using variational mean-field theory, many-body dissipative effects on the threshold law for quantum sticking and reflection of neutral and charged particles are examined. For the case of an Ohmic bosonic bath, we study the effects of the infrared divergence on the probability of sticking and obtain a nonperturbative expression for the sticking rate. We find that for weak dissipative coupling α, the low-energy threshold laws for quantum sticking are modified by an infrared singularity in the bath. The sticking probability for a neutral particle with incident energy E→0 behaves asymptotically as s˜E(1+α)/2(1-α); for a charged particle, we obtain s˜Eα/2(1-α). Thus, “quantum mirrors”—surfaces that become perfectly reflective to particles with incident energies asymptotically approaching zero—can also exist for charged particles. We provide a numerical example of the effects for electrons sticking to porous silicon via the emission of a Rayleigh phonon.
Weinberg, Steven
2010-04-15
Inflation is studied in the context of asymptotically safe theories of gravitation. Conditions are explored under which it is possible to have a long period of nearly exponential expansion that eventually comes to an end.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Pisarski, Robert D.
1982-12-01
I study the field theory of a scalar field ω with solely cubic interactions in three dimensions-(ω3)3. I insist that the ω field represents the density of a fluid, so ω must always be >=0. If there are long-range couplings in the fluid such that the inverse ω propagator is linear rather than quadratic in momentum, then (ω3)3 theory is asymptotically free. The asymptotic freedom of (ω3)3 theory is closely related to the existence of a nonzero, ultraviolet-stable fixed point in large-N (φ¯6)3 theory. There are also analogies between the asymptotic freedom of fluids (in three and six dimensions) and that of non-Abelian gauge fields (in four dimensions).
Asymptotically Safe Lorentzian Gravity
Manrique, Elisa; Rechenberger, Stefan; Saueressig, Frank
2011-06-24
The gravitational asymptotic safety program strives for a consistent and predictive quantum theory of gravity based on a nontrivial ultraviolet fixed point of the renormalization group (RG) flow. We investigate this scenario by employing a novel functional renormalization group equation which takes the causal structure of space-time into account and connects the RG flows for Euclidean and Lorentzian signature by a Wick rotation. Within the Einstein-Hilbert approximation, the {beta} functions of both signatures exhibit ultraviolet fixed points in agreement with asymptotic safety. Surprisingly, the two fixed points have strikingly similar characteristics, suggesting that Euclidean and Lorentzian quantum gravity belong to the same universality class at high energies.
Asymptotically safe Lorentzian gravity.
Manrique, Elisa; Rechenberger, Stefan; Saueressig, Frank
2011-06-24
The gravitational asymptotic safety program strives for a consistent and predictive quantum theory of gravity based on a nontrivial ultraviolet fixed point of the renormalization group (RG) flow. We investigate this scenario by employing a novel functional renormalization group equation which takes the causal structure of space-time into account and connects the RG flows for Euclidean and Lorentzian signature by a Wick rotation. Within the Einstein-Hilbert approximation, the β functions of both signatures exhibit ultraviolet fixed points in agreement with asymptotic safety. Surprisingly, the two fixed points have strikingly similar characteristics, suggesting that Euclidean and Lorentzian quantum gravity belong to the same universality class at high energies. PMID:21770628
Asymptotically safe Higgs inflation
Xianyu, Zhong-Zhi; He, Hong-Jian E-mail: hjhe@tsinghua.edu.cn
2014-10-01
We construct a new inflation model in which the standard model Higgs boson couples minimally to gravity and acts as the inflaton. Our construction of Higgs inflation incorporates the standard model with Einstein gravity which exhibits asymptotic safety in the ultraviolet region. The slow roll condition is satisfied at large field value due to the asymptotically safe behavior of Higgs self-coupling at high energies. We find that this minimal construction is highly predictive, and is consistent with both cosmological observations and collider experiments.
Asymptotically safe Lorentzian gravity.
Manrique, Elisa; Rechenberger, Stefan; Saueressig, Frank
2011-06-24
The gravitational asymptotic safety program strives for a consistent and predictive quantum theory of gravity based on a nontrivial ultraviolet fixed point of the renormalization group (RG) flow. We investigate this scenario by employing a novel functional renormalization group equation which takes the causal structure of space-time into account and connects the RG flows for Euclidean and Lorentzian signature by a Wick rotation. Within the Einstein-Hilbert approximation, the β functions of both signatures exhibit ultraviolet fixed points in agreement with asymptotic safety. Surprisingly, the two fixed points have strikingly similar characteristics, suggesting that Euclidean and Lorentzian quantum gravity belong to the same universality class at high energies.
NASA Astrophysics Data System (ADS)
Cristallini, Achille
2016-07-01
A new and intriguing machine may be obtained replacing the moving pulley of a gun tackle with a fixed point in the rope. Its most important feature is the asymptotic efficiency. Here we obtain a satisfactory description of this machine by means of vector calculus and elementary trigonometry. The mathematical model has been compared with experimental data and briefly discussed.
Dissipative Effects on Quantum Sticking
NASA Astrophysics Data System (ADS)
Zhang, Yanting; Clougherty, Dennis
2011-03-01
Using variational mean-field theory, many-body dissipative effects on the threshold law for quantum sticking and reflection of neutral particles are examined. For the case of an ohmic bosonic bath, we study the effects of the infrared divergence on the probability of sticking and obtain an analytic expression for the rate of sticking as an asymptotic expansion in the incident energy E . The low-energy threshold law for quantum sticking is found to be robust with respect to many-body effects and remains a universal scaling law to leading order in E . Non-universal many-body effects alter the coefficient of the rate law and the exponent of a subdominant term. We gratefully acknowledge support from NSF under DMR-0814377.
Quantum bouncer with quadratic dissipation
NASA Astrophysics Data System (ADS)
González, G.
2008-02-01
The energy loss due to a quadratic velocity dependent force on a quantum particle bouncing on a perfectly reflecting surface is obtained for a full cycle of motion. We approach this problem by means of a new effective phenomenological Hamiltonian which corresponds to the actual energy of the system and obtained the correction to the eigenvalues of the energy in first order quantum perturbation theory for the case of weak dissipation.
Asymptotically Disjoint Quantum States
NASA Astrophysics Data System (ADS)
Primas, Hans
A clarification of the heuristic concept of decoherence requires a consistent description of the classical behavior of some quantum Systems. We adopt algebraic quantum mechanics since it includes not only classical physics, but also permits a judicious concept of a classical mixture and explains the possibility of the emergence of a classical behavior of quantum Systems. A nonpure quantum state tan be interpreted as a classical mixture if and only if its components are disjoint. Here, two pure quantum states are called disjoint if there exists an element of the Center of the algebra of observables such that its expectation values with respect to these states are different. An appropriate automorphic dynamics tan transform a factor state into a classical mixture of asymptotically disjoint final states. Such asymptotically disjoint quantum states lead to regular decision Problems while exactly disjoint states evoke Singular Problems which engineers reject as improperly posed.
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.
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.
NASA Astrophysics Data System (ADS)
Vadas, S. L.; Liu, H.-L.
2013-05-01
We study the response of the thermosphere and ionosphere to gravity waves (GWs) excited by 6 h of deep convection in Brazil on the evening of 01 October 2005 via the use of convective plume, ray trace, and global models. We find that primary GWs excited by convection having horizontal wavelengths of λH˜70-300 km, periods of 10-60 min, and phase speeds of cH˜50-225 m/s propagate well into the thermosphere. Their density perturbations are ρ'/ρ
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.
Asymptotic symmetries from finite boxes
NASA Astrophysics Data System (ADS)
Andrade, Tomás; Marolf, Donald
2016-01-01
It is natural to regulate an infinite-sized system by imposing a boundary condition at finite distance, placing the system in a 'box.' This breaks symmetries, though the breaking is small when the box is large. One should thus be able to obtain the asymptotic symmetries of the infinite system by studying regulated systems. We provide concrete examples in the context of Einstein-Hilbert gravity (with negative or zero cosmological constant) by showing in 4 or more dimensions how the anti-de Sitter and Poincaré asymptotic symmetries can be extracted from gravity in a spherical box with Dirichlet boundary conditions. In 2 + 1 dimensions we obtain the full double-Virasoro algebra of asymptotic symmetries for AdS3 and, correspondingly, the full Bondi-Metzner-Sachs (BMS) algebra for asymptotically flat space. In higher dimensions, a related approach may continue to be useful for constructing a good asymptotically flat phase space with BMS asymptotic symmetries.
Strongly Nonlinear Stress Waves in Dissipative Metamaterials
NASA Astrophysics Data System (ADS)
Xu, Yichao; Nesterenko, Vitali
2015-06-01
We present the measurements, numerical simulations, and theoretical analysis of stress wave propagation in a one-dimensional strongly nonlinear dissipative metamaterial composed of steel disks and Nitrile O-rings. A stress wave of bell shape is generated by impactor with different masses. A strongly nonlinear double power-law is used to describe the nonlinear viscoelastic force interaction between the disks due to the compression of rubber O-rings. Numerical modeling including a nonlinear dissipative term is developed to predict the wave shape and propagation speed. The shape of generated stress wave can be dramatically changed by the viscous dissipation, which may prevent the pulse from splitting into trains of solitary waves. This strongly nonlinear dissipative metamaterial has a potential for attenuation of dynamic loading and allows an enhanced tunability of signal speed.
Hindmarsh, Mark; Litim, Daniel; Rahmede, Christoph E-mail: d.litim@sussex.ac.uk
2011-07-01
We study quantum modifications to cosmology in a Friedmann-Robertson-Walker universe with and without scalar fields by taking the renormalisation group running of gravitational and matter couplings into account. We exploit the Bianchi identity to relate the renormalisation group scale with scale factor and derive the improved cosmological evolution equations. We find two types of cosmological fixed points where the renormalisation group scale either freezes in, or continues to evolve with scale factor. We discuss the implications of each of these, and classify the different cosmological fixed points with and without gravity displaying an asymptotically safe renormalisation group fixed point. We state conditions of existence for an inflating ultraviolet cosmological fixed point for Einstein gravity coupled to a scalar field. We also discuss other fixed point solutions such as 'scaling' solutions, or fixed points with equipartition between kinetic and potential energies.
NASA Astrophysics Data System (ADS)
Yan, Weigen; Zhang, Zuhe
2009-04-01
The energy of a simple graph G arising in chemical physics, denoted by E(G), is defined as the sum of the absolute values of eigenvalues of G. As the dimer problem and spanning trees problem in statistical physics, in this paper we propose the energy per vertex problem for lattice systems. In general for a type of lattice in statistical physics, to compute the entropy constant with toroidal, cylindrical, Mobius-band, Klein-bottle, and free boundary conditions are different tasks with different hardness and may have different solutions. We show that the energy per vertex of plane lattices is independent of the toroidal, cylindrical, Mobius-band, Klein-bottle, and free boundary conditions. In particular, the asymptotic formulae of energies of the triangular, 33.42, and hexagonal lattices with toroidal, cylindrical, Mobius-band, Klein-bottle, and free boundary conditions are obtained explicitly.
Quantum bouncer with dissipation
NASA Astrophysics Data System (ADS)
Lopez, Gustavo; Gonzalez, Gabriel
2004-05-01
Effects on the spectra of the quantum bouncer due to dissipation are given when a linear or quadratic dissipation is taken into account. Classical constants of motions and Hamiltonians are deduced for these systems and their quantized eigenvalues are estimated through perturbation theory. Differences were found comparing the eigenvalues of these two quantities.
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.
Dynamics of Dollard asymptotic variables. Asymptotic fields in Coulomb scattering
NASA Astrophysics Data System (ADS)
Morchio, G.; Strocchi, F.
2016-03-01
Generalizing Dollard’s strategy, we investigate the structure of the scattering theory associated to any large time reference dynamics UD(t) allowing for the existence of Møller operators. We show that (for each scattering channel) UD(t) uniquely identifies, for t →±∞, asymptotic dynamics U±(t); they are unitary groups acting on the scattering spaces, satisfy the Møller interpolation formulas and are interpolated by the S-matrix. In view of the application to field theory models, we extend the result to the adiabatic procedure. In the Heisenberg picture, asymptotic variables are obtained as LSZ-like limits of Heisenberg variables; their time evolution is induced by U±(t), which replace the usual free asymptotic dynamics. On the asymptotic states, (for each channel) the Hamiltonian can by written in terms of the asymptotic variables as H = H±(qout/in,pout/in), H±(q,p) the generator of the asymptotic dynamics. As an application, we obtain the asymptotic fields ψout/in in repulsive Coulomb scattering by an LSZ modified formula; in this case, U±(t) = U0(t), so that ψout/in are free canonical fields and H = H0(ψout/in).
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.
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.
Asymptotic entropic uncertainty relations
NASA Astrophysics Data System (ADS)
Adamczak, Radosław; Latała, Rafał; Puchała, Zbigniew; Życzkowski, Karol
2016-03-01
We analyze entropic uncertainty relations for two orthogonal measurements on a N-dimensional Hilbert space, performed in two generic bases. It is assumed that the unitary matrix U relating both bases is distributed according to the Haar measure on the unitary group. We provide lower bounds on the average Shannon entropy of probability distributions related to both measurements. The bounds are stronger than those obtained with use of the entropic uncertainty relation by Maassen and Uffink, and they are optimal up to additive constants. We also analyze the case of a large number of measurements and obtain strong entropic uncertainty relations, which hold with high probability with respect to the random choice of bases. The lower bounds we obtain are optimal up to additive constants and allow us to prove a conjecture by Wehner and Winter on the asymptotic behavior of constants in entropic uncertainty relations as the dimension tends to infinity. As a tool we develop estimates on the maximum operator norm of a submatrix of a fixed size of a random unitary matrix distributed according to the Haar measure, which are of independent interest.
Singularities, trapped sets, and cosmic censorship in asymptotically flat space-times
Krolak, A. ); Rudnicki, W. )
1993-01-01
We show that space-time is future asymptotically predictable from a regular partial Cauchy provided that singularities are causally preceded by trapped sets. Future asymptotic predictability is a formal statement of cosmic censorship in asymptotically flat space-times. A regular partial Cauchy surface means that singularities in gravitational collapse can arise only from regular initial data. Our result confirms a supposition by Hawking that singularities forced by singularity theorems cannot be naked.
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 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.
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.
Heterogeneous dissipation and size dependencies of dissipative processes in nanoscale interactions.
Gadelrab, Karim R; Santos, Sergio; Chiesa, Matteo
2013-02-19
Here, processes through which the energy stored in an atomic force microscope cantilever dissipates in the tip-sample interaction are first decoupled qualitatively. A formalism is then presented and shown to allow quantification of fundamental aspects of nanoscale dissipation such as deformation, viscosity, and surface energy hysteresis. Accurate quantification of energy dissipation requires precise calibration of the conversion of the oscillation amplitude from volts to nanometers. In this respect, an experimental methodology is presented that allows such calibration with errors of 3% or less. It is shown how simultaneous decoupling and quantification of dissipative processes and in situ tip radius quantification provide the required information to analyze dependencies of dissipative mechanisms on the relative size of the interacting bodies, that is, tip and surface. When there is chemical affinity, atom-atom dissipative interactions approach the energies of chemical bonds. Such atom-atom interactions are found to be independent of cantilever properties and tip geometry thus implying that they are intensive properties of the system; these interactions prevail in the form of surface energy hysteresis. Viscoelastic dissipation on the other hand is shown to depend on the size of the probe and operational parameters. PMID:23336271
Local equilibrium hypothesis and Taylor’s dissipation law
NASA Astrophysics Data System (ADS)
Goto, Susumu; Vassilicos, J. C.
2016-04-01
To qualitatively investigate the validity of Kolmogorov local equilibrium hypothesis and the Taylor dissipation law, we conduct direct numerical simulations of the three-dimensional turbulent Kolmogorov flow. Since strong scale-by-scale (i.e. Richardson-type) energy cascade events occur quasi-periodically, the kinetic energy of the turbulence and its dissipation rate evolve quasi-periodically too. In this unsteady turbulence driven by a steady force, instantaneous values of the dissipation rate obey the scaling recently discovered in wind tunnel experiments (Vassilicos 2015 Ann. Rev. Fluid Mech. 47 95-114) instead of the Taylor dissipation law. The Taylor dissipation law does not hold because the local equilibrium hypothesis does not hold in a relatively low wave-number range. The breakdown of this hypothesis is caused by the finite time needed for the energy at such large scales to reach the dissipative scale by the scale-by-scale energy cascade.
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…
Bistability in a Driven-Dissipative Superfluid.
Labouvie, Ralf; Santra, Bodhaditya; Heun, Simon; Ott, Herwig
2016-06-10
We experimentally study a driven-dissipative Josephson junction array, realized with a weakly interacting Bose-Einstein condensate residing in a one-dimensional optical lattice. Engineered losses on one site act as a local dissipative process, while tunneling from the neighboring sites constitutes the driving force. We characterize the emerging steady states of this atomtronic device. With increasing dissipation strength γ the system crosses from a superfluid state, characterized by a coherent Josephson current into the lossy site, to a resistive state, characterized by an incoherent hopping transport. For intermediate values of γ, the system exhibits bistability, where a superfluid and an incoherent branch coexist. We also study the relaxation dynamics towards the steady state, where we find a critical slowing down, indicating the presence of a nonequilibrium phase transition. PMID:27341243
Bistability in a Driven-Dissipative Superfluid
NASA Astrophysics Data System (ADS)
Labouvie, Ralf; Santra, Bodhaditya; Heun, Simon; Ott, Herwig
2016-06-01
We experimentally study a driven-dissipative Josephson junction array, realized with a weakly interacting Bose-Einstein condensate residing in a one-dimensional optical lattice. Engineered losses on one site act as a local dissipative process, while tunneling from the neighboring sites constitutes the driving force. We characterize the emerging steady states of this atomtronic device. With increasing dissipation strength γ the system crosses from a superfluid state, characterized by a coherent Josephson current into the lossy site, to a resistive state, characterized by an incoherent hopping transport. For intermediate values of γ , the system exhibits bistability, where a superfluid and an incoherent branch coexist. We also study the relaxation dynamics towards the steady state, where we find a critical slowing down, indicating the presence of a nonequilibrium phase transition.
NASA Astrophysics Data System (ADS)
Grant, Leah D.; Heever, Susan C.
2016-02-01
The mechanisms by which sensible heat fluxes (SHFs) alter cold pool characteristics and dissipation rates are investigated in this study using idealized two-dimensional numerical simulations and an environment representative of daytime, dry, continental conditions. Simulations are performed with no SHFs, SHFs calculated using a bulk formula, and constant SHFs for model resolutions with horizontal (vertical) grid spacings ranging from 50 m (25 m) to 400 m (200 m). In the highest resolution simulations, turbulent entrainment of environmental air into the cold pool is an important mechanism for dissipation in the absence of SHFs. Including SHFs enhances cold pool dissipation rates, but the processes responsible for the enhanced dissipation differ depending on the SHF formulation. The bulk SHFs increase the near-surface cold pool temperatures, but their effects on the overall cold pool characteristics are small, while the constant SHFs influence the near-surface environmental stability and the turbulent entrainment rates into the cold pool. The changes to the entrainment rates are found to be the most significant of the SHF effects on cold pool dissipation. SHFs may also influence the timing of cold pool-induced convective initiation by altering the environmental stability and the cold pool intensity. As the model resolution is coarsened, cold pool dissipation is found to be less sensitive to SHFs. Furthermore, the coarser resolution simulations not only poorly but sometimes wrongly represent the SHF impacts on the cold pools. Recommendations are made regarding simulating the interaction of cold pools with convection and the land surface in cloud-resolving models.
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.
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…
Quantum Chaotic Attractor in a Dissipative System
NASA Astrophysics Data System (ADS)
Liu, W. Vincent; Schieve, William C.
1997-04-01
A dissipative quantum system is treated here by coupling it with a heat bath of harmonic oscillators. Through quantum Langevin equations and Ehrenfest's theorem, we establish explicitly the quantum Duffing equations with a double-well potential chosen. A quantum noise term appears the only driving force in dynamics. Numerical studies show that the chaotic attractor exists in this system while chaos is certainly forbidden in the classical counterpart.
External Dissipation in Driven Two-Dimensional Turbulence
NASA Astrophysics Data System (ADS)
Rivera, Michael; Wu, X. L.
2000-07-01
Turbulence in a freely suspended soap film is created by electromagnetic forcing and measured by particle tracking. The velocity fluctuations are shown to be adequately described by the forced Navier-Stokes equation for an incompressible two-dimensional fluid with a linear drag term to model the frictional coupling to the surrounding air. Using this equation, the energy dissipation rates due to air friction and the film's internal viscosity are measured, as is the rate of energy injection from the electromagnetic forcing. Comparison of these rates demonstrates that the air friction is a significant energy dissipation mechanism in the system.
Constraining isopycnal and diapycnal dissipation in the SPURS area
NASA Astrophysics Data System (ADS)
Schanze, Julian; Schmitt, Raymond; Lagerloef, Gary; Dohan, Kathleen
2016-04-01
The distribution of salinity and temperature in the ocean is controlled by surface forcing at the air-sea interface in the form of heat- and freshwater fluxes, advection by currents, and internal mixing processes. Here, we use the concept of 'power integrals' to relate the surface forcing to the dissipation in the ocean interior. In the global ocean, the density (buoyancy) forcing at the surface is related to the diapycnal dissipation in the interior, while the spiciness forcing is related to isopycnal dissipation. Using a number of remote-sensing derived surface flux products, we show that there is broadly an equipartition between isopycnal and diapycnal dissipation, despite the drastically different length-scales involved in both processes. This result holds true for both the time-mean as well as seasonal, monthly and daily temporal solutions and is robust between different flux products. During the Salinity Processes in the Upper Ocean Regional Study (SPURS) in 2012-2013, a detailed dataset of salinity, temperature, velocities and microstructure measurements was recorded. This dataset is augmented with satellite-derived sea surface salinity and sea surface temperature data, Argo data, a number of remote-sensing derived surface flux products and three-dimensional ocean velocities and used to construct isothermal, isohaline, isopycnal and iso-spiciness budgets. Akin to the global case described above, the density (buoyancy) forcing at the surface can be related to diapycnal dissipation and the surface spiciness forcing can be related to isopycnal dissipation processes. Here, these relationships are used to diagnose the relative magnitudes of interior dissipation within a control volume. This approach allows new insights into local thermohaline budgets and complements previous budgets produced in the SPURS region.
Theoretical Consolidation of Acoustic Dissipation
NASA Technical Reports Server (NTRS)
Casiano, M. J.; Zoladz, T. F.
2012-01-01
In many engineering problems, the effects of dissipation can be extremely important. Dissipation can be represented by several parameters depending on the context and the models that are used. Some examples of dissipation-related parameters are damping ratio, viscosity, resistance, absorption coefficients, pressure drop, or damping rate. This Technical Memorandum (TM) describes the theoretical consolidation of the classic absorption coefficients with several other dissipation parameters including linearized resistance. The primary goal of this TM is to theoretically consolidate the linearized resistance with the absorption coefficient. As a secondary goal, other dissipation relationships are presented.
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 .
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.
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.
Efficient Simulation of Dissipative Dynamics
NASA Astrophysics Data System (ADS)
Noh, Kyungjoo; Albert, Victor V.; Shen, Chao; Jiang, Liang
Open quantum systems with engineered dissipations may have more than one steady states. These steady states may form a non-trivial decoherence free subspace (DFS) that can store quantum information against major decoherences. Besides unitary operations within DFS, it is also useful to have dissipative/cooling operations within the DFS. We investigate the possibility of using Hamiltonian perturbation to the engineered dissipation to induce an effective dissipative dynamics within the DFS in a controlled manner. The major challenge is to simulate all the Lindblad jump operators in the master equation. By designing the dissipation within the subspace complementary to the DFS, we can simply use the Hamiltonian perturbation to the designed dissipation with a single jump operator to produce an effective dissipation with multiple Lindblad jump operators.
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.
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.
Asymptotic entanglement dynamics phase diagrams for two electromagnetic field modes in a cavity
Drumond, R. C.; Souza, L. A. M.; Terra Cunha, M.
2010-10-15
We investigate theoretically an open dynamics for two modes of electromagnetic field inside a microwave cavity. The dynamics is Markovian and determined by two types of reservoirs: the ''natural'' reservoirs due to dissipation and temperature of the cavity, and an engineered one, provided by a stream of atoms passing trough the cavity, as devised by Pielawa et al. [Phys. Rev. Lett. 98, 240401 (2007)]. We found that, depending on the reservoir parameters, the system can have distinct ''phases'' for the asymptotic entanglement dynamics: it can disentangle at finite time or it can have persistent entanglement for large times, with the transition between them characterized by the possibility of asymptotical disentanglement. Incidentally, we also discuss the effects of dissipation on the scheme proposed in the above reference for generation of entangled states.
Asymptotic safety: A simple example
NASA Astrophysics Data System (ADS)
Braun, Jens; Gies, Holger; Scherer, Daniel D.
2011-04-01
We use the Gross-Neveu model in 2
Asymptotic safety: A simple example
Braun, Jens; Gies, Holger; Scherer, Daniel D.
2011-04-15
We use the Gross-Neveu model in 2
The dissipative Budden problem
NASA Astrophysics Data System (ADS)
Kaufman, A. N.; Morehead, J. J.; Brizard, A. J.; Tracy, E. R.
1997-11-01
The linear conversion of a magnetosonic wave (MW) to an ion-hybrid wave (HW) in a tokamak is a two-step process: first the (low-field) incident MW converts to a low-k HW, which propagates in k-space and then partially converts to an outgoing ``reflected" MW, the remainder being transmitted to become the desired high-k HW. In the absence of dissipation, this process would repeat indefinitely, as the ``reflected" MW returns to the plasma core after a true reflection at the outer edge of the plasma. In the presence of fusion alphas, however, we show that the intermediate (low-k) HW is extinguished by strong gyroresonant damping^. We demonstrate this effect by solving a modified Budden equation for this process with finite k-dependent dissipation which acts only on the HW mode. \\vspace*.2cm ^dagA. N. Kaufman, J. J. Morehead, A. J. Brizard & E. R. Tracy, to appear in the Proceedings of the 12th Topical Conference on RF Power in Plasmas, Savannah, GA (AIP, 1997). \\vspace*.2cm This work was supported by the US DOE.
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
Asymptotic dynamics of reflecting spiral waves.
Langham, Jacob; Biktasheva, Irina; Barkley, Dwight
2014-12-01
Resonantly forced spiral waves in excitable media drift in straight-line paths, their rotation centers behaving as pointlike objects moving along trajectories with a constant velocity. Interaction with medium boundaries alters this velocity and may often result in a reflection of the drift trajectory. Such reflections have diverse characteristics and are known to be highly nonspecular in general. In this context we apply the theory of response functions, which via numerically computable integrals, reduces the reaction-diffusion equations governing the whole excitable medium to the dynamics of just the rotation center and rotation phase of a spiral wave. Spiral reflection trajectories are computed by this method for both small- and large-core spiral waves in the Barkley model. Such calculations provide insight into the process of reflection as well as explanations for differences in trajectories across parameters, including the effects of incidence angle and forcing amplitude. Qualitative aspects of these results are preserved far beyond the asymptotic limit of weak boundary effects and slow resonant drift. PMID:25615159
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.
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
Dissipation of wave energy and turbulence in a shallow coral reef lagoon
NASA Astrophysics Data System (ADS)
Huang, Zhi-Cheng; Lenain, Luc; Melville, W. Kendall; Middleton, Jason H.; Reineman, Benjamin; Statom, Nicholas; McCabe, Ryan M.
2012-03-01
Simultaneous in situ measurements of waves, currents and turbulence are presented to describe dissipation rates of wave energy and turbulent kinetic energy in the windward coral reef-lagoon system at Lady Elliot Island (LEI), Australia. The dissipation of wave energy in the lagoon is tidally modulated and strongly correlates with frictional dissipation due to the presence of the extremely rough bottom boundary. The observed turbulent kinetic energy (TKE) dissipation rate, ɛ, in this wave-dominated lagoon is much larger than recently reported values for unidirectional flows over natural fringing coral reefs. The correlation between the wave dissipation and ɛ is examined. The average rate of dissipation induced by the rough turbulent flow was estimated directly from the observed ɛ coupled with both a depth-integrated approach and with a bottom boundary layer scaling. Rates of TKE dissipation estimated using the two approaches approximate well, within a factor of 1.5 to 2.4, to the surface-wave energy dissipation rate. The wave dissipation and friction factor in the lagoon can be described by a spectral wave-frictional model with a bottom roughness length scale that is approximately constant across the lagoon. We also present estimates of dissipation induced by the canopy drag force of the coral heads. The dissipation in this case is enhanced and becomes more significant for the total energy dissipation when the water depth in the lagoon is comparable to the height of the coral heads.
Gravitational self-force on a particle in eccentric orbit around a Schwarzschild black hole
Barack, Leor; Sago, Norichika
2010-04-15
We present a numerical code for calculating the local gravitational self-force acting on a pointlike particle in a generic (bound) geodesic orbit around a Schwarzschild black hole. The calculation is carried out in the Lorenz gauge: For a given geodesic orbit, we decompose the Lorenz-gauge metric perturbation equations (sourced by the delta-function particle) into tensorial harmonics, and solve for each harmonic using numerical evolution in the time domain (in 1+1 dimensions). The physical self-force along the orbit is then obtained via mode-sum regularization. The total self-force contains a dissipative piece as well as a conservative piece, and we describe a simple method for disentangling these two pieces in a time-domain framework. The dissipative component is responsible for the loss of orbital energy and angular momentum through gravitational radiation; as a test of our code we demonstrate that the work done by the dissipative component of the computed force is precisely balanced by the asymptotic fluxes of energy and angular momentum, which we extract independently from the wave-zone numerical solutions. The conservative piece of the self-force does not affect the time-averaged rate of energy and angular-momentum loss, but it influences the evolution of the orbital phases; this piece is calculated here for the first time in eccentric strong-field orbits. As a first concrete application of our code we recently reported the value of the shift in the location and frequency of the innermost stable circular orbit due to the conservative self-force [Phys. Rev. Lett. 102, 191101 (2009)]. Here we provide full details of this analysis, and discuss future applications.
Inflation with Thermal Dissipation
NASA Astrophysics Data System (ADS)
Lee, Wo-Lung
We study thermally induced density perturbations during inflation. This scenario is characterized by two thermodynamic conditions: (i) the primordial perturbations originate in the epoch when the inflationary universe contains a thermalized heat bath; (ii) the perturbations of the inflationary scalar field are given by the fluctuation-dissipation relation. We show that (1) the power spectrum of the primordial density perturbations follows a tilted power law behavior; (2) the relation between the amplitude and the power index of the spectrum exhibits a ``thermodynamic'' feature-it depends mainly on the thermodynamic variable M, the inflation energy scale; (3) both the adiabatic mode and the isocurvature mode of density perturbations appear during the inflation epoch, and the resultant power spectrum on super-horizon scales is substantially suppressed. These results are found to be very consistent with observations of the temperature fluctuations in the cosmic microwave background if the energy scale of the inflation is about 1015-10 16 GeV.
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
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 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.
Flow around spheres by dissipative particle dynamics
NASA Astrophysics Data System (ADS)
Chen, Shuo; Phan-Thien, Nhan; Khoo, Boo Cheong; Fan, Xi Jun
2006-10-01
The dissipative particle dynamics (DPD) method is used to study the flow behavior past a sphere. The sphere is represented by frozen DPD particles while the surrounding fluids are modeled by simple DPD particles (representing a Newtonian fluid). For the surface of the sphere, the conventional model without special treatment and the model with specular reflection boundary condition proposed by Revenga et al. [Comput. Phys. Commun. 121-122, 309 (1999)] are compared. Various computational domains, in which the sphere is held stationary at the center, are investigated to gage the effects of periodic conditions and walls for Reynolds number (Re)=0.5 and 50. Two types of flow conditions, uniform flow and shear flow are considered, respectively, to study the drag force and torque acting on the stationary sphere. It is found that the calculated drag force imposed on the sphere based on the model with specular reflection is slightly lower than the conventional model without special treatment. With the conventional model the drag force acting on the sphere is in better agreement with experimental correlation obtained by Brown and Lawler [J. Environ. Eng. 129, 222 (2003)] for the case of larger radius up to Re of about 5. The computed torque also approaches the analytical Stokes value when Re <1. For a force-free and torque-free sphere, its motion in the flow is captured by solving the translational and rotational equations of motion. The effects of different DPD parameters (a, γ, and σ) on the drag force and torque are studied. It shows that the dissipative coefficient (γ) mainly affects the drag force and torque, while random and conservative coefficient have little influence on them. Furthermore the settling of a single sphere in square tube is investigated, in which the wall effect is considered. Good agreement is found with the experiments of Miyamura et al. [Int. J. Multiphase Flow 7, 31 (1981)] and lattice-Boltzmann simulation results of Aidun et al. [J. Fluid Mech
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
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.
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.
From quantum correlations in dissipative quantum walk to two-qubit systems
NASA Astrophysics Data System (ADS)
Nizama, Marco; Cáceres, Manuel O.
2014-04-01
A dissipative quantum walk (according to the semigroup approach) has been used as the starting point from which to study quantum correlations in an open system. This system is a fruitful model that allows the definition of several bipartite systems (sets of qubits). Thus the quantum correlations and the decoherence properties induced by a phonon bath can be investigated analytically using tools from quantum information. In particular we have studied the negativity, concurrence and quantum discord for different bipartitions in our dissipative system, and we have found analytical expression for these measures, using a local initial condition for the density matrix of the walker. In general quantum correlations are affected by dissipation in a complex non-monotonic way, showing at long time an expected asymptotic decrease with the increase of the dissipation. In addition, our results for the quantum correlations can be used as an indicator of the transition from the quantum to the classical regimen, as has recently been shown experimentally.
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.
Numerical Asymptotic Solutions Of Differential Equations
NASA Technical Reports Server (NTRS)
Thurston, Gaylen A.
1992-01-01
Numerical algorithms derived and compared with classical analytical methods. In method, expansions replaced with integrals evaluated numerically. Resulting numerical solutions retain linear independence, main advantage of asymptotic solutions.
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.
Oscillatory dissipation of a simple confined liquid.
Maali, Abdelhamid; Cohen-Bouhacina, Touria; Couturier, Gérard; Aimé, Jean-Pierre
2006-03-01
We present a sensitive measurement of the dissipation and the effective viscosity of a simple confined liquid (octamethylcyclotetrasiloxane) using an atomic force microscope. The experimental data show that the damping and the effective viscosity increase and present oscillations as the gap between the cantilever tip and the surface is diminished. To our knowledge, the damping and the viscosity modulation are reported here with such good accuracy for the first time. Such an experimental result is different from what has been reported earlier where only a continuous increase of the damping and the viscosity are observed. PMID:16606201
NASA Technical Reports Server (NTRS)
Collins, William
1989-01-01
The dispersion equation of Barnes (1966) is used to study the dissipation of asymptotic wave packets generated by localized periodic sources. The solutions of the equation are linear waves, damped by Landau and transit-time processes, in a collisionless warm plasma. For the case of an ideal MHD system, most of the waves emitted from a source are shown to cancel asympotically through destructive interference. The modes transporting significant flux to asymptotic distances are found to be Alfven waves and fast waves with theta (the angle between the magnetic field and the characteristics of the far-field waves) of about 0 and about pi/2.
Thermodynamics of asymptotically safe theories
NASA Astrophysics Data System (ADS)
Rischke, Dirk H.; Sannino, Francesco
2015-09-01
We investigate the thermodynamic properties of a novel class of gauge-Yukawa theories that have recently been shown to be completely asymptotically safe, because their short-distance behavior is determined by the presence of an interacting fixed point. Not only do all the coupling constants freeze at a constant and calculable value in the ultraviolet, their values can even be made arbitrarily small for an appropriate choice of the ratio Nc/Nf of fermion colors and flavors in the Veneziano limit. Thus, a perturbative treatment can be justified. We compute the pressure, entropy density, and thermal degrees of freedom of these theories to next-to-next-to-leading order in the coupling constants.
Asymptotically optimal topological quantum compiling.
Kliuchnikov, Vadym; Bocharov, Alex; Svore, Krysta M
2014-04-11
We address the problem of compiling quantum operations into braid representations for non-Abelian quasiparticles described by the Fibonacci anyon model. We classify the single-qubit unitaries that can be represented exactly by Fibonacci anyon braids and use the classification to develop a probabilistically polynomial algorithm that approximates any given single-qubit unitary to a desired precision by an asymptotically depth-optimal braid pattern. We extend our algorithm in two directions: to produce braids that allow only single-strand movement, called weaves, and to produce depth-optimal approximations of two-qubit gates. Our compiled braid patterns have depths that are 20 to 1000 times shorter than those output by prior state-of-the-art methods, for precisions ranging between 10(-10) and 10(-30). PMID:24765934
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.
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.
8. Asymptotically Flat and Regular Cauchy Data
NASA Astrophysics Data System (ADS)
Dain, Sergio
I describe the construction of a large class of asymptotically flat initial data with non-vanishing mass and angular momentum for which the metric and the extrinsic curvature have asymptotic expansions at space-like infinity in terms of powers of a radial coordinate. I emphasize the motivations and the main ideas behind the proofs.
Tsirelson's problem and asymptotically commuting unitary matrices
Ozawa, Narutaka
2013-03-15
In this paper, we consider quantum correlations of bipartite systems having a slight interaction, and reinterpret Tsirelson's problem (and hence Kirchberg's and Connes's conjectures) in terms of finite-dimensional asymptotically commuting positive operator valued measures. We also consider the systems of asymptotically commuting unitary matrices and formulate the Stronger Kirchberg Conjecture.
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.
A single ion anharmonic mechanical oscillator with nonlinear dissipation
NASA Astrophysics Data System (ADS)
Akerman, Nitzan; Kotler, Shlomi; Glickman, Yinnon; Keselman, Anna; Dallal, Yehonatan; Ozeri, Roee
2010-03-01
A driven, damped, nearly harmonic oscillator with a small cubic term in the force, is known as the Duffing oscillator. The Duffing oscillator shows various interesting features of non-linear response such as bistability and hysteresis. Several features of the Duffing instability have been recently measured using superconducting qubits and nano-mechanical resonators. Linear Paul traps can be well approximated as harmonic but have a small an-harmonicity due to their deviation from an ideal quadruple geometry. We study the steady state motion of a single trapped Sr^+ ion, subject to a near-resonance drive and dissipation in a linear Paul trap with a small anharmonicity. The driving force is applied by an oscillating voltage on the trap end-caps. Dissipation is the result of laser Doppler cooling. We measure both the amplitude and phase of the driven oscillations and find a good agreement with the Duffing oscillator model. When the cooling laser is close to resonance the standard Duffing model has to be extended to account for non-linearity in the dissipative force. Both the linear and the nonlinear terms of the dissipative force for various cooling laser detunings are determined by the line-shape of the - cooling transition and the cooling laser intensity and can therefore be conveniently controlled.
Frictional Dissipation Pathways Mediated by Hydrated Alkali Metal Ions.
Gaisinskaya-Kipnis, Anastasia; Ma, Liran; Kampf, Nir; Klein, Jacob
2016-05-17
Frictional energy dissipation between sliding solid surfaces in aqueous media may proceed by different pathways. Using a surface force balance (SFB), we have examined systematically how such dissipation is mediated by the series of hydrated cations M(+) = Li(+), Na(+), and K(+) that are trapped between two atomically smooth, negatively charged, mica surfaces sliding across the ionic solutions over many orders of magnitude loading. By working at local contact pressures up to ca. 30 MPa (∼300 atm), up to 2 orders of magnitude higher than earlier studies, we could show that the frictional dissipation at constant sliding velocity, represented by the coefficient of sliding friction μM+, decreased as μLi+ > μNa+ ≳ μK+. This result contrasts with the expectation (in conceptual analogy with the Hofmeister series) that the lubrication would improve with the extent of ionic hydration, since that would have led to the opposite μM+ sequence. It suggests, rather, that frictional forces, even in such simple systems, can be dominated by rate-activated pathways where the size of the hydration shell becomes a dissipative liability, rather than by the hydration-shell dissipation expected via the hydration lubrication mechanism. PMID:27089022
NASA Astrophysics Data System (ADS)
Vadas, Sharon; Nicolls, Michael
2012-07-01
Gravity waves (GWs) excited in the lower atmosphere can greatly affect the thermosphere and ionosphere via body forcing (dissipation), ion drag, etc. Therefore, understanding how deeply GWs penetrate before dissipating in the thermosphere is critical for understanding the strength and importance of this coupling mechanism. In this paper, we compare the linear solutions for GWs propagating and dissipating in the thermosphere if the GWs are excited by 1) a spatially and temporally localized source using a ray trace model (Vadas and Fritts, 2005), and 2) a steady-state, horizontally-uniform source using a "full-wave" model (similar to Walterscheid and Hickey, 2011). If a GW is excited by a spatially and temporally-localized source, its vertical wavelength (lz) increases/decreases somewhat, or stays the same, as it strongly dissipates. In contrast, because of continuous contributions from neighboring sources, the lz profile increases exponentially with altitude (until asymptoting to a constant value at great altitudes) while strongly dissipating in the full wave model. This causes a GW to dissipate at a much higher altitude (and with a much larger amplitude) than if this GW were instead excited by a spatially and temporally-localized source. Therefore, if a GW is excited by a spatially and temporally-localized source, and the full wave model is (incorrectly) used to model its propagation and dissipation, the GW's amplitude and penentration altitude in the thermosphere will be significantly overestimated. Next, we study the vertical wavelength (lz) and ion velocity perturbation profiles (vion) for recently observed GWs with the Arecibo Observatory (AO). These GWs are from unknown sources. We find that in nearly all of the cases, lz increases somewhat, is approximately constant, or decreases somewhat above the altitude where vion is maximum. This result is consistent with excitation from spatially and temporally-localized sources. In the few cases where lz increases
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. ...
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.
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.
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. PMID:27415219
Friction and relative energy dissipation in sheared granular materials.
Wang, Wan-Jing; Kong, Xiang-Zhao; Zhu, Zhen-Gang
2007-04-01
The oscillating cylinder of a low-frequency inverted torsion pendulum is immersed into layers of noncohesive granular materials, including fine sand and glass beads. The relative energy dissipation and relative modulus of the granular system versus the amplitude and immersed depth of the oscillating cylinder are measured. A rheological model based on a mesoscopic picture is presented. The experimental results and rheological model indicate that small slides in the inhomogeneous force chains are responsible for the energy dissipation of the system, and the friction of the grains plays two different roles in the mechanical response of sheared granular material: damping the energy and enhancing the elasticity. PMID:17500887
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.
Asymptotic flame theory with complex chemistry
Fife, P.C.; Nicolaenko, B.
1982-01-01
We investigate the structure of laminar flames with general complex chemistry networks in the limit of high activation energy asymptotics. Depending on the specific reaction network and other given thermomechanical data, a wide variety of flame configurations are possible. Here we present a first version of a systematic asymptotic reduction of complex chemistry networks and give practical criteria to determine the dominant reactions when transport and chemistry are coupled.
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.
Tracking dissipation in capture reactions
Materna, T.; Bouchat, V.; Kinnard, V.; Hanappe, F.; Dorvaux, O.; Stuttge, L.; Schmitt, C.; Siwek-Wilczynska, K.; Aritomo, Y.; Bogatchev, A.; Prokhorova, E.; Ohta, M.
2004-04-12
Nuclear dissipation in capture reactions is investigated using backtracing. Combining the analysis procedure with dynamical models, the difficult and long-standing problem of competition and mixing of quasi-fission and fusion-fission is solved for the first time. At low excitation energy a new protocol able to handle low statistics data gives access to the precession neutron multiplicity in two different systems 48Ca + 208Pb, Pu. The results are in agreement with a domination of fusion-fission in the case of 256No and an equal mixing of quasi-fission and fusion-fission in the case of Z = 114. The nature of the relevant dissipation is determined as one-body dissipation.
NASA Astrophysics Data System (ADS)
Sakalli, I.
2011-08-01
We show in detail that the entropic force of the static spherically symmetric spacetimes with unusual asymptotics can be calculated through the Verlinde's arguments. We introduce three different holographic screen candidates, which are first employed thoroughly by Myung and Kim [Phys. Rev. D 81, 105012 (2010)] for Schwarzschild black hole solutions, in order to identify the entropic force arising between a charged dilaton black hole and a test particle. The significance of the dilaton parameter on the entropic force is highlighted, and shown graphically.
Phase slips and dissipation of Alfvenic intermediate shocks and solitons
Laveder, D.; Passot, T.; Sulem, P. L.
2012-09-15
The time evolution of a rotational discontinuity, characterized by a change of the magnetic-field direction by an angle {Delta}{theta} such that {pi}<|{Delta}{theta}|<2{pi} and no amplitude variation, is considered in the framework of asymptotic models that, through reductive perturbative expansions, isolate the dynamics of parallel or quasi-parallel Alfven waves. In the presence of viscous and Ohmic dissipation, and for a zero or sufficiently weak dispersion (originating from the Hall effect), an intermediate shock rapidly forms, steepens and undergoes reconnection through a quasi gradient collapse, leading to a reduction of |{Delta}{theta}| by an amount of 2{pi}, which can be viewed as the breaking of a topological constraint. Afterwards, as |{Delta}{theta}|<{pi}, the intermediate shock broadens and slowly dissipates. In the case of a phase jump |{Delta}{theta}|>3{pi}, which corresponds to a wave train limited on both sides by uniform fields, a sequence of such reconnection processes takes place. Differently, in the presence of a strong enough dispersion, the rotational discontinuity evolves, depending on the sign of {Delta}{theta}, to a dark or bright soliton displaying a 2{pi} phase variation. The latter is then eliminated, directly by reconnection in the case of a dark soliton, or through a more complex process involving a quasi amplitude collapse in that of a bright soliton. Afterwards, the resulting structure is progressively damped. For a prescribed initial rotational discontinuity, both quasi gradient and amplitude collapses lead to a sizeable energy decay that in the collisional regime is independent of the diffusion coefficient {eta} but requires a time scaling like 1/{eta}. In the non-collisional regime where dissipation originates from Landau resonance, the amount of dissipated energy during the event is independent of the plasma {beta}, but the process becomes slower for smaller {beta}.
High dissipative nonminimal warm inflation
NASA Astrophysics Data System (ADS)
Nozari, Kourosh; Shoukrani, Masoomeh
2016-09-01
We study a model of warm inflation in which both inflaton field and its derivatives are coupled nonminimally to curvature. We survey the spectrum of the primordial perturbations in high dissipative regime. By expanding the action up to the third order, the amplitude of the non-Gaussianity is studied both in the equilateral and orthogonal configurations. Finally, by adopting four sort of potentials, we compare our model with the Planck 2015 released observational data and obtain some constraints on the model's parameters space in the high dissipation regime.
Dissipative processes in galaxy formation.
Silk, J
1993-01-01
A galaxy commences its life in a diffuse gas cloud that evolves into a predominantly stellar aggregation. Considerable dissipation of gravitational binding energy occurs during this transition. I review here the dissipative processes that determine the critical scales of luminous galaxies and the generation of their morphology. The universal scaling relations for spirals and ellipticals are shown to be sensitive to the history of star formation. Semiphenomenological expressions are given for star-formation rates in protogalaxies and in starbursts. Implications are described for elliptical galaxy formation and for the evolution of disk galaxies. PMID:11607396
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 Dissipation in Nanomechanical Oscillators
NASA Astrophysics Data System (ADS)
Zolfagharkhani, G.; Gaidarzhy, A.; Badzey, R. L.; Mohanty, P.
2004-03-01
Dissipation or energy relaxation of a resonant mode in a nanomechanical device occurs by its coupling to environment degrees of freedom, which also acquire quantum mechanical correlations at millikelvin temperatures. We report measurements of temperature and magnetic field dependence of dissipation in single crystal silicon nanobeams in MHz up to 1 GHz frequency range. We extend our measurements down to temperatures of 20 millikelvin and up to fields of 16 tesla. The fabrication of our Nano-Electro-Mechanical Systems (NEMS) involves e-beam lithography, as well as various deposition and plasma etching processes. This work is supported by NSF and the Sloan Foundation.
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.
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.
Muscle power attenuation by tendon during energy dissipation
Konow, Nicolai; Azizi, Emanuel; Roberts, Thomas J.
2012-01-01
An important function of skeletal muscle is deceleration via active muscle fascicle lengthening, which dissipates movement energy. The mechanical interplay between muscle contraction and tendon elasticity is critical when muscles produce energy. However, the role of tendon elasticity during muscular energy dissipation remains unknown. We tested the hypothesis that tendon elasticity functions as a mechanical buffer, preventing high (and probably damaging) velocities and powers during active muscle fascicle lengthening. We directly measured lateral gastrocnemius muscle force and length in wild turkeys during controlled landings requiring rapid energy dissipation. Muscle-tendon unit (MTU) strain was measured via video kinematics, independent of muscle fascicle strain (measured via sonomicrometry). We found that rapid MTU lengthening immediately following impact involved little or no muscle fascicle lengthening. Therefore, joint flexion had to be accommodated by tendon stretch. After the early contact period, muscle fascicles lengthened and absorbed energy. This late lengthening occurred after most of the joint flexion, and was thus mainly driven by tendon recoil. Temporary tendon energy storage led to a significant reduction in muscle fascicle lengthening velocity and the rate of energy absorption. We conclude that tendons function as power attenuators that probably protect muscles against damage from rapid and forceful lengthening during energy dissipation. PMID:21957134
Impacts on Dissipative Sonic Vacuum
NASA Astrophysics Data System (ADS)
Xu, Yichao; Nesterenko, Vitali
We investigate the propagating compression bell shape stress waves generated by the strikers with different masses impacting the sonic vacuum - the discrete dissipative strongly nonlinear metamaterial with zero long wave sound speed. The metamaterial is composed of alternating steel disks and Nitrile O-rings. Being a solid material, it has exceptionally low speed of the investigated stress waves in the range of 50 - 74 m/s, which is a few times smaller than the speed of sound or shock waves in air generated by blast. The shape of propagating stress waves was dramatically changed by the viscous dissipation. It prevented the incoming pulses from splitting into trains of solitary waves, a phenomenon characteristic of the non-dissipative strongly nonlinear discrete systems when the striker mass is larger than the cell mass. Both high-speed camera images and numerical simulations demonstrate the unusual rattling behavior of the top disk between the striker and the rest of the system. The linear momentum and energy from the striker were completely transferred to the metamaterial. This strongly nonlinear dissipative metamaterial can be designed for the optimal attenuation of dynamic loads generated by impact or contact explosion. Author 1 wants to acknowledge the support provided by UCSD.
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.
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.
Maximal hypersurfaces in asymptotically stationary spacetimes
NASA Astrophysics Data System (ADS)
Chrusciel, Piotr T.; Wald, Robert M.
1992-12-01
The purpose of the work is to extend the results on the existence of maximal hypersurfaces to encompass some situations considered by other authors. The existence of maximal hypersurface in asymptotically stationary spacetimes is proven. Existence of maximal surface and of foliations by maximal hypersurfaces is proven in two classes of asymptotically flat spacetimes which possess a one parameter group of isometries whose orbits are timelike 'near infinity'. The first class consists of strongly causal asymptotically flat spacetimes which contain no 'blackhole or white hole' (but may contain 'ergoregions' where the Killing orbits fail to be timelike). The second class of space times possess a black hole and a white hole, with the black and white hole horizon intersecting in a compact 2-surface S.
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.
Dispersive shock wave interactions and asymptotics.
Ablowitz, Mark J; Baldwin, Douglas E
2013-02-01
Dispersive shock waves (DSWs) are physically important phenomena that occur in systems dominated by weak dispersion and weak nonlinearity. The Korteweg-de Vries (KdV) equation is the universal model for systems with weak dispersion and weak, quadratic nonlinearity. Here we show that the long-time-asymptotic solution of the KdV equation for general, steplike data is a single-phase DSW; this DSW is the "largest" possible DSW based on the boundary data. We find this asymptotic solution using the inverse scattering transform and matched-asymptotic expansions. So while multistep data evolve to have multiphase dynamics at intermediate times, these interacting DSWs eventually merge to form a single-phase DSW at large time. PMID:23496590
Dynamics of Dissipative Temporal Solitons
NASA Astrophysics Data System (ADS)
Peschel, U.; Michaelis, D.; Bakonyi, Z.; Onishchukov, G.; Lederer, F.
The properties and the dynamics of localized structures, frequently termed solitary waves or solitons, define, to a large extent, the behavior of the relevant nonlinear system [1]. Thus, it is a crucial and fundamental issue of nonlinear dynamics to fully characterize these objects in various conservative and dissipative nonlinear environments. Apart from this fundamental point of view, solitons (henceforth we adopt this term, even for localized solutions of non-integrable systems) exhibit a remarkable potential for applications, particularly if optical systems are considered. Regarding the type of localization, one can distinguish between temporal and spatial solitons. Spatial solitons are self-confined beams, which are shape-invariant upon propagation. (For an overview, see [2, 3]). It can be anticipated that they could play a vital role in all-optical processing and logic, since we can use their complex collision behavior [4]. Temporal solitons, on the other hand, represent shapeinvariant (or breathing) pulses. It is now common belief that robust temporal solitons will play a major role as elementary units (bits) of information in future all-optical networks [5, 6]. Until now, the main emphasis has been on temporal and spatial soliton families in conservative systems, where energy is conserved. Recently, another class of solitons, which are characterized by a permanent energy exchange with their environment, has attracted much attention. These solitons are termed dissipative solitons or auto-solitons. They emerge as a result of a balance between linear (delocalization and losses) and nonlinear (self-phase modulation and gain/loss saturation) effects. Except for very few cases [7], they form zero-parameter families and their features are entirely fixed by the underlying optical system. Cavity solitons form a prominent type. They appear as spatially-localized transverse peaks in transmission or reflection, e.g. from a Fabry-Perot cavity. They rely strongly on the
Asymptotic theory of an infectious disease model.
Whitman, Alan M; Ashrafiuon, Hashem
2006-08-01
In this paper, we present asymptotic theory as a viable alternative solution method for infectious disease models. We consider a particular model of a pathogen attacking a host whose immune system responds defensively, that has been studied previously [Mohtashemi and Levins in J. Math. Biol. 43: 446-470 (2001)]. On rendering this model dimensionless, we can reduce the number of parameters to two and note that one of them has a large value that suggests an asymptotic analysis. On doing this analysis, we obtain a satisfying qualitative description of the dynamic evolution of each population, together with simple analytic expressions for their main features, from which we can compute accurate quantitative values.
Dissipation by a crystallization process
NASA Astrophysics Data System (ADS)
Dorosz, Sven; Voigtmann, Thomas; Schilling, Tanja
2016-01-01
We discuss crystallization as a non-equilibrium process. In a system of hard spheres under compression at a constant rate, we quantify the amount of heat that is dissipated during the crystallization process. We interpret the dissipation as arising from the resistance of the system against phase transformation. An intrinsic compression rate is identified that separates a quasi-static regime from one of rapidly driven crystallization. In the latter regime the system crystallizes more easily, because new relaxation channels are opened, at the cost of forming a higher fraction of non-equilibrium crystal structures. We rationalize the change in the crystallization mechanism by analogy with shear thinning, in terms of a kinetic competition between near-equilibrium relaxation and external driving.
Tidal dissipation in the large icy satellites: implications for their thermal evolution.
NASA Astrophysics Data System (ADS)
Tobie, G.; Mocquet, A.; Sotin, C.
2003-04-01
Tidal dissipation is a large heat source that controls the thermal evolution of several bodies of the Solar system, notably Europa and Titan. In order to investigate how tidal heating affects the present and past thermal states of these icy satellites, we perform numerical calculations of tidal dissipation distribution for different internal structures and different viscoelastic properties of their interiors. The numerical method is developed after the elastic formulation of free spheroidal oscillations of a compressible self-gravitating planet and adapted to a tidally forced viscoelastic response of the body. We test systematically the dependence of tidal dissipation on the rheological parameters namely, the viscosity eta, the shear modulus μ, and the bulk modulus K, as well as on the orbital parameters, i.e. the eccentricity e and the forcing frequency ω. The effects of tidal dissipation on heat balance in the outer icy layers are investigated with a 2D thermal convection model. We show that the tidal dissipation in the icy layers of Europa and Titan is very large, and that it allows for the long-term existence of a subsurface ocean below a convective ice I layer. We are also investigating thermal evolution models of the rocky core to address the question of tidal dissipation in the silicates. Although tidal dissipation in the rocky core is not required for an ocean to exist, it may provide an additional heating source for seafloor volcanism to occur. In addition, we show that the tidal dissipation in a floating icy layer mainly depends on its viscous structure and that the lateral viscosity variations modify the local dissipation and the value of the global dissipation up to 30%.
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.
Charge-Dissipative Electrical Cables
NASA Technical Reports Server (NTRS)
Kolasinski, John R.; Wollack, Edward J.
2004-01-01
Electrical cables that dissipate spurious static electric charges, in addition to performing their main functions of conducting signals, have been developed. These cables are intended for use in trapped-ion or ionizing-radiation environments, in which electric charges tend to accumulate within, and on the surfaces of, dielectric layers of cables. If the charging rate exceeds the dissipation rate, charges can accumulate in excessive amounts, giving rise to high-current discharges that can damage electronic circuitry and/or systems connected to it. The basic idea of design and operation of charge-dissipative electrical cables is to drain spurious charges to ground by use of lossy (slightly electrically conductive) dielectric layers, possibly in conjunction with drain wires and/or drain shields (see figure). In typical cases, the drain wires and/or drain shields could be electrically grounded via the connector assemblies at the ends of the cables, in any of the conventional techniques for grounding signal conductors and signal shields. In some cases, signal shields could double as drain shields.
Dissipative chaos in semiconductor superlattices
Alekseev, K.N.; Berman, G.P. ||; Campbell, D.K.; Cannon, E.H.; Cargo, M.C.
1996-10-01
We consider the motion of ballistic electrons in a miniband of a semiconductor superlattice (SSL) under the influence of an external, time-periodic electric field. We use a semiclassical, balance-equation approach, which incorporates elastic and inelastic scattering (as dissipation) and the self-consistent field generated by the electron motion. The coupling of electrons in the miniband to the self-consistent field produces a cooperative nonlinear oscillatory mode which, when interacting with the oscillatory external field and the intrinsic Bloch-type oscillatory mode, can lead to complicated dynamics, including dissipative chaos. For a range of values of the dissipation parameters we determine the regions in the amplitude-frequency plane of the external field in which chaos can occur. Our results suggest that for terahertz external fields of the amplitudes achieved by present-day free-electron lasers, chaos may be observable in SSL{close_quote}s. We clarify the nature of this interesting nonlinear dynamics in the superlattice{endash}external-field system by exploring analogies to the Dicke model of an ensemble of two-level atoms coupled with a resonant cavity field, and to Josephson junctions. {copyright} {ital 1996 The American Physical Society.}
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. PMID:21405769
Asymptotic iteration approach to supersymmetric bistable potentials
NASA Astrophysics Data System (ADS)
Ciftci, H.; Özer, O.; P., Roy
2012-01-01
We examine quasi exactly solvable bistable potentials and their supersymmetric partners within the framework of the asymptotic iteration method (AIM). It is shown that the AIM produces excellent approximate spectra and that sometimes it is found to be more useful to use the partner potential for computation. We also discuss the direct application of the AIM to the Fokker—Planck equation.
Exponential asymptotics of the Voigt functions
NASA Astrophysics Data System (ADS)
Paris, R. B.
2015-06-01
We obtain the asymptotic expansion of the Voigt functionss K( x, y) and L( x, y) for large (real) values of the variables x and y, paying particular attention to the exponentially small contributions. A Stokes phenomenon is encountered as with x > 0 fixed. Numerical examples are presented to demonstrate the accuracy of these new expansions.
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.
Tides on the Moon: Theory and determination of dissipation
NASA Astrophysics Data System (ADS)
Williams, James G.; Boggs, Dale. H.
2015-04-01
Solid body tides on the Moon vary by about ±0.1 m each month. In addition to changes in shape, the Moon's gravity field and orientation in space are affected by tides. The tidal expressions for an elastic sphere are compact, but dissipation introduces modifications that depend on the forcing period. Consequently, a Fourier representation of the tide-raising potential is needed. A mathematical model for the distortion-caused tidal potential may be used for the analysis of precise spacecraft tracking data. Since tides affect gravitational torques on the Moon from the Earth's attraction, the lunar orientation is also affected. Expressions for five periodic perturbations of orientation are presented. The rheological properties of lunar materials determine how the Moon responds to different tidal periods. New lunar laser ranging solutions for the tidal orientation terms are presented. The quality factor Q is 38 ± 4 at 1 month, 41 ± 9 at 1 year, ≥74 at 3 years, and ≥58 at 6 years. The ranging results can be matched with absorption band models that peak at ~120 days and single relaxation time models that peak at ~100 days. Combined models are possibilities. Dissipation can modify laser ranging solutions; previously reported core flattening is too uncertain to be useful. Strong lunar tidal dissipation, modeled to arise in the deep hot mantle, appears to be from a region with radius ≥535 km. Classical Maxwell-type dissipation is too weak to detect at 3 and 6 year periods.
Phase spaces for asymptotically de Sitter cosmologies
NASA Astrophysics Data System (ADS)
Kelly, William R.; Marolf, Donald
2012-10-01
We construct two types of phase spaces for asymptotically de Sitter Einstein-Hilbert gravity in each spacetime dimension d ⩾ 3. One type contains solutions asymptotic to the expanding spatially-flat (k = 0) cosmological patch of de Sitter space while the other is asymptotic to the expanding hyperbolic (k = -1) patch. Each phase space has a non-trivial asymptotic symmetry group (ASG) which includes the isometry group of the corresponding de Sitter patch. For d = 3 and k = -1 our ASG also contains additional generators and leads to a Virasoro algebra with vanishing central charge. Furthermore, we identify an interesting algebra (even larger than the ASG) containing two Virasoro algebras related by a reality condition and having imaginary central charges +/- i \\frac{3\\ell }{2G}. Our charges agree with those obtained previously using dS/CFT methods for the same asymptotic Killing fields showing that (at least some of) the dS/CFT charges act on a well-defined phase space. Along the way we show that, despite the lack of local degrees of freedom, the d = 3, k = -1 phase space is non-trivial even in pure Λ > 0 Einstein-Hilbert gravity due to the existence of a family of ‘wormhole’ solutions labeled by their angular momentum, a mass-like parameter θ0, the topology of future infinity (I+), and perhaps additional internal moduli. These solutions are Λ > 0 analogues of BTZ black holes and exhibit a corresponding mass gap relative to empty de Sitter.
The asymptotic structure of a slender coiling fluid thread
NASA Astrophysics Data System (ADS)
Blount, Maurice; Lister, John
2010-11-01
The buckling of a viscous fluid thread as it falls through air onto a stationary surface is a well-known breakfast-time phenomenon which exhibits a rich variety of dynamical regimes [1]. Since the bending resistance of a slender thread is small, bending motion is largely confined to a short region of coiling near the surface. If the height of fall is large enough, then the thread above the coiling region forms a `tail' that falls nearly vertically under gravity but is deflected slightly due to forces exerted on it by the coil. Although it is possible to use force balances in the coil to estimate scalings for the coiling frequency, we analyse the solution structure of the entire thread in the asymptotic limit of a very slender thread and thereby include the dynamic interaction between the coil and the tail. Quantitative predictions of the coiling frequency are obtained which demonstrate the existence of leading-order corrections to scalings previously derived. In particular, we show that in the regime where the deflection of the tail is governed by a balance between centrifugal acceleration, hoop stress and gravity, the tail behaves as a flexible circular pendulum that is forced by bending stress exerted by the coil. The amplitude of the response is calculated and the previously observed resonance when the coiling frequency coincides with one of the eigenfrequencies of a free flexible pendulum is thereby explained. [1] N.M. Ribe et al., J. Fluid Mech. 555, 275-297.
Harnessing spin precession with dissipation
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. PMID:26816050
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.
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
Tidal disruption of dissipative planetesimals
NASA Astrophysics Data System (ADS)
Mizuno, H.; Boss, A. P.
1985-07-01
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.
The semi-diurnal cycle of dissipation in a ROFI: model-measurement comparisons
NASA Astrophysics Data System (ADS)
Simpson, John H.; Burchard, Hans; Fisher, Neil R.; Rippeth, Tom P.
2002-07-01
The Liverpool Bay Region of Freshwater Influence in the Irish Sea exhibits strong horizontal gradients which interact with the dominant tidal flow. A 25 h series of measurements of the cycle of turbulent dissipation with the FLY dissipation profiler shows a strong asymmetry between ebb and flood which is associated with a cycle of increasing stratification on the ebb and progressive mixing on the flood which results in vertical homogeneity as high water is approached. At this time strong dissipation extends throughout the water column in contrast to the ebb when there is a near shutdown of dissipation in the upper half of the column. The cycle of stratification and dissipation is closely consistent for the two semi-diurnal tidal cycles observed. We have attempted to simulate this situation, which involves a complex suite of processes including tidal straining and mixing, using a version of the k-ɛ closure scheme in a 1-d dynamical model which is forced by a combination of the observed tidal flow and horizontal temperature and salinity gradients. The latter were measured directly at the end of the observational series but, in order to focus on the cycle of dissipation, the correct reproduction of the temperature and salinity cycle can be assured by a nudging procedure which obliges the model temperature and salinity values to track the observations. With or without this procedure, the model gives a reasonable account of the dissipation and its asymmetric behaviour on ebb and flood although nudging improves the timing of peak dissipation in the upper part of the water column near highwater. The model has also been used to examine the ratio of shear production (P/ɛ) and buoyancy inputs to dissipation (B/ɛ). The variation of these quantities over the tidal cycle confirms the important role of convective motions forced by tidal straining near the end of the flood phase of the tide.
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. PMID:27176280
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.
Class of compound dissipative solitons as a result of collisions in one and two spatial dimensions.
Descalzi, Orazio; Brand, Helmut R
2014-08-01
We study the interaction of quasi-one-dimensional (quasi-1D) dissipative solitons (DSs). Starting with quasi-1D solutions of the cubic-quintic complex Ginzburg-Landau (CGL) equation in their temporally asymptotic state as the initial condition, we find, as a function of the approach velocity and the real part of the cubic interaction of the two counterpropagating envelopes: interpenetration, one compound state made of both envelopes or two compound states. For the latter class both envelopes show DSs superposed at two different locations. The stability of this class of compound states is traced back to the quasilinear growth rate associated with the coupled system. We show that this mechanism also works for 1D coupled cubic-quintic CGL equations. For quasi-1D states that are not in their asymptotic state before the collision, a breakup along the crest can be observed, leading to nonunique results after the collision of quasi-1D states.
On asymptotic flatness and Lorentz charges
NASA Astrophysics Data System (ADS)
Compère, Geoffrey; Dehouck, François; Virmani, Amitabh
2011-07-01
In this paper we establish two results concerning four-dimensional asymptotically flat spacetimes at spatial infinity. First, we show that the six conserved Lorentz charges are encoded in two unique, distinct, but mutually dual symmetric divergence-free tensors that we construct from the equations of motion. Second, we show that the integrability of Einstein's equations in the asymptotic expansion is sufficient to establish the equivalence between counter-term charges defined from the variational principle and charges defined by Ashtekar and Hansen. These results clarify earlier constructions of conserved charges in the hyperboloid representation of spatial infinity. In showing this, the parity condition on the mass aspect is not needed. Along the way in establishing these results, we prove two lemmas on tensor fields on three-dimensional de Sitter spacetime stated by Ashtekar-Hansen and Beig-Schmidt and state and prove three additional lemmas. A la mémoire de notre ami et professeur Laurent Houart.
Asymptotically anti-de Sitter Proca stars
NASA Astrophysics Data System (ADS)
Duarte, Miguel; Brito, Richard
2016-09-01
We show that complex, massive spin-1 fields minimally coupled to Einstein's gravity with a negative cosmological constant, admit asymptotically anti-de Sitter self-gravitating solutions. Focusing on four-dimensional spacetimes, we start by obtaining analytical solutions in the test-field limit, where the Proca field equations can be solved in a fixed anti-de Sitter background, and then find fully nonlinear solutions numerically. These solutions are a natural extension of the recently found asymptotically flat Proca stars and share similar properties with scalar boson stars. In particular, we show that they are stable against spherically symmetric linear perturbations for a range of fundamental frequencies limited by their point of maximum mass. We finish with an overview of the behavior of Proca stars in five dimensions.
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.
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
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.
Coalescence cascade of dissipative solitons in parametrically driven systems.
Clerc, M G; Coulibaly, S; Gordillo, L; Mujica, N; Navarro, R
2011-09-01
Parametrically driven spatially extended systems exhibit uniform oscillations which are modulationally unstable. The resulting periodic state evolves to the creation of a gas of dissipative solitons. Driven by the interaction of dissipative solitons, the multisoliton state undergoes a cascade of coalescence processes, where the average soliton separation distance obeys a temporal self-similar law. Starting from the soliton pair interaction law, we have derived analytically and characterized the law of this multisoliton coarsening process. A comparison of numerical results obtained with different models such as the parametrically driven damped nonlinear Schrödinger equation, a vertically driven chain of pendula, and a parametrically forced magnetic wire, shows remarkable agreement. Both phenomena, the pair interaction law and the coarsening process, are also observed experimentally in a quasi-one-dimensional layer of Newtonian fluid which is oscillated vertically. PMID:22060473
Efficient Schmidt number scaling in dissipative particle dynamics.
Krafnick, Ryan C; García, Angel E
2015-12-28
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. PMID:26723591
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.
Direct coronal heating from dissipation of magnetic field
NASA Technical Reports Server (NTRS)
Parker, E. N.
1983-01-01
The visible corona of the Sun appears to be heated by direct dissipation of magnetic fields. The magnetic fields in the visible corona are tied at both ends to the photosphere where the active convection continually rotates and shuffles the footpoints in a random pattern. The twisting and wrapping of flux tubes about each other produce magnetic neutral sheets in a state of dynamical nonequilibrium such that the current sheets become increasingly concentrated with the passage of time. Dissipation of the high current densities takes place regardless of the high electrical conductivity of the fluid. The convection on the feet of the lines of force at the surface of the Sun goes directly (within a matter of 10 to 20 hours) into heat in the corona. The rate of doing work seems adequate to supply the necessary 10 to the 7th power ergs/square cm. sec for the active corona.
Grid evolution in time asymptotic problems
NASA Technical Reports Server (NTRS)
Rai, M. M.; Anderson, D. A.
1980-01-01
A technique for generating systems of coordinates for solving time asymptotic problems is described which provides a simple way of moving the mesh points in physical space and reduces the error in the solution relative to that obtained using a fixed mesh. First order partial differential equations are formulated for the grid point velocity in transient problems. Local flow information and boundary motion are used to determine the interior grid point motion.
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.
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}.
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}.
Konow, Nicolai; Roberts, Thomas J
2015-04-01
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. PMID:25716796
Periodic revival of entanglement of two strongly driven qubits in a dissipative cavity
Dukalski, Marcin; Blanter, Ya. M.
2010-11-15
We present a phenomenon of an asymptotic revival of bipartite entanglement between two stable solid-state qubits interacting via a single-mode cavity subject to dissipation. This effect is achievable in cavity quantum electrodynamics systems, assisted with strong classical pumping detuned from the cavity eigenmode, under the assumption of short system-bosonic reservoir correlation times. Moreover, we prove that this effect is independent of the initial cavity state and that all initially prepared Bell states experience the same qualitative effects. We present a method that can be used to generalize an arbitrary number of solid-state qubits.
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)].
Spectral wave dissipation over a barrier reef
NASA Astrophysics Data System (ADS)
Lowe, Ryan J.; Falter, James L.; Bandet, Marion D.; Pawlak, Geno; Atkinson, Marlin J.; Monismith, Stephen G.; Koseff, Jeffrey R.
2005-04-01
A 2 week field experiment was conducted to measure surface wave dissipation on a barrier reef at Kaneohe Bay, Oahu, Hawaii. Wave heights and velocities were measured at several locations on the fore reef and the reef flat, which were used to estimate rates of dissipation by wave breaking and bottom friction. Dissipation on the reef flat was found to be dominated by friction at rates that are significantly larger than those typically observed at sandy beach sites. This is attributed to the rough surface generated by the reef organisms, which makes the reef highly efficient at dissipating energy by bottom friction. Results were compared to a spectral wave friction model, which showed that the variation in frictional dissipation among the different frequency components could be described using a single hydraulic roughness length scale. Surveys of the bottom roughness conducted on the reef flat showed that this hydraulic roughness length was comparable to the physical roughness measured at this site. On the fore reef, dissipation was due to the combined effect of frictional dissipation and wave breaking. However, in this region the magnitude of dissipation by bottom friction was comparable to wave breaking, despite the existence of a well-defined surf zone there. Under typical wave conditions the bulk of the total wave energy incident on Kaneohe Bay is dissipated by bottom friction, not wave breaking, as is often assumed for sandy beach sites and other coral reefs.
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. PMID:26382391
Dissipative adaptation in driven self-assembly
NASA Astrophysics Data System (ADS)
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
2014-11-01
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. PMID:25197982
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.
[Forced Oscillations of DNA Bases].
Yakushevich, L V; Krasnobaeva, L A
2016-01-01
This paper presents the results of the studying of forced angular oscillations of the DNA bases with the help of the mathematical model consisting of two coupled nonlinear differential equations that take into account the effects of dissipation and the influence of an external periodic field. The calculation results are illustrated for sequence of gene encoding interferon alpha 17 (IFNA 17).
[Forced Oscillations of DNA Bases].
Yakushevich, L V; Krasnobaeva, L A
2016-01-01
This paper presents the results of the studying of forced angular oscillations of the DNA bases with the help of the mathematical model consisting of two coupled nonlinear differential equations that take into account the effects of dissipation and the influence of an external periodic field. The calculation results are illustrated for sequence of gene encoding interferon alpha 17 (IFNA 17). PMID:27192830
Internal dissipation of a polymer.
Deutsch, J M
2010-06-01
The dynamics of flexible polymer molecules are often assumed to be governed by hydrodynamics of the solvent. However there is considerable evidence that internal dissipation of a polymer contributes as well. Here we investigate the dynamics of a single chain in the absence of solvent to characterize the nature of this internal friction. We model the chains as freely hinged but with localized bond angles and threefold symmetric dihedral angles. We show that the damping is close but not identical to Kelvin damping, which depends on the first temporal and second spatial derivative of monomer position. With no internal potential between monomers, the magnitude of the damping is small for long wavelengths and weakly damped oscillatory time dependent behavior is seen for a large range of spatial modes. When the size of the internal potential is increased, such oscillations persist, but the damping becomes larger. However underdamped motion is present even with quite strong dihedral barriers for long enough wavelengths. PMID:20866433
Dissipation Bound for Thermodynamic Control.
Machta, Benjamin B
2015-12-31
Biological and engineered systems operate by coupling function to the transfer of heat and/or particles down a thermal or chemical gradient. In idealized deterministically driven systems, thermodynamic control can be exerted reversibly, with no entropy production, as long as the rate of the protocol is made slow compared to the equilibration time of the system. Here we consider fully realizable, entropically driven systems where the control parameters themselves obey rules that are reversible and that acquire directionality in time solely through dissipation. We show that when such a system moves in a directed way through thermodynamic space, it must produce entropy that is on average larger than its generalized displacement as measured by the Fisher information metric. This distance measure is subextensive but cannot be made small by slowing the rate of the protocol. PMID:26764981
Dissipation Bound for Thermodynamic Control
NASA Astrophysics Data System (ADS)
Machta, Benjamin B.
2015-12-01
Biological and engineered systems operate by coupling function to the transfer of heat and/or particles down a thermal or chemical gradient. In idealized deterministically driven systems, thermodynamic control can be exerted reversibly, with no entropy production, as long as the rate of the protocol is made slow compared to the equilibration time of the system. Here we consider fully realizable, entropically driven systems where the control parameters themselves obey rules that are reversible and that acquire directionality in time solely through dissipation. We show that when such a system moves in a directed way through thermodynamic space, it must produce entropy that is on average larger than its generalized displacement as measured by the Fisher information metric. This distance measure is subextensive but cannot be made small by slowing the rate of the protocol.
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.
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-Assisted Prethermalization in Long-Range Interacting Atomic Ensembles
NASA Astrophysics Data System (ADS)
Schütz, Stefan; Jäger, Simon B.; Morigi, Giovanna
2016-08-01
We theoretically characterize the semiclassical dynamics of an ensemble of atoms after a sudden quench across a driven-dissipative second-order phase transition. The atoms are driven by a laser and interact via conservative and dissipative long-range forces mediated by the photons of a single-mode cavity. These forces can cool the motion and, above a threshold value of the laser intensity, induce spatial ordering. We show that the relaxation dynamics following the quench exhibits a long prethermalizing behavior which is first dominated by coherent long-range forces and then by their interplay with dissipation. Remarkably, dissipation-assisted prethermalization is orders of magnitude longer than prethermalization due to the coherent dynamics. We show that it is associated with the creation of momentum-position correlations, which remain nonzero for even longer times than mean-field predicts. This implies that cavity cooling of an atomic ensemble into the self-organized phase can require longer time scales than the typical experimental duration. In general, these results demonstrate that noise and dissipation can substantially slow down the onset of thermalization in long-range interacting many-body systems.
Dissipation-Assisted Prethermalization in Long-Range Interacting Atomic Ensembles.
Schütz, Stefan; Jäger, Simon B; Morigi, Giovanna
2016-08-19
We theoretically characterize the semiclassical dynamics of an ensemble of atoms after a sudden quench across a driven-dissipative second-order phase transition. The atoms are driven by a laser and interact via conservative and dissipative long-range forces mediated by the photons of a single-mode cavity. These forces can cool the motion and, above a threshold value of the laser intensity, induce spatial ordering. We show that the relaxation dynamics following the quench exhibits a long prethermalizing behavior which is first dominated by coherent long-range forces and then by their interplay with dissipation. Remarkably, dissipation-assisted prethermalization is orders of magnitude longer than prethermalization due to the coherent dynamics. We show that it is associated with the creation of momentum-position correlations, which remain nonzero for even longer times than mean-field predicts. This implies that cavity cooling of an atomic ensemble into the self-organized phase can require longer time scales than the typical experimental duration. In general, these results demonstrate that noise and dissipation can substantially slow down the onset of thermalization in long-range interacting many-body systems. PMID:27588853
Dissipation-Assisted Prethermalization in Long-Range Interacting Atomic Ensembles.
Schütz, Stefan; Jäger, Simon B; Morigi, Giovanna
2016-08-19
We theoretically characterize the semiclassical dynamics of an ensemble of atoms after a sudden quench across a driven-dissipative second-order phase transition. The atoms are driven by a laser and interact via conservative and dissipative long-range forces mediated by the photons of a single-mode cavity. These forces can cool the motion and, above a threshold value of the laser intensity, induce spatial ordering. We show that the relaxation dynamics following the quench exhibits a long prethermalizing behavior which is first dominated by coherent long-range forces and then by their interplay with dissipation. Remarkably, dissipation-assisted prethermalization is orders of magnitude longer than prethermalization due to the coherent dynamics. We show that it is associated with the creation of momentum-position correlations, which remain nonzero for even longer times than mean-field predicts. This implies that cavity cooling of an atomic ensemble into the self-organized phase can require longer time scales than the typical experimental duration. In general, these results demonstrate that noise and dissipation can substantially slow down the onset of thermalization in long-range interacting many-body systems.
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.
Entanglement and dephasing of quantum dissipative systems
Stauber, T.; Guinea, F.
2006-04-15
The von Neumann entropy of various quantum dissipative models is calculated in order to discuss the entanglement properties of these systems. First, integrable quantum dissipative models are discussed, i.e., the quantum Brownian motion and the quantum harmonic oscillator. In the case of the free particle, the related entanglement of formation shows no nonanalyticity. In the case of the dissipative harmonic oscillator, there is a nonanalyticity at the transition of underdamped to overdamped oscillations. We argue that this might be a general property of dissipative systems. We show that similar features arise in the dissipative two-level system and study different regimes using sub-Ohmic, Ohmic, and super-Ohmic baths, within a scaling approach.
Holographic renormalization of asymptotically flat gravity
NASA Astrophysics Data System (ADS)
Park, Miok; Mann, Robert B.
2012-12-01
We compute the boundary stress tensor associated with Mann-Marolf counterterm in asymptotically flat and static spacetime for a cylindrical boundary surface as r → ∞, andfindthattheformoftheboundarystresstensoristhesameasthehyperbolic boundary case in 4 dimensions, but has additional terms in more than 4 dimensions. We find that these additional terms are impotent and do not contribute to conserved charges. We also check the conservation of the boundary stress tensor D a T ab = 0, and apply our result to the ( n + 3)-dimensional static black hole solution. As a result, we show that the stress boundary tensor with the Mann-Marolf counterterm works well for standard boundary surfaces.
Exact and asymptotic distributions of LULU smoothers
NASA Astrophysics Data System (ADS)
Conradie, W. J.; de Wet, T.; Jankowitz, M.
2006-02-01
This paper considers a class of non-linear smoothers, called LULU smoothers, introduced by Rohwer in the late eighties in the mathematics literature, and since then investigated fairly extensively by a number of authors for its mathematical properties. They have been successfully applied in various engineering and scientific problems. However, to date their distribution theory has not received any attention in the literature. In this paper we derive their exact as well as asymptotic distributions and show their relationship to the upper order statistics.
Asymptotic symmetries of Yang-Mills theory
NASA Astrophysics Data System (ADS)
Strominger, Andrew
2014-07-01
Asymptotic symmetries at future null infinity ( +) of Minkowski space for electrodynamics with massless charged fields, as well as nonabelian gauge theories with gauge group G, are considered at the semiclassical level. The possibility of charge/color flux through + suggests the symmetry group is infinite-dimensional. It is conjectured that the symmetries include a G Kac-Moody symmetry whose generators are "large" gauge transformations which approach locally holomorphic functions on the conformal two-sphere at + and are invariant under null translations. The Kac-Moody currents are constructed from the gauge field at the future boundary of +. The current Ward identities include Weinberg's soft photon theorem and its colored extension.
Asymptotic curved interface models in piezoelectric composites
NASA Astrophysics Data System (ADS)
Serpilli, Michele
2016-10-01
We study the electromechanical behavior of a thin interphase, constituted by a piezoelectric anisotropic shell-like thin layer, embedded between two generic three-dimensional piezoelectric bodies by means of the asymptotic analysis in a general curvilinear framework. After defining a small real dimensionless parameter ε, which will tend to zero, we characterize two different limit models and their associated limit problems, the so-called weak and strong piezoelectric curved interface models, respectively. Moreover, we identify the non-classical electromechanical transmission conditions at the interface between the two three-dimensional bodies.
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
Uncontrollable dissipative systems: observability and embeddability
NASA Astrophysics Data System (ADS)
Karikalan, Selvaraj; Belur, Madhu N.; Athalye, Chirayu D.; Razak, Rihab Abdul
2014-01-01
The theory of dissipativity is well developed for controllable systems. A more appropriate definition of dissipativity in the context of uncontrollable systems is in terms of the existence of a storage function, namely a function such that, along every system trajectory, its rate of change at each time instant is at most the power supplied to the system at that time. However, even when the supplied power is expressible in terms of just the external variables, the dissipativity property for uncontrollable systems crucially hinges on whether or not the storage function depends on variables unobservable/hidden from the external variables: this paper investigates the key aspects of both cases, and also proposes another intuitive definition of dissipativity. These three definitions are compared: we show that drawbacks of one definition are addressed by another. Dealing first with observable storage functions, under the conditions that no two uncontrollable poles add to zero and that dissipativity is strict as frequency tends to infinity, we prove that the dissipativities of a system and its controllable part are equivalent. We use the behavioural approach for formalising key notions: a system behaviour is the set of all system trajectories. We prove that storage functions have to be unobservable for 'lossless' uncontrollable systems. It is known, however, that unobservable storage functions result in certain 'fallacious' examples of lossless systems. We propose an intuitive definition of dissipativity: a system/behaviour is called dissipative if it can be embedded in a controllable dissipative superbehaviour. We prove embeddability results and use them to resolve the fallacy in the example termed 'lossless' due to unobservable storage functions. We next show that, quite unreasonably, the embeddability definition admits behaviours that are both strictly dissipative and strictly antidissipative. Drawbacks of the embeddability definition in the context of RLC circuits are
Convergence towards asymptotic state in 1-D mappings: A scaling investigation
NASA Astrophysics Data System (ADS)
Teixeira, Rivania M. N.; Rando, Danilo S.; Geraldo, Felipe C.; Costa Filho, R. N.; de Oliveira, Juliano A.; Leonel, Edson D.
2015-06-01
Decay to asymptotic steady state in one-dimensional logistic-like mappings is characterized by considering a phenomenological description supported by numerical simulations and confirmed by a theoretical description. As the control parameter is varied bifurcations in the fixed points appear. We verified at the bifurcation point in both; the transcritical, pitchfork and period-doubling bifurcations, that the decay for the stationary point is characterized via a homogeneous function with three critical exponents depending on the nonlinearity of the mapping. Near the bifurcation the decay to the fixed point is exponential with a relaxation time given by a power law whose slope is independent of the nonlinearity. The formalism is general and can be extended to other dissipative mappings.
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...
Hydrodynamical scaling laws to explore the physics of tidal dissipation in star-planet systems
NASA Astrophysics Data System (ADS)
Auclair-Desrotour, P.; Mathis, S.; Le Poncin-Lafitte, C.
2015-10-01
Fluid celestial bodies can be strongly affected by tidal perturbations, which drive the evolution of close planetary systems over long timescales. While the tidal response of solid bodies varies smoothly with the tidal frequency, fluid bodies present a highly frequency-resonant tidal dissipation resulting from the complex hydrodynamical response. In these bodies, tides have the form of a combination of inertial waves restored by the Coriolis acceleration and gravity waves in the case of stably stratified layers, which are restored by the Archimedean force. Because of processes such as viscous friction and thermal diffusion, the energy given by the tidal forcing is dissipated. This directly impact the architecture of planetary systems. In this study, we detail a local analytical model which makes us able to characterize the internal dissipation of fluid bodies as functions of identified control parameters such as the inertial, Brunt-Väisälä and tidal frequencies, and the Ekman and Prandtl numbers.
Vacuum polarization in asymptotically Lifshitz black holes
NASA Astrophysics Data System (ADS)
Quinta, Gonçalo M.; Flachi, Antonino; Lemos, José P. S.
2016-06-01
There has been considerable interest in applying the gauge-gravity duality to condensed matter theories with particular attention being devoted to gravity duals (Lifshitz spacetimes) of theories that exhibit anisotropic scaling. In this context, black hole solutions with Lifshitz asymptotics have also been constructed, focused on incorporating finite temperature effects. The goal here is to look at quantum polarization effects in these spacetimes and, to this aim, we develop a way to compute the coincidence limit of the Green's function for massive, nonminimally coupled scalar fields, adapting to the present situation the analysis developed for the case of asymptotically anti-de Sitter black holes. The basics are similar to previous calculations; however, in the Lifshitz case, one needs to extend the previous results to include a more general form for the metric and dependence on the dynamical exponent. All formulas are shown to reduce to the anti-de Sitter (AdS) case studied before once the value of the dynamical exponent is set to unity and the metric functions are accordingly chosen. The analytical results we present are general and can be applied to a variety of cases, in fact, to all spherically symmetric Lifshitz black hole solutions. We also implement the numerical analysis choosing some known Lifshitz black hole solutions as illustration.
Asymptotically Lifshitz brane-world black holes
Ranjbar, Arash Sepangi, Hamid Reza Shahidi, Shahab
2012-12-15
We study the gravity dual of a Lifshitz field theory in the context of a RSII brane-world scenario, taking into account the effects of the extra dimension through the contribution of the electric part of the Weyl tensor. We study the thermodynamical behavior of such asymptotically Lifshitz black holes. It is shown that the entropy imposes the critical exponent z to be bounded from above. This maximum value of z corresponds to a positive infinite entropy as long as the temperature is kept positive. The stability and phase transition for different spatial topologies are also discussed. - Highlights: Black-Right-Pointing-Pointer Studying the gravity dual of a Lifshitz field theory in the context of brane-world scenario. Black-Right-Pointing-Pointer Studying the thermodynamical behavior of asymptotically Lifshitz black holes. Black-Right-Pointing-Pointer Showing that the entropy imposes the critical exponent z to be bounded from above. Black-Right-Pointing-Pointer Discussing the phase transition for different spatial topologies.
Asymptotic accuracy of two-class discrimination
Ho, T.K.; Baird, H.S.
1994-12-31
Poor quality-e.g. sparse or unrepresentative-training data is widely suspected to be one cause of disappointing accuracy of isolated-character classification in modern OCR machines. We conjecture that, for many trainable classification techniques, it is in fact the dominant factor affecting accuracy. To test this, we have carried out a study of the asymptotic accuracy of three dissimilar classifiers on a difficult two-character recognition problem. We state this problem precisely in terms of high-quality prototype images and an explicit model of the distribution of image defects. So stated, the problem can be represented as a stochastic source of an indefinitely long sequence of simulated images labeled with ground truth. Using this sequence, we were able to train all three classifiers to high and statistically indistinguishable asymptotic accuracies (99.9%). This result suggests that the quality of training data was the dominant factor affecting accuracy. The speed of convergence during training, as well as time/space trade-offs during recognition, differed among the classifiers.
Asymptotic role of entanglement in quantum metrology
NASA Astrophysics Data System (ADS)
Augusiak, R.; Kołodyński, J.; Streltsov, A.; Bera, M. N.; Acín, A.; Lewenstein, M.
2016-07-01
Quantum systems allow one to sense physical parameters beyond the reach of classical statistics—with resolutions greater than 1 /N , where N is the number of constituent particles independently probing a parameter. In the canonical phase-sensing scenario the Heisenberg limit 1 /N2 may be reached, which requires, as we show, both the relative size of the largest entangled block and the geometric measure of entanglement to be nonvanishing as N →∞ . Yet, we also demonstrate that in the asymptotic N limit any precision scaling arbitrarily close to the Heisenberg limit (1 /N2 -ɛ with any ɛ >0 ) may be attained, even though the system gradually becomes noisier and separable, so that both the above entanglement quantifiers asymptotically vanish. Our work shows that sufficiently large quantum systems achieve nearly optimal resolutions despite their relative amount of entanglement being arbitrarily small. In deriving our results, we establish the continuity relation of the quantum Fisher information evaluated for a phaselike parameter, which lets us link it directly to the geometry of quantum states, and hence naturally to the geometric measure of entanglement.
Smallest zeros of some types of orthogonal polynomials: asymptotics
NASA Astrophysics Data System (ADS)
Moreno-Balcazar, Juan Jose
2005-07-01
We establish Mehler-Heine-type formulas for orthogonal polynomials related to rational modifications of Hermite weight on the real line and for Hermite-Sobolev orthogonal polynomials. These formulas give us the asymptotic behaviour of the smallest zeros of the corresponding orthogonal polynomials. Furthermore, we solve a conjecture posed in a previous paper about the asymptotics of the smallest zeros of the Hermite-Sobolev polynomials as well as an open problem concerning the asymptotics of these Sobolev orthogonal polynomials.
Some contributions to asymptotic theory for turbulent flows
NASA Astrophysics Data System (ADS)
Gersten, K.
The applicability of the asymptotic theory for the boundary layer of laminar flows to turbulent flows is discussed, with special attention given to the effect of the Reynolds number on the Blasius solution. Examples are presented on the application of the asymptotic theory for describing and predicting turbulent flows, including the Couette flow and the Couette-Poiseuille flow. Examples of other turbulent flows investigated in the past by asymptotic theory are given.
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.
Quantum dissipation in unbounded systems.
Maddox, Jeremy B; Bittner, Eric R
2002-02-01
In recent years trajectory based methodologies have become increasingly popular for evaluating the time evolution of quantum systems. A revival of the de Broglie--Bohm interpretation of quantum mechanics has spawned several such techniques for examining quantum dynamics from a hydrodynamic perspective. Using techniques similar to those found in computational fluid dynamics one can construct the wave function of a quantum system at any time from the trajectories of a discrete ensemble of hydrodynamic fluid elements (Bohm particles) which evolve according to nonclassical equations of motion. Until very recently these schemes have been limited to conservative systems. In this paper, we present our methodology for including the effects of a thermal environment into the hydrodynamic formulation of quantum dynamics. We derive hydrodynamic equations of motion from the Caldeira-Leggett master equation for the reduced density matrix and give a brief overview of our computational scheme that incorporates an adaptive Lagrangian mesh. Our applications focus upon the dissipative dynamics of open unbounded quantum systems. Using both the Wigner phase space representation and the linear entropy, we probe the breakdown of the Markov approximation of the bath dynamics at low temperatures. We suggest a criteria for rationalizing the validity of the Markov approximation in open unbound systems and discuss decoherence, energy relaxation, and quantum/classical correspondence in the context of the Bohmian paths.
Bifurcations in dissipative fermionic dynamics
NASA Astrophysics Data System (ADS)
Napolitani, Paolo; Colonna, Maria; Di Prima, Mariangela
2014-05-01
The Boltzmann-Langevin One-Body model (BLOB), is a novel one-body transport approach, based on the solution of the Boltzmann-Langevin equation in three dimensions; it is used to handle large-amplitude phase-space fluctuations and has a broad applicability for dissipative fermionic dynamics. We study the occurrence of bifurcations in the dynamical trajectories describing heavy-ion collisions at Fermi energies. The model, applied to dilute systems formed in such collisions, reveals to be closer to the observation than previous attempts to include a Langevin term in Boltzmann theories. The onset of bifurcations and bimodal behaviour in dynamical trajectories, determines the fragment-formation mechanism. In particular, in the proximity of a threshold, fluctuations between two energetically favourable mechanisms stand out, so that when evolving from the same entrance channel, a variety of exit channels is accessible. This description gives quantitative indications about two threshold situations which characterise heavy-ion collisions at Fermi energies. First, the fusion-to-multifragmentation threshold in central collisions, where the system either reverts to a compact shape, or splits into several pieces of similar sizes. Second, the transition from binary mechanisms to neck fragmentation (in general, ternary channels), in peripheral collisions.
Dissipative Properties of Quantum Systems
Grecos, A. P.; Prigogine, I.
1972-01-01
We consider the dissipative properties of large quantum systems from the point of view of kinetic theory. The existence of a nontrivial collision operator imposes restrictions on the possible collisional invariants of the system. We consider a model in which a discrete level is coupled to a set of quantum states and which, in the limit of a large “volume,” becomes the Friedrichs model. Because of its simplicity this model allows a direct calculation of the collision operator as well as of related operators and the constants of the motion. For a degenerate spectrum the calculations become more involved but the conclusions remain simple. The special role played by the invariants that are functions of the Hamiltonion is shown to be a direct consequence of the existence of a nonvanishing collision operator. For a class of observables we obtain ergodic behavior, and this reformulation of the ergodic problem may be used in statistical mechanics to study the ergodicity of large quantum systems containing a small physical parameter such as the coupling constant or the concentration. PMID:16591994
Ohmic Dissipation in Mini-Neptunes
NASA Astrophysics Data System (ADS)
Valencia, Diana; Pu, Michael
2015-12-01
In the quest of characterizing low-mass exoplanets, it is important to consider all sources that may contribute to the interpretation of planetary composition given mass and a radius measurements. While it has been firmly established that inferring the composition of super-Earths and mini-Neptunes suffers from the inherent problem of compositional degeneracy, the effect from ohmic dissipation on these planets and its connection to compositional interpretation has not been studied so far. Ohmic dissipation is arguably the leading theory that aims to explain the large radii seen in highly-irradiated exo-Jupiters. In this study, we determine the strength of ohmic dissipation on mini-Neptunes and its effect on their H/He envelope structure as a function of insolation temperature and planetary mass. We find that ohmic dissipation is strong enough to halt the contraction of mini-Neptunes during their thermal evolution and therefore, inflate their radii in comparison to planets that do not suffer dissipation. This means that the radius of highly irradiated of this class of planets may be explained by the presence of volatiles and ohmic dissipation. In other words, there is a trade-off between ohmic dissipation and H/He content for hot mini-Neptunes.
Wingtip vortex dissipator for aircraft
NASA Technical Reports Server (NTRS)
Patterson, J. C., Jr. (Inventor)
1976-01-01
A means for attenuating the vortex created at aircraft wingtips which consists of a retractable planar surface transverse to the airstream and attached downstream of the wingtip which creates a positive pressure gradient just downstream from the wing is presented. The positive pressure forces a break up of the rotational air flow of the vortex.
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.
Asymptotic theory of the pre-transitional laminar streaks and comparison with experiments
NASA Astrophysics Data System (ADS)
Ricco, Pierre
The response of the Blasius boundary layer to free-stream vortical disturbances of the convected gust type is studied. The vorticity signature of the boundary layer is computed through the boundary-region equations, which are the rigorous asymptotic limit of the Navier-Stokes equations for low-frequency disturbances. The method of matched asymptotic expansion is employed to obtain the initial and outer boundary conditions. The gust viscous dissipation and upward displacement due to the mean boundary layer produce significant changes on the fluctuations within the viscous region. The boundary-layer response induced by a threedimensional gust with spanwise wavelength comparable with the boundary-layer thickness is computed with first-order accuracy in the outer part of the boundary layer and with second-order accuracy in the core of it. The boundary-layer fluctuations of the streamwise velocity match the corresponding free-stream velocity component so that a realistic streak profile is obtained. A good agreement with the experimental data by [4] is found.
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.
Structure of Finite-RSB Asymptotic Gibbs Measures in the Diluted Spin Glass Models
NASA Astrophysics Data System (ADS)
Panchenko, Dmitry
2016-01-01
We suggest a possible approach to proving the Mézard-Parisi formula for the free energy in the diluted spin glass models, such as diluted K-spin or random K-sat model at any positive temperature. In the main contribution of the paper, we show that a certain small modification of the Hamiltonian in any of these models forces all finite-RSB asymptotic Gibbs measures in the sense of the overlaps to satisfy the Mézard-Parisi ansatz for the distribution of spins. Unfortunately, what is still missing is a description of the general full-RSB asymptotic Gibbs measures. If one could show that the general case can be approximated by finite-RSB case in the right sense then one could a posteriori remove the small modification of the Hamiltonian to recover the Mézard-Parisi formula for the original model.
Asymptotic Governing Equation for Wave Propagation Along Weakly Non-Uniform EULER-BERNOULLI Beams
NASA Astrophysics Data System (ADS)
BURR, K. P.; TRIANTAFYLLOU, M. S.; YUE, D. K. P.
2001-11-01
Non-uniformity in beams arises either from manufacturing imperfections or by design, and can have a singular impact on the qualitative properties of the vibratory response of the beam. To describe the mechanism causing such large changes on the dynamics of the beam, we derived asymptotically a simpler equation, in the formχss+Q (s) χ (s)=0. The coefficient function Q (s) is given by equation (52) herein in terms of the beam flexural rigidity, the mass per unit length and the tensile force applied to the beam. The equation is asymptotic to the non-uniformity of the beam, but under certain restrictions, namely of having constant tension and a constant product of the beam mass per unit length and flexural rigidity, it is an exact governing equation for wave propagation along Bernoulli-Euler beams and it has a Helmholtz-like form. The behavior of the equation is systematically explored and illustrated through numerical results.
Caustics in asymptotic Green Function transmission models
NASA Astrophysics Data System (ADS)
Roberts, R. A.
2000-05-01
Green Function-based beam transmission models are attractive due to their ability to explicitly handle transmission through complicated geometrical surfaces, such as flat-to-circular arc compound profiles. The beam model considered in this paper integrates the field generated by a point source positioned within a solid body over a radiating aperture surface (transducer face) in a fluid medium exterior to the solid body. In full generality, evaluation of the Green function at a point on the aperture surface requires an integration over the component surface (solid-water interface). For geometries of practical interest, this integration can be effectively evaluated by applying high-frequency asymptotic techniques (stationary phase analysis=ray theory). However, first-order asymptotic methods fail at focusing caustics, that is, when the component surface curvature focuses the field generated by the interior point source onto the aperture surface. Uniform asymptotic methods are available to treat such problems. However, implementation of uniform expansion methods in an algorithm applicable to arbitrarily curved component surfaces entails a complexity that outweighs algorithm utility. Past algorithms have therefore evaluated the Green function in these anomalous cases by performing an explicit numerical integration over the component surface. Work reported here hypothesizes that the singularity in the Green function amplitude from first-order analysis is an integrable singularity, and hence can be handled in the aperture surface integration through appropriate integration variable transformation. It is shown that an effective transformation of variables is provided by the ray coordinates which map the interior source location to points on the component surface, then onto points on the aperture surface. It is seen that zeros in the Jacobian of the surface aperture coordinate-to-ray coordinate mapping mollify the singularities in the first-order analysis Green function
Joint entropy and decoherence without dissipation in a driven harmonic oscillator
NASA Astrophysics Data System (ADS)
Fotue, A. J.; Wirngo, A. V.; Keumo Tsiaze, R. M.; Hounkonnou, M. N.
2016-09-01
The joint entropy of a non-dissipative driven harmonic oscillator for both the single and the double Gaussian states is determined. It is shown that, a non-random driving force does not influence the evolution of the system's joint entropy. For a random driving force however, the joint entropy increases almost monotonically with time, while exhibiting oscillatory behavior. The increase is a further proof of the decoherence mechanism in the system, for which we determine the duration and other characteristics.
Camerin, Fabrizio; Frezzato, Diego
2016-08-01
This study focuses on fluctuating classical systems in contact with a thermal bath, and whose configurational energetics undergoes cyclic transformations due to interaction with external perturbing agents. Under the assumptions that the configurational dynamics is a stochastic Markov process in the overdamped regime and that the nonequilibrium configurational distribution remains close to the underlying equilibrium one, we derived an analytic approximation of the average dissipated energy per cycle in the asymptotic limit (i.e., after many cycles of perturbation). The energy dissipation is then readily translated into average entropy production, per cycle, in the environment. The accuracy of the approximation was tested by comparing the outcomes with the exact values obtained by stochastic simulations of a model case: a "particle on a ring" that fluctuates in a bistable potential perturbed in two different ways. As pointed out in previous studies on the stochastic resonance phenomenon, the dependence of the average dissipation on the perturbation period may unveil the inner spectrum of the system's fluctuation rates. In this respect, the analytical approximation presented here makes it possible to unveil the connection between average dissipation, intrinsic rates and modes of fluctuation of the system at the unperturbed equilibrium, and features of the perturbation itself (namely, the period of the cycle and the projections of the energy perturbation over the system's modes). The possibilities of employing the analytical results as a guide to devising and rationalizing a sort of "spectroscopic calorimetry" experiment, and of employing them in strategies aiming to optimize the system's features on the basis of a target average dissipation, are briefly discussed. PMID:27627256
NASA Astrophysics Data System (ADS)
Camerin, Fabrizio; Frezzato, Diego
2016-08-01
This study focuses on fluctuating classical systems in contact with a thermal bath, and whose configurational energetics undergoes cyclic transformations due to interaction with external perturbing agents. Under the assumptions that the configurational dynamics is a stochastic Markov process in the overdamped regime and that the nonequilibrium configurational distribution remains close to the underlying equilibrium one, we derived an analytic approximation of the average dissipated energy per cycle in the asymptotic limit (i.e., after many cycles of perturbation). The energy dissipation is then readily translated into average entropy production, per cycle, in the environment. The accuracy of the approximation was tested by comparing the outcomes with the exact values obtained by stochastic simulations of a model case: a "particle on a ring" that fluctuates in a bistable potential perturbed in two different ways. As pointed out in previous studies on the stochastic resonance phenomenon, the dependence of the average dissipation on the perturbation period may unveil the inner spectrum of the system's fluctuation rates. In this respect, the analytical approximation presented here makes it possible to unveil the connection between average dissipation, intrinsic rates and modes of fluctuation of the system at the unperturbed equilibrium, and features of the perturbation itself (namely, the period of the cycle and the projections of the energy perturbation over the system's modes). The possibilities of employing the analytical results as a guide to devising and rationalizing a sort of "spectroscopic calorimetry" experiment, and of employing them in strategies aiming to optimize the system's features on the basis of a target average dissipation, are briefly discussed.
Boltzmann's H theorem for systems with frictional dissipation.
Bizarro, João P S
2011-03-01
By use of Boltzmann's equation to describe an ensemble of particles under the influence of a friction force, Boltzmann's H theorem is refined to explicitly include frictional dissipation, the accompanying fluctuations being modeled via an added diffusive, Fokker-Planck term. If the friction force per particle mass is proportional to velocity, as is the case with viscous drag with a friction coefficient γ, Boltzmann's H theorem for the time rate of change of the quantity H reads dH/dt ≤ γ. The classical formulation stating that H can never increase is thus replaced by the statement that H cannot increase at a rate higher than γ, a general result but of particular relevance when fluctuations are negligible and the system is far from equilibrium. When the particles are not far from thermal equilibrium, an alternative, more suitable expression emerges which can be written in the form of a Clausius inequality. PMID:21517545
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.
Moving mirrors and the fluctuation-dissipation theorem
NASA Astrophysics Data System (ADS)
Stargen, D. Jaffino; Kothawala, Dawood; Sriramkumar, L.
2016-07-01
We investigate the random motion of a mirror in (1 +1 )-dimensions that is immersed in a thermal bath of massless scalar particles which are interacting with the mirror through a boundary condition. Imposing the Dirichlet or the Neumann boundary conditions on the moving mirror, we evaluate the mean radiation reaction force on the mirror and the correlation function describing the fluctuations in the force about the mean value. From the correlation function thus obtained, we explicitly establish the fluctuation-dissipation theorem governing the moving mirror. Using the fluctuation-dissipation theorem, we compute the mean-squared displacement of the mirror at finite and zero temperature. We clarify a few points concerning the various limiting behavior of the mean-squared displacement of the mirror. While we recover the standard result at finite temperature, we find that the mirror diffuses logarithmically at zero temperature, confirming similar conclusions that have been arrived at earlier in this context. We also comment on a subtlety concerning the comparison between zero temperature limit of the finite temperature result and the exact zero temperature result.
Fuel system bubble dissipation device
Iseman, W.J.
1987-11-03
This patent describes a bubble dissipation device for a fuel system wherein fuel is delivered through a fuel line from a fuel tank to a fuel control with the pressure of the fuel being progressively increased by components including at least one pump stage and an ejector in advance of the pump state. The ejector an ejector casing with a wall defining an elongate tubular flow passage which forms a portion of the fuel line to have all of the fuel flow through the tubular flow passage in flowing from the fuel tank to the fuel control, a nozzle positioned entirely within the tubular flow passage and spaced from the wall to permit fuel flow. The nozzle has an inlet and an outlet with the inlet connected to the pump stage to receive fuel under pressure continuously from the pump stage, a bubble accumulation chamber adjoining and at a level above the ejector casing and operatively connected to the fuel line in advance of the ejector casing. The bubble accumulation chamber is of a size to function as a fuel reservoir and hold an air bubble containing vapor above the level of fuel therein and having an outlet adjacent the bottom thereof operatively connected to the tubular flow passage in the ejector casing at an inlet end, a bubble accumulation chamber inlet above the level of the bubble accumulation chamber outlet whereby fuel can flow through the bubble accumulation chamber from the inlet to the outlet thereof with a bubble in the fuel rising above the fuel level in the bubble accumulation chamber.
Quantum Einstein Gravity and Asymptotic Safety
NASA Astrophysics Data System (ADS)
Forgács, Péter
2006-06-01
I review some of the salient points of the construction of a perturbative quantum theory of the dimensionally reduced pure Einstein gravity from 4 to 2 dimensions assuming that the 4 dimensional (4D) metrics admit two commuting Killing vectors. The dimensionally reduced theory corresponds to an O(1,2) symmetric σ-model coupled to two scalar fields in flat spacetime. It inherits the lack of standard perturbative renormalizability from 4D gravity, however, it turns out that strict cutoff independence can be achieved to all loop orders in a space of Lagrangians differing only by a field dependent conformal factor. The renormalization group flow possesses a unique non-Gaussian fixed point at which the trace anomaly vanishes. The existence of this non-Gaussian fixed point is compatible with Weinberg's "asymptotic safety" scenario.
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.
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. PMID:17095658
Vortex shedding by matched asymptotic vortex method
NASA Astrophysics Data System (ADS)
Guo, Xinjun; Mandre, Shreyas
2014-11-01
An extension of the Kutta condition, using matched asymptotic expansion applied to the Navier-Stokes equations, is presented for flow past a smooth body at high Reynolds number. The goal is to study the influence of unsteady fluid dynamical effects like leading edge vortex, unsteady boundary layer separation, etc. In order to capture accurately the location and strength of vortex shedding, the simplified Navier-Stokes equations in the form of boundary layer approximation are solved in the thin inner region close to the solid body. In the outer region far from the structure, the vortex methods are applied, which significantly reduces the computational cost compared to CFD in the whole domain. With this method, the flow past an airfoil with two degrees of freedom, pitching and heaving, is investigated.
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.
Asymptotic Linear Stability of Solitary Water Waves
NASA Astrophysics Data System (ADS)
Pego, Robert L.; Sun, Shu-Ming
2016-06-01
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.
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]...
Introduction to Asymptotic Giant Branch Stars
NASA Astrophysics Data System (ADS)
El Eid, Mounib F.
2016-04-01
A brief introduction on the main characteristics of the asymptotic giant branch stars (briefly: AGB) is presented. We describe a link to observations and outline basic features of theoretical modeling of these important evolutionary phases of stars. The most important aspects of the AGB stars is not only because they are the progenitors of white dwarfs, but also they represent the site of almost half of the heavy element formation beyond iron in the galaxy. These elements and their isotopes are produced by the s-process nucleosynthesis, which is a neutron capture process competing with the β- radioactive decay. The neutron source is mainly due to the reaction 13C(α,n)16O reaction. It is still a challenging problem to obtain the right amount of 13 C that can lead to s-process abundances compatible with observation. Some ideas are presented in this context.
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.
The geometric phase in nonlinear dissipative systems
Ning, C.Z.; Haken, H. )
1992-10-30
In this paper, the authors review the recent progress made in generalizing the concept of the geometric phase to nonlinear dissipative systems. The authors first illustrate the usual form of the parallel transport law with an elementary example of the parallel shift of a line on the complex plane. Important results about the non-adiabatical geometric (Aharonov and Anandan or AA) phase [sup 18] for the Schrodinger equations are reviewed in order to make a comparison with results for dissipative systems. The authors show that a geometric phase can be defined for dissipative systems with the cyclic attractors. Systems undergoing the Hopf bifurcation with a continuous symmetry are shown to possess such cyclic attractors. Examples from laser physics are discussed to exhibit the applicability of our formalism and the widespread existence of the geometric phase in dissipative systems.
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.
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.
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.
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
Dissipation, correlation and lags in heat engines
NASA Astrophysics Data System (ADS)
Campisi, Michele; Fazio, Rosario
2016-08-01
By modelling heat engines as driven multi-partite system we show that their dissipation can be expressed in terms of the lag (relative entropy) between the perturbed state of each partition and their equilibrium state, and the correlations that build up among the partitions. We show that the non-negativity of the overall dissipation implies Carnot formulation of the second law. We illustrate the rich interplay between correlations and lags with a two-qubit device driven by a quantum gate.
A Mechanism of Energy Dissipation in Cyanobacteria
Berera, Rudi; van Stokkum, Ivo H.M.; d'Haene, Sandrine; Kennis, John T.M.; van Grondelle, Rienk; Dekker, Jan P.
2009-01-01
When grown under a variety of stress conditions, cyanobacteria express the isiA gene, which encodes the IsiA pigment-protein complex. Overexpression of the isiA gene under iron-depletion stress conditions leads to the formation of large IsiA aggregates, which display remarkably short fluorescence lifetimes and thus a strong capacity to dissipate energy. In this work we investigate the underlying molecular mechanism responsible for chlorophyll fluorescence quenching. Femtosecond transient absorption spectroscopy allowed us to follow the process of energy dissipation in real time. The light energy harvested by chlorophyll pigments migrated within the system and eventually reaches a quenching site where the energy is transferred to a carotenoid-excited state, which dissipates it by decaying to the ground state. We compare these findings with those obtained for the main light-harvesting complex in green plants (light-harvesting complex II) and artificial light-harvesting antennas, and conclude that all of these systems show the same mechanism of energy dissipation, i.e., one or more carotenoids act as energy dissipators by accepting energy via low-lying singlet-excited S1 states and dissipating it as heat. PMID:19289052
Asymptotic behaviour of the Boltzmann equation as a cosmological model
NASA Astrophysics Data System (ADS)
Lee, Ho
2016-08-01
As a Newtonian cosmological model the Vlasov-Poisson-Boltzmann system is considered, and a slightly modified Boltzmann equation, which describes the stability of an expanding universe, is derived. Asymptotic behaviour of solutions turns out to depend on the expansion of the universe, and in this paper we consider the soft potential case and will obtain asymptotic behaviour.
An unsteady time asymptotic flow in the square driven cavity
NASA Technical Reports Server (NTRS)
Goodrich, John W.
1990-01-01
Summary details of an aperiodic time asymptotic numerical solution for the square drive cavity at Re = 10000 are presented. The data presented is for 6100 less than t less than or equal to 7100, and is representative of the data that characterizes the aperiodic asymptotic state.
Asymptotic analysis, Working Note No. 1: Basic concepts and definitions
Garbey, M.; Kaper, H.G.
1993-07-01
In this note we introduce the basic concepts of asymptotic analysis. After some comments of historical interest we begin by defining the order relations O, o, and O{sup {number_sign}}, which enable us to compare the asymptotic behavior of functions of a small positive parameter {epsilon} as {epsilon} {down_arrow} 0. Next, we introduce order functions, asymptotic sequences of order functions and more general gauge sets of order functions and define the concepts of an asymptotic approximation and an asymptotic expansion with respect to a given gauge set. This string of definitions culminates in the introduction of the concept of a regular asymptotic expansion, also known as a Poincare expansion, of a function f : (0, {epsilon}{sub o}) {yields} X, where X is a normed vector space of functions defined on a domain D {epsilon} R{sup N}. We conclude the note with the asymptotic analysis of an initial value problem whose solution is obtained in the form of a regular asymptotic expansion.
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.
Analysis of leaching data using asymptotic expansion techniques
Simonson, S.A.; Machiels, A.J.
1983-01-01
Asymptotic analysis constitutes a useful technique to determine the adjustable parameters appearing in mathematical models attempting to reproduce some experimental data. In particular, asymptotic expansions of a leach model proposed by A.J. Machiels and C. Pescatore are used to interpret leaching data from PNL 76-68 glass in terms of corrosion velocities and diffusion coefficients.
Asymptotic expansion of the lattice scalar propagator in coordinate space
NASA Astrophysics Data System (ADS)
Paladini, Beatrice; Sexton, James C.
1998-02-01
The asymptotic expansion of the massive scalar field propagator on a n- dimensional lattice is derived. The method used is based on the evaluation of the asymptotic expansion of the modified Bessel function Iν(ν2β) as the order ν grows to infinity.
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.
Nonequilibrium functional renormalization for driven-dissipative Bose-Einstein condensation
NASA Astrophysics Data System (ADS)
Sieberer, L. Â. M.; Huber, S. Â. D.; Altman, E.; Diehl, S.
2014-04-01
We present a comprehensive analysis of critical behavior in the driven-dissipative Bose condensation transition in three spatial dimensions. The starting point is a microscopic description of the system in terms of a many-body quantum master equation, where coherent and driven-dissipative dynamics occur on an equal footing. An equivalent Keldysh real-time functional integral reformulation opens up the problem to a practical evaluation using the tools of quantum field theory. In particular, we develop a functional renormalization group approach to quantitatively explore the universality class of this stationary nonequilibrium system. Key results comprise the emergence of an asymptotic thermalization of the distribution function, while manifest nonequilibrium properties are witnessed in the response properties in terms of a new, independent critical exponent. Thus, the driven-dissipative microscopic nature is seen to bear observable consequences on the largest length scales. The absence of two symmetries present in closed equilibrium systems—underlying particle number conservation and detailed balance, respectively—is identified as the root of this new nonequilibrium critical behavior. Our results are relevant for broad ranges of open quantum systems on the interface of quantum optics and many-body physics, from exciton-polariton condensates to cold atomic gases.
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)
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).
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.
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.
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.
NASA Astrophysics Data System (ADS)
Jung, Gerhard; Schmid, Friederike
2016-05-01
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.
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. PMID:27250276
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.
Konow, Nicolai; Roberts, Thomas J.
2015-01-01
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. PMID:25716796
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.
Asymptotic Dynamics of Inertial Particles with Memory
NASA Astrophysics Data System (ADS)
Langlois, Gabriel Provencher; Farazmand, Mohammad; Haller, George
2015-12-01
Recent experimental and numerical observations have shown the significance of the Basset-Boussinesq memory term on the dynamics of small spherical rigid particles (or inertial particles) suspended in an ambient fluid flow. These observations suggest an algebraic decay to an asymptotic state, as opposed to the exponential convergence in the absence of the memory term. Here, we prove that the observed algebraic decay is a universal property of the Maxey-Riley equation. Specifically, the particle velocity decays algebraically in time to a limit that is {O}(ɛ )-close to the fluid velocity, where 0<ɛ ≪ 1 is proportional to the square of the ratio of the particle radius to the fluid characteristic length scale. These results follow from a sharp analytic upper bound that we derive for the particle velocity. For completeness, we also present a first proof of the global existence and uniqueness of mild solutions to the Maxey-Riley equation, a nonlinear system of fractional differential equations.
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 properties of a bold random walk
NASA Astrophysics Data System (ADS)
Serva, Maurizio
2014-08-01
In a recent paper we proposed a non-Markovian random walk model with memory of the maximum distance ever reached from the starting point (home). The behavior of the walker is different from the simple symmetric random walk only when she is at this maximum distance, where, having the choice to move either farther or closer, she decides with different probabilities. If the probability of a forward step is higher than the probability of a backward step, the walker is bold and her behavior turns out to be superdiffusive; otherwise she is timorous and her behavior turns out to be subdiffusive. The scaling behavior varies continuously from subdiffusive (timorous) to superdiffusive (bold) according to a single parameter γ ∈R. We investigate here the asymptotic properties of the bold case in the nonballistic region γ ∈[0,1/2], a problem which was left partially unsolved previously. The exact results proved in this paper require new probabilistic tools which rely on the construction of appropriate martingales of the random walk and its hitting times.
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.
MJO: Asymptotically-Nondivergent Nonlinear Wave?: A Review
NASA Astrophysics Data System (ADS)
Yano, J. I.
2014-12-01
MJO is often considered a convectively-coupled wave. The present talk is going to argue that it is best understood primarily as a nonlinear solitary wave dominated by vorticity. Role of convection is secondary,though likely catalytic. According to Charney's (1963) scale analysis, the large-scale tropical circulations are nondivergent to the leading order, i.e., dominated by rotational flows. Yano et al (2009) demonstrate indeed that is the case for a period dominated by three MJO events. The scale analysis of Yano and Bonazzola (2009, JAS) demonstrates such an asymptotically nondivergent regime is a viable alternative to the traditionally-believed equatorial-wave regime. Wedi and Smolarkiewicz (2010, JAS) in turn, show by numerical computations of a dry system that a MJO-like oscillation for a similar period can indeed be generated by free solitary nonlinear equatorial Rossby-wave dynamicswithout any convective forcing to a system. Unfortunately, this perspective is slow to be accepted with people's mind so much fixed on the role of convection. This situation may be compared to a slow historical process of acceptance of Eady and Charney's baroclinicinstability simply because it does not invoke any convection Ironically, once the nonlinear free-wave view for MJO is accepted, interpretations can more easily be developed for a recent series of numerical model experiments under a global channel configuration overthe tropics with a high-resolution of 5-50 km with or without convection parameterization. All those experiments tend to reproduce observed large-scale circulations associated with MJO rather well, though most of time, they fail to reproduce convective coherency associated with MJO.These large-scale circulations appear to be generated by lateral forcing imposed at the latitudinal walls. These lateral boundaries are reasonably far enough (30NS) to induce any direct influence to the tropics. There is no linear dry equatorial wave that supports this period either
Castanos, L. O.; Jauregui, R.
2011-06-15
We consider two two-level atoms interacting collectively with all the modes of the quantum electromagnetic field. The center-of-mass motion of each atom is quantized in three dimensions and each atom is placed in a harmonic oscillator potential. We describe a method that factorizes an approximate density operator of the two atoms in parts which evolve under different portions of the Hamiltonian. We apply this method to the system under consideration to study the effect of the uncertainty in the position of the atoms on the dissipation rates and on the entanglement between the internal degrees of freedom of the two atoms. We find that the uncertainty in position can give rise to smaller dissipation rates. This in turn affects the entanglement which may decay exponentially with smaller decay rates or may even decay asymptotically by a power law.
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.
Some Asymptotic Conditions of Worldlines in Minkowski Space. II
NASA Astrophysics Data System (ADS)
Yoneda, Gen
1994-09-01
The previous paper I of this series presented four asymptotic conditions of smooth worldlines in Minkowski space and researched the inclusion relations between them. This paper moreover presents three asymptotic conditions that are used in special relativistic particle dynamics. (1) There is no end of the worldline. (2) From any point, the perpendicular to the worldline is drawable. (3) The acceleration vanishes asymptotically. The inclusion relations between seven conditions are researched by showing some inclusion relations and by examining some examples. Then the concluding Venn diagram is obtained.
Asymptotically anti-de Sitter space-times
NASA Astrophysics Data System (ADS)
Ashtekar, A.; Magnon, A.
1984-07-01
The structure of the gravitational field at infinity of asymptotically anti-de Sitter space-times is analyzed in detail using conformal techniques. It is found that the situation differs from that in the case of asymptotically Minkowskian space-times in a number of respects. In particular, the asymptotic symmetry group is quite different from the BMS group, and there is no analogue of the Bondi news. The analysis also introduces definitions of 'conserved' quantities in terms of the curvature tensor which are free of the ambiguities present in the previous definitions based on the deviation of the physical metric from an anti-de Sitter background.
Dissipation and traversal time in Josephson junctions
Cacciari, Ilaria; Ranfagni, Anedio; Moretti, Paolo
2010-05-01
The various ways of evaluating dissipative effects in macroscopic quantum tunneling are re-examined. The results obtained by using functional integration, while confirming those of previously given treatments, enable a comparison with available experimental results relative to Josephson junctions. A criterion based on the shortening of the semiclassical traversal time tau of the barrier with regard to dissipation can be established, according to which DELTAtau/tau > or approx. N/Q, where Q is the quality factor of the junction and N is a numerical constant of order unity. The best agreement with the experiments is obtained for N=1.11, as it results from a semiempirical analysis based on an increase in the potential barrier caused by dissipative effects.
Landing Energy Dissipation for Manned Reentry Vehicles
NASA Technical Reports Server (NTRS)
1960-01-01
Landing Energy Dissipation for Manned Reentry Vehicles. The film shows experimental investigations 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 include 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. [Entire movie available on DVD from CASI as Doc ID 20070030945. Contact help@sti.nasa.gov
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
A dissipative network model with neighboring activation
NASA Astrophysics Data System (ADS)
Xiong, Fei; Liu, Yun; Zhu, Jiang; Jiang Zhang, Zhen; Chao Zhang, Yan; Zhang, Ying
2011-11-01
We propose a network model with dissipative structure taking into consideration the effect of neighboring activation and individual dissipation. Nodes may feel tired of interactions with new nodes step by step, and drop out of the network evolution. However, these dormant nodes can become active again following neighbors. During the whole evolution only active nodes have opportunities to receive new links. We analyze user behavior of a real Internet forum, and the statistical characteristics of this forum are analogous to our model. Under the influence of motivation and dissipation, the degree distribution of our network model decays as a power law with a diversity of tunable power exponents. Furthermore, the network has high clustering, small average path length and positive assortativity coefficients.
Cascaded generation of coherent Raman dissipative solitons.
Kharenko, Denis S; Bednyakova, Anastasia E; Podivilov, Evgeniy V; Fedoruk, Mikhail P; Apolonski, Alexander; Babin, Sergey A
2016-01-01
The cascaded generation of a conventional dissipative soliton (at 1020 nm) together with Raman dissipative solitons of the first (1065 nm) and second (1115 nm) orders inside a common fiber laser cavity is demonstrated experimentally and numerically. With sinusoidal (soft) spectral filtering, the generated solitons are mutually coherent at a high degree and compressible down to 300 fs. Numerical simulation shows that an even higher degree of coherence and shorter pulses could be achieved with step-like (hard) spectral filtering. The approach can be extended toward a high-order coherent Raman dissipative soliton source offering numerous applications such as frequency comb generation, pulse synthesis, biomedical imaging, and the generation of a coherent mid-infrared supercontinuum. PMID:26696187
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.
Designing Adaptive Low Dissipative High Order Schemes
NASA Technical Reports Server (NTRS)
Yee, H. C.; Sjoegreen, B.; Parks, John W. (Technical Monitor)
2002-01-01
Proper control of the numerical dissipation/filter to accurately resolve all relevant multiscales of complex flow problems while still maintaining nonlinear stability and efficiency for long-time numerical integrations poses a great challenge to the design of numerical methods. The required type and amount of numerical dissipation/filter are not only physical problem dependent, but also vary from one flow region to another. This is particularly true for unsteady high-speed shock/shear/boundary-layer/turbulence/acoustics interactions and/or combustion problems since the dynamics of the nonlinear effect of these flows are not well-understood. Even with extensive grid refinement, it is of paramount importance to have proper control on the type and amount of numerical dissipation/filter in regions where it is needed.
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
NASA Astrophysics Data System (ADS)
Jacobs, William M.; Nicholson, David A.; Zemer, Hagit; Volkov, Alexey N.; Zhigilei, Leonid V.
2012-10-01
The exchange of energy between low-frequency mechanical oscillations and high-frequency vibrational modes in carbon nanotubes (CNTs) is a process that plays an important role in a range of dynamic phenomena involving the dissipation of mechanical energy in both individual CNTs and CNT-based materials. The rates and channels through which acoustic energy deposited instantaneously in individual CNTs is dissipated are investigated in a series of atomistic molecular dynamics simulations. Several distinct regimes of energy dissipation, dependent on the initial stretching or bending deformations, are established. The onset of axial or bending buckling marks the transition from a regime of slow thermalization to a regime in which the energy associated with longitudinal and bending oscillations is rapidly damped. In the case of stretching vibrations, an intermediate regime is revealed in which dynamic coupling between longitudinal vibrational modes and the radial “squash” mode causes delayed axial buckling followed by a rapid transfer of energy to high-frequency vibrations. The results of the atomistic simulations are used in the design and parameterization of a “heat bath” description of thermal energy in a mesoscopic model, which is capable of simulating systems consisting of thousands of interacting CNTs. Two complementary methods for the description of mechanical energy dissipation in the mesoscopic model are developed. The relatively slow dissipation of acoustic vibrations in the absence of buckling is described by adding a damping force to the equations of motion of the dynamic elements of the mesoscopic model. The sharp increase in the energy dissipation rate at the onset of buckling is reproduced by incorporating a hysteresis loop into the strain energy that accounts for localized thermalization in the vicinity of buckling kinks. The ability of the mesoscopic model to reproduce the complex multistep processes of acoustic energy dissipation predicted by the
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
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.
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
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
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.
Analysis of Compaction Wave Dissipation in Porous Metalized Explosive
NASA Astrophysics Data System (ADS)
Rao, Pratap; Gonthier, Keith
2013-06-01
It is well established that the inclusion of reactive metals in explosive formulations can enhance post-detonation energy release but it remains unclear, even for idealized systems, how the composition and microstructure of metal containing porous solid explosives affects dissipative heating within compaction waves that is important for weak initiation of detonation. In this study, we perform inert meso-scale simulations to computationally examine how the initial porosity and metal mass fraction of aluminized HMX influences dissipation within compaction waves and we compare predictions to those given by a macro-scale compaction theory. The meso-scale model uses a hyperthermoelastic-viscoplastic and stick-slip friction theory to track the evolution of thermomechanical fields within individual particles that result from pore collapse within waves. Effective quasi-steady wave profiles are obtained by averaging meso-scale fields over space and time. The macro-scale theory predicts the variation in effective thermomechanical fields within waves due to imbalances in phase-specific pressures and configurational stresses. Qualitative agreement exists between meso-scale and macro-scale predictions. This research is supported by the Defense Threat Reduction Agency (DTRA) under sponsor award number HDTRA1-10-1-0018, and the Air Force Research Laboratory (AFRL-RWME) under sponsor award number FA8651-09-0021.
Entropy production and the geometry of dissipative evolution equations.
Reina, Celia; Zimmer, Johannes
2015-11-01
Purely dissipative evolution equations are often cast as gradient flow structures, z ̇=K(z)DS(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. PMID:26651657
Galapon, Eric A.; Martinez, Kay Marie L.
2014-01-01
We obtain an exactification of the Poincaré asymptotic expansion (PAE) of the Hankel integral, as , 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. PMID:24511252
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.
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.
Dynamic fission instability of dissipative protoplanets
NASA Technical Reports Server (NTRS)
Boss, A. P.; Mizuno, H.
1985-01-01
Analytical and numerical approaches are taken to consider if a rapidly rotating, viscous protoearth would have lost mass by a fission process and thereby given birth to the moon. The fast rotation is assumed as the source of the instability in the dissipative liquid protoearth. Governing hydrodynamic equations are defined for the evolution of the protoearth. Account is taken of viscous dissipation, the pressure equation of state for the atmospheric material sent on a ballistic trajectory, and the effective viscosity. The results indicate that dynamic fission was probably not the process by which the protomoon came into existence.
Landing Energy Dissipation for Manned Reentry Vehicles
NASA Technical Reports Server (NTRS)
Fisher, Loyd. L.
1960-01-01
The film shows experimental investigations 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 include 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.
Energy dissipation scaling in uniformly sheared turbulence
NASA Astrophysics Data System (ADS)
Nedić, Jovan; Tavoularis, Stavros
2016-03-01
The rate of turbulent kinetic energy dissipation in spatially developing, uniformly sheared turbulence is examined experimentally. In the far-downstream fully developed region of the flow, we confirm that the dissipation parameter Cɛ is constant. More importantly, however, we find two upstream regions where this parameter could be scaled with the local turbulent Reynolds number as Cɛ=A Reλα ; the exponents in these two regions are, respectively, α =-0.6 and 0.5 . The observed changes in scaling laws are explained by consideration of structural changes in the turbulence.
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.
Evolution of satellite resonances by tidal dissipation.
NASA Technical Reports Server (NTRS)
Greenberg, R.
1973-01-01
Analysis of a realistic model shows how satellites' gravitational interaction can halt their differential tidal evolution when resonant commensurabilities of their orbital periods are reached. The success of this study lends support to the hypothesis that orbit-orbit resonances among satellites in the solar system, including the Titan-Hyperion case, did evolve as a result of tidal energy dissipation. Consideration of the time scale for this evolution process, possible now that the capture mechanism has been revealed, can offer more sophisticated constraints on the tidal dissipation function, Q, and on past orbital conditions.
ON THE TIDAL DISSIPATION OF OBLIQUITY
Rogers, T. M.; Lin, D. N. C. E-mail: lin@ucolick.org
2013-05-20
We investigate tidal dissipation of obliquity in hot Jupiters. Assuming an initial random orientation of obliquity and parameters relevant to the observed population, the obliquity of hot Jupiters does not evolve to purely aligned systems. In fact, the obliquity evolves to either prograde, retrograde, or 90 Degree-Sign orbits where the torque due to tidal perturbations vanishes. This distribution is incompatible with observations which show that hot Jupiters around cool stars are generally aligned. This calls into question the viability of tidal dissipation as the mechanism for obliquity alignment of hot Jupiters around cool stars.
Space plasma turbulent dissipation - Reality or myth?
NASA Technical Reports Server (NTRS)
Coroniti, F. V.
1985-01-01
A prevalent approach to understanding magnetospheric dynamics is to combine a hydromagnetic description of the large scale magnetic structure and convection flows with a locally determined anomalous dissipation which develops in boundary layers. Three problems (nose and tail reconnection, auroral field-aligned currents, and diffuse auroral precipitation) are critically examined to test the validity of this theoretical philosophy. Although the expected plasma wave turbulence is observed for each case, the concept of local anomalous dissipation fails to provide an adequate or complete description of the phenomenae.
An introduction to dissipative particle dynamics.
Lu, Zhong-Yuan; Wang, Yong-Lei
2013-01-01
Dissipative particle dynamics (DPD) is a particle-based mesoscopic simulation method, which facilitates the studies of thermodynamic and dynamic properties of soft matter systems at physically interesting length and time scales. In this method, molecule groups are clustered into the dissipative beads, and this coarse-graining procedure is a very important aspect of DPD as it allows significant computational speed-up. In this chapter, we introduce the DPD methodology, including its theoretical foundation and its parameterization. With this simulation technique, we can study complex behaviors of biological systems, such as the formation of vesicles and their fusion and fission processes, and the phase behavior of lipid membranes.
Crises in a dissipative bouncing ball model
NASA Astrophysics Data System (ADS)
Livorati, André L. P.; Caldas, Iberê L.; Dettmann, Carl P.; Leonel, Edson D.
2015-11-01
The dynamics of a bouncing ball model under the influence of dissipation is investigated by using a two-dimensional nonlinear mapping. When high dissipation is considered, the dynamics evolves to different attractors. The evolution of the basins of the attracting fixed points is characterized, as we vary the control parameters. Crises between the attractors and their boundaries are observed. We found that the multiple attractors are intertwined, and when the boundary crisis between their stable and unstable manifolds occurs, it creates a successive mechanism of destruction for all attractors originated by the sinks. Also, a physical impact crisis is described, an important mechanism in the reduction of the number of attractors.
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
Dynamic fission instability of dissipative protoplanets
NASA Astrophysics Data System (ADS)
Boss, A. P.; Mizuno, H.
1985-07-01
Analytical and numerical approaches are taken to consider if a rapidly rotating, viscous protoearth would have lost mass by a fission process and thereby given birth to the moon. The fast rotation is assumed as the source of the instability in the dissipative liquid protoearth. Governing hydrodynamic equations are defined for the evolution of the protoearth. Account is taken of viscous dissipation, the pressure equation of state for the atmospheric material sent on a ballistic trajectory, and the effective viscosity. The results indicate that dynamic fission was probably not the process by which the protomoon came into existence.
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
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.
Semilocal density functional theory with correct surface asymptotics
NASA Astrophysics Data System (ADS)
Constantin, Lucian A.; Fabiano, Eduardo; Pitarke, J. M.; Della Sala, Fabio
2016-03-01
Semilocal density functional theory is the most used computational method for electronic structure calculations in theoretical solid-state physics and quantum chemistry of large systems, providing good accuracy with a very attractive computational cost. Nevertheless, because of the nonlocality of the exchange-correlation hole outside a metal surface, it was always considered inappropriate to describe the correct surface asymptotics. Here, we derive, within the semilocal density functional theory formalism, an exact condition for the imagelike surface asymptotics of both the exchange-correlation energy per particle and potential. We show that this condition can be easily incorporated into a practical computational tool, at the simple meta-generalized-gradient approximation level of theory. Using this tool, we also show that the Airy-gas model exhibits asymptotic properties that are closely related to those at metal surfaces. This result highlights the relevance of the linear effective potential model to the metal surface asymptotics.
Asymptotics for the Covariance of the Airy2 Process
NASA Astrophysics Data System (ADS)
Shinault, Gregory; Tracy, Craig A.
2011-04-01
In this paper we compute some of the higher order terms in the asymptotic behavior of the two point function {P}({A}2(0)≤ s1,A2(t)≤ s2), extending the previous work of Adler and van Moerbeke (arXiv:math.PR/0302329; Ann. Probab. 33, 1326-1361, 2005) and Widom (J. Stat. Phys. 115, 1129-1134, 2004). We prove that it is possible to represent any order asymptotic approximation as a polynomial and integrals of the Painlevé II function q and its derivative q'. Further, for up to tenth order we give this asymptotic approximation as a linear combination of the Tracy-Widom GUE density function f 2 and its derivatives. As a corollary to this, the asymptotic covariance is expressed up to tenth order in terms of the moments of the Tracy-Widom GUE distribution.
Asymptotic formula for eigenvalues of one dimensional Dirac system
NASA Astrophysics Data System (ADS)
Ulusoy, Ismail; Penahlı, Etibar
2016-06-01
In this paper, we study the spectral problem for one dimensional Dirac system with Dirichlet boundary conditions. By using Counting lemma, we give an asymptotic formulas of eigenvalues of Dirac system.
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.
Comte, J C; Marquié, P; Remoissenet, M
1999-12-01
We introduce a nonlinear Klein-Gordon lattice model with specific double-well on-site potential, additional constant external force and dissipation terms, which admits exact discrete kink or traveling wave fronts solutions. In the non-dissipative or conservative regime, our numerical simulations show that narrow kinks can propagate freely, and reveal that static or moving discrete breathers, with a finite but long lifetime, can emerge from kink-antikink collisions. In the general dissipative regime, the lifetime of these breathers depends on the importance of the dissipative effects. In the overdamped or diffusive regime, the general equation of motion reduces to a discrete reaction diffusion equation; our simulations show that, for a given potential shape, discrete wave fronts can travel without experiencing any propagation failure but their collisions are inelastic. PMID:11970697
Comte, J C; Marquié, P; Remoissenet, M
1999-12-01
We introduce a nonlinear Klein-Gordon lattice model with specific double-well on-site potential, additional constant external force and dissipation terms, which admits exact discrete kink or traveling wave fronts solutions. In the non-dissipative or conservative regime, our numerical simulations show that narrow kinks can propagate freely, and reveal that static or moving discrete breathers, with a finite but long lifetime, can emerge from kink-antikink collisions. In the general dissipative regime, the lifetime of these breathers depends on the importance of the dissipative effects. In the overdamped or diffusive regime, the general equation of motion reduces to a discrete reaction diffusion equation; our simulations show that, for a given potential shape, discrete wave fronts can travel without experiencing any propagation failure but their collisions are inelastic.
NASA Astrophysics Data System (ADS)
Sedighi, Mehdi; Palasantzas, George
2014-02-01
Casimir and hydrodynamic dissipation forces can strongly influence the actuation of microelectromechanical systems in ambient conditions. The dissipative and stiction dynamics of an actuating system is shown to depend on surface physical processes related to fluid slip and the size of the actuating components. Using phase change materials the Casimir force magnitude can be modulated via amorphous-crystalline phase transitions. The dissipative motion between amorphous coated phase change material components can be changed towards stiction upon crystallization and suitable choice of restoring spring constants. By contrast, amorphization can augment switching from stiction to dissipative dynamics.
NASA Astrophysics Data System (ADS)
Tong, Mai; Liebner, Thomas
2007-03-01
In a viscous damping device under cyclic loading, after the piston reaches a peak stroke, the reserve movement that follows may sometimes experience a short period of delayed or significantly reduced device force output. A similar delay or reduced device force output may also occur at the damper’s initial stroke as it moves away from its neutral position. This phenomenon is referred to as the effect of “deadzone”. The deadzone can cause a loss of energy dissipation capacity and less efficient vibration control. It is prominent in small amplitude vibrations. Although there are many potential causes of deadzone such as environmental factors, construction, material aging, and manufacture quality, in this paper, its general effect in linear and nonlinear viscous damping devices is analyzed. Based on classical dynamics and damping theory, a simple model is developed to capture the effect of deadzone in terms of the loss of energy dissipation capacity. The model provides several methods to estimate the loss of energy dissipation within the deadzone in linear and sublinear viscous fluid dampers. An empirical equation of loss of energy dissipation capacity versus deadzone size is formulated, and the equivalent reduction of effective damping in SDOF systems has been obtained. A laboratory experimental evaluation is carried out to verify the effect of deadzone and its numerical approximation. Based on the analysis, a modification is suggested to the corresponding formulas in FEMA 356 for calculation of equivalent damping if a deadzone is to be considered.
Power Dissipation and Electrical Breakdown in Black Phosphorus.
Engel, Michael; Steiner, Mathias; Han, Shu-Jen; Avouris, Phaedon
2015-10-14
We report operating temperatures and heating coefficients measured in a multilayer black phosphorus device as a function of injected electrical power. By combining micro-Raman spectroscopy and electrical transport measurements, we have observed a linear temperature increase up to 600 K at a power dissipation rate of 0.896 K μm(3)/mW. By further increasing the bias voltage, we determined the threshold power and temperature for electrical breakdown and analyzed the fracture in the black phosphorus layer that caused the device failure by means of scanning electron microscopy and atomic force microscopy. The results will benefit the research and development of electronics and optoelectronics based on novel two-dimensional materials.
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.
Theory of minimum dissipation of energy for the steady state
Chu, T.K.
1992-02-01
The magnetic configuration of an inductively driven steady-state plasma bounded by a surface (or two adjacent surfaces) on which B{center dot}n = 0 is force-free: {del}{times}B = 2{alpha}B, where {alpha} is a constant, in time and in space. {alpha} is the ratio of the Poynting flux to the magnetic helicity flux at the boundary. It is also the ratio of the dissipative rates of the magnetic energy to the magnetic helicity in the plasma. The spatial extent of the configuration is noninfinitesimal. This global constraint is a result of the requirement that, for a steady-state plasma, the rate of change of the vector potential, {partial derivative}A/{partial derivative}t, is constant in time and uniform in space.
Theory of minimum dissipation of energy for the steady state
Chu, T.K.
1992-02-01
The magnetic configuration of an inductively driven steady-state plasma bounded by a surface (or two adjacent surfaces) on which B{center_dot}n = 0 is force-free: {del}{times}B = 2{alpha}B, where {alpha} is a constant, in time and in space. {alpha} is the ratio of the Poynting flux to the magnetic helicity flux at the boundary. It is also the ratio of the dissipative rates of the magnetic energy to the magnetic helicity in the plasma. The spatial extent of the configuration is noninfinitesimal. This global constraint is a result of the requirement that, for a steady-state plasma, the rate of change of the vector potential, {partial_derivative}A/{partial_derivative}t, is constant in time and uniform in space.
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.
Asymptotic Normality Through Factorial Cumulants and Partition Identities
Bobecka, Konstancja; Hitczenko, Paweł; López-Blázquez, Fernando; Rempała, Grzegorz; Wesołowski, Jacek
2013-01-01
In the paper we develop an approach to asymptotic normality through factorial cumulants. Factorial cumulants arise in the same manner from factorial moments as do (ordinary) cumulants from (ordinary) moments. Another tool we exploit is a new identity for ‘moments’ of partitions of numbers. The general limiting result is then used to (re-)derive asymptotic normality for several models including classical discrete distributions, occupancy problems in some generalized allocation schemes and two models related to negative multinomial distribution. PMID:24591773
Asymptotics of solutions of the discrete string equation
NASA Astrophysics Data System (ADS)
Vereschagin, Vadim L.
The main subject of the paper is the so-called Discrete Painlevé-1 Equation (DP1). Solutions of DP1 are classified under the criterion of their behavior while the argument tends to infinity. The Isomonodromic Deformations Method (IDM) yields asymptotic formulae for regular solutions of DP1. DP1 is an integrable system, which allows to develop the appropriate Whitham theory. Asymptotics of singular solutions of DP1 are calculated by using the Whitham method.
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.
The development of jet mixing toward the asymptotic similar solution
NASA Technical Reports Server (NTRS)
Brink, D. F.; Chow, W. L.
1974-01-01
An analytic study of the development of an initially nonsimilar jet mixing velocity profile toward the final asymptotic, similar solution, is made. The corresponding incompressible boundary layer equations are solved for each of the streams above and below the dividing streamline by using Meksyn's asymptotic method of integration. The behavior of this flow development toward the final similar solution, as influenced by the initial condition, is properly described and discussed.
Asymptotic stability of vacuum twisting type II metrics
NASA Astrophysics Data System (ADS)
Natorf, Włodzimierz
2012-02-01
We generalize the result of Lukács et al. on asymptotic stability of the Schwarzschild metric with respect to perturbations in the Robinson-Trautman class of metrics to the case of Petrov type II twisting metrics, under the condition of asymptotic flatness at future null infinity. The Bondi energy is used as the Lyapunov functional and we prove that the "final state" of such metrics is the Kerr metric.
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 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.
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.
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.
Magnetic dissipation in the Crab nebula
NASA Astrophysics Data System (ADS)
Komissarov, Serguei S.
2013-01-01
Magnetic dissipation is frequently invoked as a way of powering the observed emission of relativistic flows in Gamma-ray bursts and active galactic nuclei. Pulsar Wind Nebulae provide closer to home cosmic laboratories which can be used to test the hypothesis. To this end, we reanalyze the observational data on the spindown power of the Crab pulsar, energetics of the Crab nebula and its magnetic field. We show that unless the magnetic inclination angle of the Crab pulsar is very close to 90 degrees the overall magnetization of the striped wind after total dissipation of its stripes is significantly higher than that deduced in the Kennel-Coroniti model and recent axisymmetric simulations of Pulsar Wind Nebulae. On the other hand, higher wind magnetization is in conflict with the observed low magnetic field of the Crab nebula, unless it is subject to efficient dissipation inside the nebula as well. For the likely inclination angle of 45 degrees the data require magnetic dissipation on the time-scale of about 80 years, which is short compared to the lifetime of the nebula but long compared to the time-scale of Crab's gamma-ray flares.
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).
Kinetic foundations of relativistic dissipative fluid dynamics
NASA Astrophysics Data System (ADS)
Denicol, G. S.
2014-12-01
In this contribution we discuss in detail the most widespread formalisms employed to derive relativistic dissipative fluid dynamics from the Boltzmann equation: Chapman-Enskog expansion and Israel-Stewart theory. We further point out the drawbacks of each theory and explain possible ways to circumvent them. Recent developments in the derivation of fluid dynamics from the Boltzmann equation are also discussed.
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.
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 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.
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.
Wu Kun; Wu Bing; Feng, C.-Q.; Du Xianbin; Huang Huan; Yin Zejie; Zhu Daming
2006-03-15
We describe a simple dissipative quartz crystal microbalance (QCM) and two simple methods for determining the dissipation factor. The microbalance consists of an oscillator circuit interfaced with a personal computer. The oscillation voltages are undersampled through a low speed data acquisition card. Both methods for determining the resonant frequency and the dissipation factor assume a limited variation of the resonant frequency, which is the case for general applications of QCMs. The first method directly fits the undersampled data with a nonlinear function. The second method determines the resonant frequency of a quartz crystal by Fourier transformation of the acquired data. The dissipation factor is obtained by rectifying the undersampled data and then fitting them with an exponential function.
Classical and quantum dissipation of bright solitons in a bosonic superfluid
NASA Astrophysics Data System (ADS)
Efimkin, Dmitry K.; Hofmann, Johannes B.; Galitski, Victor
We consider the quantum dissipation of a bright soliton in a quasi-one-dimensional bosonic superfluid. The dissipation appears due to interaction of the soliton with Bogoliubov excitations, which act as a bath for the soliton. Using a collective coordinate approach and the Keldysh formalism, we derive a Langevin equation for the soliton motion which contains both a friction and a stochastic force. We argue that due to the integrability of the original problem, Ohmic friction is absent, rendering the dynamics non-Markovian. We furthermore show that the resulting friction can be interpreted as the backreaction of Bogoliubov quasiparticles emitted by an accelerating soliton, which represents an analogue of the Abraham-Lorentz force known in electrodynamic.
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
Smetanin, Igor V.
2012-07-11
The process of stimulated Raman backscattering of laser pulse in underdense plasma is considered self-consistently in 1D model. Solutions to this problem in the form of backward-propagating bright solitons (the Stokes scattered pulse and the plasma density wave) coupled with the dark soliton in the pump laser pulse are found. These solitary solutions exist both in the non-dissipative (non-collisional plasma) case and in the dissipative (collisional plasma) case.
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.
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.
Theory of multifrequency atomic force microscopy.
Lozano, Jose R; Garcia, Ricardo
2008-02-22
We develop a theory that explains the origin of the high force sensitivity observed in multifrequency force microscopy experiments. The ability of the microscope to extract complementary information on the surface properties is increased by the simultaneous excitation of several flexural cantilever modes. The force sensitivity in multifrequency operation is about 0.2 pN. The analytical model identifies the virial and the energy dissipated by the tip-surface forces as the parameters responsible for the material contrast. The agreement obtained among the theory, experiments and numerical simulations validates the model.
Payam, Amir F; Ramos, Jorge R; Garcia, Ricardo
2012-06-26
We demonstrate that the phase contrast observed with an amplitude modulation atomic force microscope depends on two factors, the generation of higher harmonics components and the energy dissipated on the sample surface. Those factors are ultimately related to the chemical composition and structure of the surface. Our findings are general, but they specifically describe the results obtained while imaging soft materials in liquid. Molecular resolution experiments performed on a protein membrane surface in liquid confirm the theory. PMID:22578176
Payam, Amir F; Ramos, Jorge R; Garcia, Ricardo
2012-06-26
We demonstrate that the phase contrast observed with an amplitude modulation atomic force microscope depends on two factors, the generation of higher harmonics components and the energy dissipated on the sample surface. Those factors are ultimately related to the chemical composition and structure of the surface. Our findings are general, but they specifically describe the results obtained while imaging soft materials in liquid. Molecular resolution experiments performed on a protein membrane surface in liquid confirm the theory.
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.
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
NASA Astrophysics Data System (ADS)
Sadiek, Gehad; Almalki, Samaher
2016-07-01
We consider a finite one-dimensional Heisenberg XYZ spin chain under the influence of a dissipative Lindblad environment obeying the Born-Markovian constraint in presence of an external magnetic field with closed and open boundary conditions. We present an exact numerical solution for the Lindblad master equation of the system in the Liouville space. The dynamics and asymptotic behavior of the nearest-neighbor and beyond-nearest-neighbor pairwise entanglements in the system are investigated under the effect of spatial anisotropy, temperature, system size, and different initial states. The entanglements in the free spin system exhibit nonuniform oscillatory behavior that varies significantly depending on the system size, anisotropy, and initial state. The x y spatial anisotropy dictates the asymptotic behavior of the different entanglements in the system under the influence of the environment regardless of the initial state. Higher anisotropy yields higher steady-state value of the nearest-neighbor entanglement whereas a complete isotropy wipes it out. The longer range entanglements respond differently to the anisotropy variation. The anisotropy in the z direction may enhance the entanglements depending on the interplay with the magnetic field applied in the same direction. As the temperature is raised, the steady state of the short-range entanglements is found to be robust within very small nonzero temperature range that depends critically on the spatial anisotropy. Moreover, the end to end entanglement transfer time and speed through the open boundary chain vary considerably based on the degree of anisotropy and temperature of the environment.
Diamond nanoelectromechanical resonators: Dissipation and superconductivity
NASA Astrophysics Data System (ADS)
Imboden, Matthias
Nanoelectromechanical systems (NEMS) have become a viable commercial technology and are becoming more and more prevalent in research applications. Through miniaturization, the mechanical response to external sources becomes ever more sensitive. This transduction, coupled to an electrical readout circuit, results in unprecedented sensitivity. This thesis examines dissipation in diamond NEMS resonators in the MHz to GHz range. NCD (Nano-crystalline diamond) has extraordinary properties that make it an intriguing material to study. To begin with, the mechanical hardness allows for a boost in resonance frequency, but beyond that, boron-doped diamond also shows extraordinary electrical behavior. Although scaling benefits speed and sensitivity, dissipation increases dramatically with miniaturization, negating some of the gains in sensitivity. The dissipative mechanisms at play in the MHz range are identified at high temperatures. It is found that extrinsic dissipation mechanisms, mainly circuit and clamping losses, can limit the quality factor (inverse of the dissipation). Furthermore, due to the high surface-to-volume ratio of NEMS, surface defects become significant at the nano-scale. For the first time, quantum dissipation due to assisted phonon tunneling of two level systems is observed in diamond NEMS resonators at millikelvin temperatures. Through scaling, it is shown that the low temperature behavior is universal for a broad range of MHz resonators, including silicon and gallium arsenide, as well as graphene and carbon-nanotubes. Beyond the mechanical response, the superconducting properties of highly boron-doped diamond (BDD) are studied. It is found that the critical temperature of 3.3 K for the thin-film is maintained at the nano-scale. The high critical field, on the order of 3 T for thin-films, is strongly suppressed, already at the micro-scale. The zero resistance state is compromised with fields as low as 0.1 T for submicron wide constrictions. It is known
Superradiant instabilities of asymptotically anti-de Sitter black holes
NASA Astrophysics Data System (ADS)
Green, Stephen R.; Hollands, Stefan; Ishibashi, Akihiro; Wald, Robert M.
2016-06-01
We study the linear stability of asymptotically anti-de Sitter black holes in general relativity in spacetime dimension d≥slant 4. Our approach is an adaptation of the general framework of Hollands and Wald, which gives a stability criterion in terms of the sign of the canonical energy, { E }. The general framework was originally formulated for static or stationary and axisymmetric black holes in the asymptotically flat case, and the stability analysis for that case applies only to axisymmetric perturbations. However, in the asymptotically anti-de Sitter case, the stability analysis requires only that the black hole have a single Killing field normal to the horizon and there are no restrictions on the perturbations (apart from smoothness and appropriate behavior at infinity). For an asymptotically anti-de Sitter black hole, we define an ergoregion to be a region where the horizon Killing field is spacelike; such a region, if present, would normally occur near infinity. We show that for black holes with ergoregions, initial data can be constructed such that { E }\\lt 0, so all such black holes are unstable. To obtain such initial data, we first construct an approximate solution to the constraint equations using the WKB method, and then we use the Corvino-Schoen technique to obtain an exact solution. We also discuss the case of charged asymptotically anti-de Sitter black holes with generalized ergoregions.
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
Superradiant instabilities of asymptotically anti-de Sitter black holes
NASA Astrophysics Data System (ADS)
Green, Stephen R.; Hollands, Stefan; Ishibashi, Akihiro; Wald, Robert M.
2016-06-01
We study the linear stability of asymptotically anti-de Sitter black holes in general relativity in spacetime dimension d≥slant 4. Our approach is an adaptation of the general framework of Hollands and Wald, which gives a stability criterion in terms of the sign of the canonical energy, { E }. The general framework was originally formulated for static or stationary and axisymmetric black holes in the asymptotically flat case, and the stability analysis for that case applies only to axisymmetric perturbations. However, in the asymptotically anti-de Sitter case, the stability analysis requires only that the black hole have a single Killing field normal to the horizon and there are no restrictions on the perturbations (apart from smoothness and appropriate behavior at infinity). For an asymptotically anti-de Sitter black hole, we define an ergoregion to be a region where the horizon Killing field is spacelike; such a region, if present, would normally occur near infinity. We show that for black holes with ergoregions, initial data can be constructed such that { E }\\lt 0, so all such black holes are unstable. To obtain such initial data, we first construct an approximate solution to the constraint equations using the WKB method, and then we use the Corvino–Schoen technique to obtain an exact solution. We also discuss the case of charged asymptotically anti-de Sitter black holes with generalized ergoregions.
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
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.
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.
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.
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.
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.
Dissipative self-assembly of vesicular nanoreactors.
Maiti, Subhabrata; Fortunati, Ilaria; Ferrante, Camilla; Scrimin, Paolo; Prins, Leonard J
2016-07-01
Dissipative self-assembly is exploited by nature to control important biological functions, such as cell division, motility and signal transduction. The ability to construct synthetic supramolecular assemblies that require the continuous consumption of energy to remain in the functional state is an essential premise for the design of synthetic systems with lifelike properties. Here, we show a new strategy for the dissipative self-assembly of functional supramolecular structures with high structural complexity. It relies on the transient stabilization of vesicles through noncovalent interactions between the surfactants and adenosine triphosphate (ATP), which acts as the chemical fuel. It is shown that the lifetime of the vesicles can be regulated by controlling the hydrolysis rate of ATP. The vesicles sustain a chemical reaction but only as long as chemical fuel is present to keep the system in the out-of-equilibrium state. The lifetime of the vesicles determines the amount of reaction product produced by the system.
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
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. PMID:26636851
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.
Bloch oscillations in optical dissipative lattices.
Efremidis, Nikolaos K; Christodoulides, Demetrios N
2004-11-01
We show that Bloch oscillations are possible in dissipative optical waveguide lattices with a linearly varying propagation constant. These oscillations occur in spite of the fact that the Bloch wave packet experiences coupling gain and (or) loss. Experimentally, this process can be observed in different settings, such as in laser arrays and lattices of semiconductor optical amplifiers. In addition, we demonstrate that these systems can suppress instabilities arising from preferential mode noise growth.
Optical realization of the dissipative quantum oscillator.
Longhi, Stefano; Eaton, Shane M
2016-04-15
An optical realization of the damped quantum oscillator, based on transverse light dynamics in an optical resonator with slowly-moving mirrors, is theoretically suggested. The optical resonator setting provides a simple implementation of the time-dependent Caldirola-Kanai Hamiltonian of the dissipative quantum oscillator and enables the visualization of the effects of damped oscillations in the classical (ray optics) limit and wave packet collapse in the quantum (wave optics) regime.
On the Jarzynski relation for dissipative quantumdynamics
Crooks, Gavin E
2008-10-30
In this note, we will discuss how to compactly express the Jarzynski identity for an open quantum system with dissipative dynamics. In quantum dynamics we must avoid explicitly measuring the work directly, which is tantamount to continuously monitoring the state of the system, and instead measure the heat ?ow from the environment. These measurements can be concisely represented with Hermitian map superoperators, which provide a convenient and compact representations of correlation functions and sequential measurements of quantum systems.
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.
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
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.
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.
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.
Viscous Energy Dissipation in Frozen Cryogens
NASA Astrophysics Data System (ADS)
Meitner, S. J.; Pfotenhauer, J. M.; Andraschko, M. R.
2008-03-01
ITER is an international research and development project with the goal of demonstrating the feasibility of fusion power. The fuel for the ITER plasma is injected in the form of frozen deuterium pellets; the current injector design includes a batch extruder, cooled by liquid helium. A more advanced fuel system will produce deuterium pellets continuously using a twin-screw extruder, cooled by a cryocooler. One of the critical design parameters for the advanced system is the friction associated with the shearing planes of the frozen deuterium in the extruder; the friction determines the required screw torque as well as the cryocooler heat load. An experiment has been designed to measure the energy dissipation associated with shearing frozen deuterium. Deuterium gas is cooled to its freezing point in the gap between a stationary outer canister and a rotating inner cylinder. The dissipation is measured mechanically and through calorimetric means. The experiment has also been used to measure dissipation in other cryogens, such as neon, as a function of rotational velocity and temperature. This paper describes the design and construction of the experiment and presents measurements over a range of cryogens and test conditions.
Energy localization in weakly dissipative resonant chains
NASA Astrophysics Data System (ADS)
Kovaleva, Agnessa
2016-08-01
Localization of energy in oscillator arrays has been of interest for a number of years, with special attention paid to the role of nonlinearity and discreteness in the formation of localized structures. This work examines a different type of energy localization arising due to the presence of dissipation in nonlinear resonance arrays. As a basic model, we consider a Klein-Gordon chain of finite length subjected to a harmonic excitation applied at an edge of the chain. It is shown that weak dissipation may be a key factor preventing the emergence of resonance in the entire chain, even if its nondissipative analog is entirely captured into resonance. The resulting process in the dissipative oscillator array represents large-amplitude resonant oscillations in a part of the chain adjacent to the actuator and small-amplitude oscillations in the distant part of the chain. The conditions of the emergence of resonance as well as the conditions of energy localization are derived. An agreement between the obtained analytical results and numerical simulations is demonstrated.
Dissipation mechanism in 3D magnetic reconnection
Fujimoto, Keizo
2011-11-15
Dissipation processes responsible for fast magnetic reconnection in collisionless plasmas are investigated using 3D electromagnetic particle-in-cell simulations. The present study revisits the two simulation runs performed in the previous study (Fujimoto, Phys. Plasmas 16, 042103 (2009)); one with small system size in the current density direction, and the other with larger system size. In the case with small system size, the reconnection processes are almost the same as those in 2D reconnection, while in the other case a kink mode evolves along the current density and deforms the current sheet structure drastically. Although fast reconnection is achieved in both the cases, the dissipation mechanism is very different between them. In the case without kink mode, the electrons transit the electron diffusion region without thermalization, so that the magnetic dissipation is supported by the inertia resistivity alone. On the other hand, in the kinked current sheet, the electrons are not only accelerated in bulk, but they are also partly scattered and thermalized by the kink mode, which results in the anomalous resistivity in addition to the inertia resistivity. It is demonstrated that in 3D reconnection the thickness of the electron current sheet becomes larger than the local electron inertia length, consistent with the theoretical prediction in Fujimoto and Sydora (Phys. Plasmas 16, 112309 (2009)).
Stochastic Migration in a Dissipating Disk
NASA Astrophysics Data System (ADS)
Mills, Sean; Fabrycky, Daniel C.
2016-10-01
It is yet unclear whether the majority of planets formed in situ in their presently observed locations or if they formed distant from their current locations and migrated through the gas and dust protoplanetary disk extant early in their host star's lifetime. Migration simulations generally produce an abundance of planets near mean motion resonances (MMRs); however, statistical analysis of the observed population of exoplanets shows only a very modest enhancement of planets near MMRs and a large number in a continuum of period ratios. It has previously been suggested that migration through a turbulent, dissipating disk may disrupt the resonances formed via migration and approximately reproduce the period ratios of pairs of planets observed in planets observed by Kepler. Here we expand on this analysis to include more realistic dissipation and turbulence parameterizations and compare the results of our simulations to the architectures of higher multiplicity systems observed by Kepler as well as individual planet pairs. We thus place tighter constraints on the turbulence and dissipation properties of disks during planet formation and migration.
Energy localization in weakly dissipative resonant chains.
Kovaleva, Agnessa
2016-08-01
Localization of energy in oscillator arrays has been of interest for a number of years, with special attention paid to the role of nonlinearity and discreteness in the formation of localized structures. This work examines a different type of energy localization arising due to the presence of dissipation in nonlinear resonance arrays. As a basic model, we consider a Klein-Gordon chain of finite length subjected to a harmonic excitation applied at an edge of the chain. It is shown that weak dissipation may be a key factor preventing the emergence of resonance in the entire chain, even if its nondissipative analog is entirely captured into resonance. The resulting process in the dissipative oscillator array represents large-amplitude resonant oscillations in a part of the chain adjacent to the actuator and small-amplitude oscillations in the distant part of the chain. The conditions of the emergence of resonance as well as the conditions of energy localization are derived. An agreement between the obtained analytical results and numerical simulations is demonstrated. PMID:27627299
Inducing transport in a dissipation-free lattice with super Bloch oscillations.
Haller, Elmar; Hart, Russell; Mark, Manfred J; Danzl, Johann G; Reichsöllner, Lukas; Nägerl, Hanns-Christoph
2010-05-21
Particles in a perfect lattice potential perform Bloch oscillations when subject to a constant force, leading to localization and preventing conductivity. For a weakly interacting Bose-Einstein condensate of Cs atoms, we observe giant center-of-mass oscillations in position space with a displacement across hundreds of lattice sites when we add a periodic modulation to the force near the Bloch frequency. We study the dependence of these "super" Bloch oscillations on lattice depth, modulation amplitude, and modulation frequency and show that they provide a means to induce linear transport in a dissipation-free lattice.
No-go theorem in many-body dissipative particle dynamics.
Warren, Patrick B
2013-04-01
Many body dissipative particle dynamics (MDPD) is a particle-based simulation method in which the interaction potential is a sum of self energies depending on locally sampled density variables. This functional form gives rise to density-dependent pairwise forces; however, not all such force laws are derivable from a potential, and the integrability condition for this to be the case provides a strong constraint. A strategy to assess the implications of this constraint is illustrated here by the derivation of a useful no-go theorem for multicomponent MDPD.
Inducing transport in a dissipation-free lattice with super Bloch oscillations.
Haller, Elmar; Hart, Russell; Mark, Manfred J; Danzl, Johann G; Reichsöllner, Lukas; Nägerl, Hanns-Christoph
2010-05-21
Particles in a perfect lattice potential perform Bloch oscillations when subject to a constant force, leading to localization and preventing conductivity. For a weakly interacting Bose-Einstein condensate of Cs atoms, we observe giant center-of-mass oscillations in position space with a displacement across hundreds of lattice sites when we add a periodic modulation to the force near the Bloch frequency. We study the dependence of these "super" Bloch oscillations on lattice depth, modulation amplitude, and modulation frequency and show that they provide a means to induce linear transport in a dissipation-free lattice. PMID:20867014
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.
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.
Hybrid molecular-continuum simulations using smoothed dissipative particle dynamics
NASA Astrophysics Data System (ADS)
Petsev, Nikolai D.; Leal, L. Gary; Shell, M. Scott
2015-01-01
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.
Fluctuation-Dissipation Relation for Systems with Spatially Varying Friction
NASA Astrophysics Data System (ADS)
Farago, Oded; Grønbech-Jensen, Niels
2014-09-01
When a particle diffuses in a medium with spatially dependent friction coefficient at constant temperature , it drifts toward the low friction end of the system even in the absence of any real physical force . This phenomenon, which has been previously studied in the context of non-inertial Brownian dynamics, is termed "spurious drift", although the drift is real and stems from an inertial effect taking place at the short temporal scales. Here, we study the diffusion of particles in inhomogeneous media within the framework of the inertial Langevin equation. We demonstrate that the quantity which characterizes the dynamics with non-uniform is not the displacement of the particle (where is the initial position), but rather , where is the primitive function of . We derive expressions relating the mean and variance of to , , and the duration of the dynamics . For a constant friction coefficient , these expressions reduce to the well known forms of the force-drift and fluctuation-dissipation relations. We introduce a very accurate method for Langevin dynamics simulations in systems with spatially varying , and use the method to validate the newly derived expressions.
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.
Detailed ultraviolet asymptotics for AdS scalar field perturbations
NASA Astrophysics Data System (ADS)
Evnin, Oleg; Jai-akson, Puttarak
2016-04-01
We present a range of methods suitable for accurate evaluation of the leading asymptotics for integrals of products of Jacobi polynomials in limits when the degrees of some or all polynomials inside the integral become large. The structures in question have recently emerged in the context of effective descriptions of small amplitude perturbations in anti-de Sitter (AdS) spacetime. The limit of high degree polynomials corresponds in this situation to effective interactions involving extreme short-wavelength modes, whose dynamics is crucial for the turbulent instabilities that determine the ultimate fate of small AdS perturbations. We explicitly apply the relevant asymptotic techniques to the case of a self-interacting probe scalar field in AdS and extract a detailed form of the leading large degree behavior, including closed form analytic expressions for the numerical coefficients appearing in the asymptotics.
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.
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.
Asymptotic analysis of plane turbulent Couette-Poiseuille flows
NASA Astrophysics Data System (ADS)
Lund, K. O.; Bush, W. B.
1980-01-01
Matched asymptotic expansions are used to describe turbulent Couette-Poiseuille flow (plane duct flow with a pressure gradient and a moving wall). A special modification of conventional eddy-diffusivity closure accounts for the experimentally observed non-coincidence of the locations of zero shear stress and maximum velocity. An asymptotic solution is presented which is valid as the Reynolds number tends to infinity for the whole family of Couette-Poiseuille flows (adverse, favorable, and zero pressure gradients in combination with a moving wall). It is shown that plane Poiseuille flow is a limiting case of Couette-Poiseuille flow. The solution agrees with experimental data for plane Couette flow, for the limiting plane Poiseuille flow, and for a special case having zero net flow and an adverse pressure gradient. The asymptotic analysis shows that conventional eddy diffusivity closures are inadequate for general Couette-Poiseuille flows.
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.
Stability of Non-Isolated Asymptotic Profiles for Fast Diffusion
NASA Astrophysics Data System (ADS)
Akagi, Goro
2016-07-01
The stability of asymptotic profiles of solutions to the Cauchy-Dirichlet problem for fast diffusion equation (FDE, for short) is discussed. The main result of the present paper is the stability of any asymptotic profiles of least energy. It is noteworthy that this result can cover non-isolated profiles, e.g., those for thin annular domain cases. The method of proof is based on the Łojasiewicz-Simon inequality, which is usually used to prove the convergence of solutions to prescribed limits, as well as a uniform extinction estimate for solutions to FDE. Besides, local minimizers of an energy functional associated with this issue are characterized. Furthermore, the instability of positive radial asymptotic profiles in thin annular domains is also proved by applying the Łojasiewicz-Simon inequality in a different way.
NASA Astrophysics Data System (ADS)
Su, Hongling; Li, Shengtai
2016-04-01
In this paper, 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. 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. PMID:25948099
Role of shape dependence of dissipation on nuclear fission
Sadhukhan, Jhilam; Pal, Santanu
2010-03-15
We examine the validity of extending Kramers' expression for fission width to systems with shape-dependent dissipations. For a system with a shape-dependent dissipation, Kramers' width obtained with the presaddle dissipation strength is found to be different from the stationary width obtained from the corresponding Langevin equations. It is demonstrated that the probability of a hot compound nucleus undergoing fission depends on both the presaddle and the postsaddle dynamics of collective nuclear motion. The predictions for prescission neutron multiplicity and evaporation residue cross section from statistical model calculations are also found to be different from those obtained from Langevin dynamical calculations when a shape-dependent dissipation is considered. For systems with shape-dependent dissipations, we conclude that the strength of 'presaddle dissipation' determined by fitting experimental data in statistical model calculations does not represent the true strength of presaddle dissipation.
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.
NASA Astrophysics Data System (ADS)
Latifi, A.
2016-07-01
A special case of coupled integrable nonlinear equations with a singular dispersion law is derived in the context of the small amplitude limit of general wave equations in a fluid-type warm electrons/cold ions plasma irradiated by a continuous laser beam. This model accounts for a nonlinear mode coupling of the electrostatic wave with the ion sound wave and is shown to be highly unstable. Its instability is understood as a continuous secular transfer of energy from the electrostatic wave to the ion sound wave through the ponderomotive force. The exact asymptotic solution of the system is constructed and shows that the dynamics of the energy transfer results in a singular asymptotic behavior of the ion sound wave, which explains the low penetration of the incident laser beam.
NASA Astrophysics Data System (ADS)
Latifi, A.
2016-07-01
A special case of coupled integrable nonlinear equations with a singular dispersion law is derived in the context of the small amplitude limit of general wave equations in a fluid-type warm electrons/cold ions plasma irradiated by a continuous laser beam. This model accounts for a nonlinear mode coupling of the electrostatic wave with the ion sound wave and is shown to be highly unstable. Its instability is understood as a continuous secular transfer of energy from the electrostatic wave to the ion sound wave through the ponderomotive force. The exact asymptotic solution of the system is constructed and shows that the dynamics of the energy transfer results in a singular asymptotic behavior of the ion sound wave, which explains the low penetration of the incident laser beam.
Machleidt, R.
2013-06-10
These lectures present an introduction into the theory of nuclear forces. We focus mainly on the modern approach, in which the forces between nucleons emerge from low-energy QCD via chiral effective field theory.
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.
NASA Astrophysics Data System (ADS)
Kaihatu, J. M.; Goertz, J.; Sheremet, A.; Weiss, R.
2014-12-01
It has been observed that the front face of landfalling tsunamis often feature dispersive "fission" waves. These are short, almost monochromatic coherent waves which result from the piling up of water as the tsunami rapidly decelerates upon encountering land. Photographs taken during the 2004 Indian Ocean tsunami show these waves to resemble cnoidal waves in shape and have a spatial and temporal scale of the same order as swell waves. As part of our goal to study the tsunami in concert with other aspects of the physical environment, we investigate possible physical linkages between the background random swell, monochromatic fission waves, and the long-scale tsunami waves. This particular investigation involves the modification of the dissipation characteristics of random surface waves when interacting with a coherent wavefield (e.g., laboratory proxies for the fission wave or the tsunami). Data from laboratory experiments conducted at the Large Wave Flume at Oregon State University (part of the Network for Earthquake Engineering Simulation supported by the National Science Foundation) were analyzed and the dissipation characteristics inferred using a steepness-regulated instantaneous dissipation mechanism. It is shown that, for random waves, the instances of significant dissipation events temporally correspond to the appearance of high frequency energy in the time-frequency spectrogram. Furthermore, these observations are strongly affected by the presence of an underlying coherent wave signal, particularly in the case of interaction with a tsunami. We further discuss the possible effect of these interactions on the forces in the hydrodynamic field responsible for sediment transport.
Asymptotic analysis of rf-heated collisional plasma
Fisch, N.J.; Karney, C.F.F.
1985-03-01
It is shown that a distribution of electrons in resonance with traveling waves, but colliding with background distributions of electrons and ions, evolves to a steady state. Details of the steady state are given analytically in the asymptotic limit of high electron energy and are compared with numerical solutions. The asymptotic analytic solution may be useful for quickly relating emission data to likely excitations and is more reliable than conventional numerical solutions at high energy. A method of improving numerics at high energy is suggested.
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.
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.
An asymptotic analysis of supersonic reacting mixing layers
NASA Technical Reports Server (NTRS)
Jackson, T. L.; Hussaini, M. Y.
1987-01-01
The purpose of this paper is to present an asymptotic analysis of the laminar mixing of the simultaneous chemical reaction between parallel supersonic streams of two reacting species. The study is based on a one-step irreversible Arrhenius reaction and on large activation energy asymptotics. Essentially it extends the work of Linan and Crespo to include the effect of free shear and Mach number on the ignition regime, the deflagration regime and the diffusion flame regime. It is found that the effective parameter is the product of the characteristic Mach number and a shear parameter.
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.
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.
Large Time Asymptotics for the Kadomtsev-Petviashvili Equation
NASA Astrophysics Data System (ADS)
Hayashi, Nakao; Naumkin, Pavel I.
2014-08-01
We study the large time asymptotic behavior of solutions to the Kadomtsev-Petviashvili equations ut + u_{xxx} + σ partialx^{-1}u_{yy} = -partialxu2, quad quad (x, y) in {R}2, t in {R},\\ u(0, x, y) = u0( x, y), quad quad qquad qquad (x, y) in {R}2, where σ = ±1 and {partialx^{-1} = int_{-infty}xdx^' } . We prove that the large time asymptotics of the derivative u x of the solution has a quasilinear character.
Asymptotic stability of delayed stochastic genetic regulatory networks with impulses
NASA Astrophysics Data System (ADS)
Sakthivel, R.; Raja, R.; Anthoni, S. Marshal
2010-11-01
In this paper, the asymptotic stability analysis problem is considered for a class of delayed stochastic genetic regulatory networks with impulses. Based on the Lyapunov stability technique and stochastic analysis theory, stability criteria are proposed in terms of linear matrix inequalities (LMI). It is shown that the addressed stochastic genetic regulatory networks are globally asymptotically stable if four LMIs are feasible, where the feasibility of LMIs can be readily checked by Matlab LMI toolbox. Finally, a numerical example is given to demonstrate the usefulness of the proposed result.
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.
Asymptotically Optimal Quantum Circuits for d-Level Systems
Bullock, Stephen S.; O'Leary, Dianne P.; Brennen, Gavin K.
2005-06-17
Scalability of a quantum computation requires that the information be processed on multiple subsystems. However, it is unclear how the complexity of a quantum algorithm, quantified by the number of entangling gates, depends on the subsystem size. We examine the quantum circuit complexity for exactly universal computation on many d-level systems (qudits). Both a lower bound and a constructive upper bound on the number of two-qudit gates result, proving a sharp asymptotic of {theta}(d{sup 2n}) gates. This closes the complexity question for all d-level systems (d finite). The optimal asymptotic applies to systems with locality constraints, e.g., nearest neighbor interactions.
NASA Astrophysics Data System (ADS)
Levinson, A.; Globus, N.
2016-05-01
The dynamics of a dissipative Poynting-dominated flow subject to a radiation drag due to Compton scattering of ambient photons by relativistic electrons accelerated in reconnecting current sheets is studied. It is found that the efficiency at which magnetic energy is converted to radiation is limited to a maximum value of ɛc = 3ldis σ0/4(σ0 + 1), where σ0 is the initial magnetization of the flow and ldis ≤ 1 the fraction of initial Poynting flux that can dissipate. The asymptotic Lorentz factor satisfies Γ∞ ≥ Γ0(1 + ldis σ0/4), where Γ0 is the initial Lorentz factor. This limit is approached in cases where the cooling time is shorter than the local dissipation time. A somewhat smaller radiative efficiency is expected if radiative losses are dominated by synchrotron and Synchrotron Self-Compton emissions. It is suggested that under certain conditions magnetic field dissipation may occur in two distinct phases: On small scales, asymmetric magnetic fields that are advected into the polar region and dragged out by the outflow dissipate to a more stable configuration. The dissipated energy is released predominantly as gamma rays. On much larger scales, the outflow encounters a flat density profile medium and re-collimates. This leads to further dissipation and wobbling of the jet head by the kink instability, as found recently in 3D magnetohydrodynamic simulations. Within the framework of a model proposed recently to explain the dichotomy of radio loud active galactic nuclei (AGN), this scenario can account for the unification of gamma-ray blazars with Fanaroff-Riley type I and Fanaroff-Riley type II radio sources.
ERIC Educational Resources Information Center
Occupational Outlook Quarterly, 2012
2012-01-01
The labor force is the number of people ages 16 or older who are either working or looking for work. It does not include active-duty military personnel or the institutionalized population, such as prison inmates. Determining the size of the labor force is a way of determining how big the economy can get. The size of the labor force depends on two…
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.
Wang, Dong-Yang; Bai, Cheng-Hua; Wang, Hong-Fu; Zhu, Ai-Dong; Zhang, Shou
2016-01-01
Quantum squeezing of mechanical resonator is important for studying the macroscopic quantum effects and the precision metrology of weak forces. Here we give a theoretical study of a hybrid atom-optomechanical system in which the steady-state squeezing of the mechanical resonator can be generated via the mechanical nonlinearity and cavity cooling process. The validity of the scheme is assessed by simulating the steady-state variance of the mechanical displacement quadrature numerically. The scheme is robust against dissipation of the optical cavity, and the steady-state squeezing can be effectively generated in a highly dissipative cavity. PMID:27091072
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.
Comparative toxicity based on similar asymptotic endpoints (journal version)
Shirazi, M.A.; Lowrie, L.
1988-01-01
Results of the laboratory tests are used in assessing the environmental risk of exposure to industrial chemicals. The combined effects of dose-level exposure and time-duration exposure are tested in the laboratory, but only a single endpoint reflecting the dose-level exposure at the end of the test period is routinely reported and used. At times, this might be sufficient, or the data otherwise inappropriate for calculation of more than a single endpoint. Nevertheless, an approach that makes a more complete use of existing sufficient test information is needed. One method is presented in this paper, the focus of which is the evaluation of an LC50 endpoint at a calculated exposure time. This calculation determines a condition for the toxicity curve to become established along the time axis. The authors refer to this condition of the dose-response curve as an asymptotic state and the LC50 calculated from it as the asymptotic LC50. An analysis of 152 toxicity tests using fathead minnows show that the 96-hr LC50 is 25% more conservative than the asymptotic LC50. The calculation of LC50 under asymptotic conditions better enables comparing toxicities of different chemicals on the basis of comparable dose-level and time-duration exposures.
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.
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…
Surface family with a common involute asymptotic curve
NASA Astrophysics Data System (ADS)
Bayram, Ergi˙n; Bi˙li˙ci˙, Mustafa
2016-03-01
We construct a surface family possessing an involute of a given curve as an asymptotic curve. We express necessary and sufficient conditions for that curve with the above property. We also present natural results for such ruled surfaces. Finally, we illustrate the method with some examples, e.g. circles and helices as given curves.
Quantum dissipation and neural net dynamics.
Pessa, E; Vitiello, G
1999-05-01
Inspired by the dissipative quantum model of brain, we model the states of neural nets in terms of collective modes by the help of the formalism of Quantum Field Theory. We exhibit an explicit neural net model which allows to memorize a sequence of several informations without reciprocal destructive interference, namely we solve the overprinting problem in such a way last registered information does not destroy the ones previously registered. Moreover, the net is able to recall not only the last registered information in the sequence, but also anyone of those previously registered.
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.
Exceptional points in coupled dissipative dynamical systems.
Ryu, Jung-Wan; Son, Woo-Sik; Hwang, Dong-Uk; Lee, Soo-Young; Kim, Sang Wook
2015-05-01
We study the transient behavior in coupled dissipative dynamical systems based on the linear analysis around the steady state. We find that the transient time is minimized at a specific set of system parameters and show that at this parameter set, two eigenvalues and two eigenvectors of the Jacobian matrix coalesce at the same time; this degenerate point is called the exceptional point. For the case of coupled limit-cycle oscillators, we investigate the transient behavior into the amplitude death state, and clarify that the exceptional point is associated with a critical point of frequency locking, as well as the transition of the envelope oscillation.
Magnetorotational instability in dissipative dusty plasmas
Ren Haijun; Wu Zhengwei; Cao Jintao; Chu, Paul K.
2009-12-15
The magnetorotational instability (MRI) in differential rotating dusty plasmas with dissipative effects is investigated by using local linear analysis. We assume that the dust grains are heavy enough to be immobile so that the dust effects are contained in our model only by introducing an electric field term in the one-fluid equation of plasma motion. The general local dispersion relation is derived and two limiting cases are discussed with respect to the dust-induced effect. The instability criterions in the different limiting cases are presented and the growth rate of local MRI in the last case is demonstrated.
Atom-mirror entanglement via cavity dissipation
NASA Astrophysics Data System (ADS)
Li, Lingchao; Hu, Xiangming; Rao, Shi; Xu, Jun
2015-05-01
We present a cavity dissipation scheme to prepare a hybrid system of an atomic ensemble and a moving mirror in squeezed and entangled states. This scheme is based on four-wave mixing in the atoms and radiation pressure on the mirror, both of which combine to lead to Bogoliubov interactions of the atoms and the mirror with the cavity fields. Under adiabatic conditions, the cavity fields cause the hybrid Bogoliubov modes to evolve into the vacuum states, which correspond to the two-mode squeezed and entangled states. The dependence of the hybrid entanglement on the system parameters is also presented in and beyond the Bogoliubov interactions.
Nonlinear Internal Waves - Evolution and Energy Dissipation
NASA Astrophysics Data System (ADS)
Orr, M.; Mignerey, P.
2003-04-01
Nonlinear internal waves have been observed propagating up the slope of the South China Sea during the recent ONR Asian Seas International Acoustics Experiment. Energy dissipation rates have been extracted. The location of the initiation of the depression to elevation conversion has been identified. Scaling parameters have been extracted and used to initialize a two-layer evolution equation model simulation. Mode1, 2 linear and nonlinear internal waves and instabilities have been observed near the shelf break of the United States of America New Jersey Shelf. Acoustic flow visualization records will be presented. Work supported by the Office of Naval Research (ONR) Ocean Acoustics Program and ONR's NRL base funding.
Caustics, counting maps and semi-classical asymptotics
NASA Astrophysics Data System (ADS)
Ercolani, N. M.
2011-02-01
This paper develops a deeper understanding of the structure and combinatorial significance of the partition function for Hermitian random matrices. The coefficients of the large N expansion of the logarithm of this partition function, also known as the genus expansion (and its derivatives), are generating functions for a variety of graphical enumeration problems. The main results are to prove that these generating functions are, in fact, specific rational functions of a distinguished irrational (algebraic) function, z0(t). This distinguished function is itself the generating function for the Catalan numbers (or generalized Catalan numbers, depending on the choice of weight of the parameter t). It is also a solution of the inviscid Burgers equation for certain initial data. The shock formation, or caustic, of the Burgers characteristic solution is directly related to the poles of the rational forms of the generating functions. As an intriguing application, one gains new insights into the relation between certain derivatives of the genus expansion, in a double-scaling limit, and the asymptotic expansion of the first Painlevé transcendent. This provides a precise expression of the Painlevé asymptotic coefficients directly in terms of the coefficients of the partial fractions expansion of the rational form of the generating functions established in this paper. Moreover, these insights point towards a more general program relating the first Painlevé hierarchy to the higher order structure of the double-scaling limit through the specific rational structure of generating functions in the genus expansion. The paper closes with a discussion of the relation of this work to recent developments in understanding the asymptotics of graphical enumeration. As a by-product, these results also yield new information about the asymptotics of recurrence coefficients for orthogonal polynomials with respect to exponential weights, the calculation of correlation functions for certain
Fast evaluation of asymptotic waveforms from gravitational perturbations
NASA Astrophysics Data System (ADS)
Benedict, Alex G.; Field, Scott E.; Lau, Stephen R.
2013-03-01
In the context of black hole perturbation theory, we describe both exact evaluation of an asymptotic waveform from a time series recorded at a finite radial location and its numerical approximation. From the user’s standpoint our technique is easy to implement, affords high accuracy, and works for both axial (Regge-Wheeler) and polar (Zerilli) sectors. Our focus is on the ease of implementation with publicly available numerical tables, either as part of an existing evolution code or a post-processing step. Nevertheless, we also present a thorough theoretical discussion of asymptotic waveform evaluation and radiation boundary conditions, which need not be understood by a user of our methods. In particular, we identify (both in the time and frequency domains) analytical asymptotic waveform evaluation kernels, and describe their approximation by techniques developed by Alpert, Greengard, and Hagstrom. This paper also presents new results on the evaluation of far-field signals for the ordinary (acoustic) wave equation. We apply our method to study late-time decay tails at null-infinity, ‘teleportation’ of a signal between two finite radial values, and luminosities from extreme-mass-ratio binaries. Through numerical simulations with the outer boundary as close in as r = 30M, we compute asymptotic waveforms with late-time t-4 decay (ℓ = 2 perturbations), and also luminosities from circular and eccentric particle-orbits that respectively match frequency domain results to relative errors of better than 10-12 and 10-9. Furthermore, we find that asymptotic waveforms are especially prone to contamination by spurious junk radiation.
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
Mesoscopic simulation of a thinning liquid bridge using the dissipative particle dynamics method.
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. PMID:26382504
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.
Dynamics and stability of mechanical systems with follower forces
NASA Technical Reports Server (NTRS)
Herrmann, G.
1971-01-01
A monograph on problems of stability of equilibrium of mechanical systems with follower forces is presented. Concepts of stability and criteria of stability are reviewed briefly, together with means of analytical specification of follower forces. Nondissipative systems with two degrees of freedom are discussed, and destabilizing effects due to various types of dissipative forces both in discrete and continuous systems, are treated. The analyses are accompanied by some quantative experiments and observations on demonstrational laboratory models.
Asymptotic analysis of microtubule-based transport by multiple identical molecular motors.
McKinley, Scott A; Athreya, Avanti; Fricks, John; Kramer, Peter R
2012-07-21
We describe a system of stochastic differential equations (SDEs) which model the interaction between processive molecular motors, such as kinesin and dynein, and the biomolecular cargo they tow as part of microtubule-based intracellular transport. We show that the classical experimental environment fits within a parameter regime which is qualitatively distinct from conditions one expects to find in living cells. Through an asymptotic analysis of our system of SDEs, we develop a means for applying in vitro observations of the nonlinear response by motors to forces induced on the attached cargo to make analytical predictions for two parameter regimes that have thus far eluded direct experimental observation: (1) highly viscous in vivo transport and (2) dynamics when multiple identical motors are attached to the cargo and microtubule.
NASA Astrophysics Data System (ADS)
Morozova, Viktoriya; Ahmedov, Bobomurat; Rezzolla, Luciano
2016-07-01
We extend the Wald solution for magnetic field to a black hole that is also moving at constant velocity. In particular, we derive analytic solutions for the Maxwell equations for a rotating black hole moving at constant speed in an asymptotically uniform magnetic test field. By adopting Kerr-Schild coordinates we avoid singular behaviors at the horizon and obtain a complete description of the charge and current distributions in terms of the black-hole spin and velocity. Using this solution, we compute the energy losses expected when charged particles are accelerated along the magnetic field lines, improving previous estimates that had to cope with singular electromagnetic fields on the horizon. When used to approximate the emission from binary black holes in a uniform magnetic field, our estimates match reasonably well those from numericalrelativity calculations in the force-free approximation.