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)
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)
The asymptotic behavior of Buneman instability in dissipative plasma
NASA Astrophysics Data System (ADS)
Rostomyan, Eduard V.
2017-10-01
The problem of time evolution of initial perturbation excited at the development of the Buneman instability (BI) in plasma with dissipation is solved. Developing fields are presented in the form of a wave train with slowly varying amplitude. It is shown that the evolution of the initial pulse in space and time is given by the differential equation of third order. The equation is solved and the expression for the asymptotic pulse shape is obtained. The expression gives the most complete information on the instability: the space-time distribution of the fields, growth rates, velocities of unstable perturbations, the influence of the collisions/dissipation on the instability, its character, (absolute/convective), etc. All these characteristics of the BI are carried out by analyzing the expression for the shape. The obtained results may be applied to any system in which the red-shifted electron stream oscillations resonantly interact with ions. Asymptotic shapes of the BI are presented for various levels of dissipation.
Asymptotic boundary conditions for dissipative waves: General theory
NASA Technical Reports Server (NTRS)
Hagstrom, Thomas
1990-01-01
An outstanding issue in the computational analysis of time dependent problems is the imposition of appropriate radiation boundary conditions at artificial boundaries. Accurate conditions are developed which are based on the asymptotic analysis of wave propagation over long ranges. Employing the method of steepest descents, dominant wave groups are identified and simple approximations to the dispersion relation are considered in order to derive local boundary operators. The existence of a small number of dominant wave groups may be expected for systems with dissipation. Estimates of the error as a function of domain size are derived under general hypotheses, leading to convergence results. Some practical aspects of the numerical construction of the asymptotic boundary operators are also discussed.
Asymptotic boundary conditions for dissipative waves - General theory
NASA Technical Reports Server (NTRS)
Hagstrom, Thomas
1991-01-01
An outstanding issue in 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.
Asymptotic analysis of dissipative waves with applications to their numerical simulation
NASA Technical Reports Server (NTRS)
Hagstrom, Thomas
1990-01-01
Various problems involving the interplay of asymptotics and numerics in the analysis of wave propagation in dissipative systems are studied. A general approach to the asymptotic analysis of linear, dissipative waves is developed. It was applied to the derivation of asymptotic boundary conditions for numerical solutions on unbounded domains. Applications include the Navier-Stokes equations. Multidimensional traveling wave solutions to reaction-diffusion equations are also considered. A preliminary numerical investigation of a thermo-diffusive model of flame propagation in a channel with heat loss at the walls is presented.
NASA Astrophysics Data System (ADS)
Frank, T. D.; Patanarapeelert, K.; Beek, P. J.
2008-05-01
We derive a fundamental relationship between the mean and the variability of isometric force. The relationship arises from an optimal collection of active motor units such that the force variability assumes a minimum (optimal isometric force). The relationship is shown to be independent of the explicit motor unit properties and of the dynamical features of isometric force production. A constant coefficient of variation in the asymptotic regime and a nonequilibrium fluctuation-dissipation theorem for optimal isometric force are predicted.
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.
Energy transfer and dissipation in forced isotropic turbulence
NASA Astrophysics Data System (ADS)
Linkmann, Moritz; McComb, W. David; Berera, Arjun; Yoffe, Samuel
2014-11-01
A model for the Reynolds number dependence of the dimensionless dissipation rate Cɛ is derived from the dimensionless Kármán-Howarth equation, resulting in Cɛ =Cɛ , ∞ + C /RL , where RL is the integral scale Reynolds number. The coefficients C and Cɛ , ∞ arise from asymptotic expansions of the dimensionless second- and third-order structure functions. The model equation is fitted to data from direct numerical simulations (DNS) of forced isotropic turbulence for integral scale Reynolds numbers up to RL = 5875 (Rλ = 435), which results in an asymptote for Cɛ in the infinite Reynolds number limit Cɛ , ∞ = 0 . 47 +/- 0 . 01 . Since the coefficients in the model equation are scale-dependent while the dimensionless dissipation rate is not, we modelled the scale dependences of the coefficients by an ad hoc profile function such that they cancel out, leaving the model equation scale-independent, as it must be. The profile function was compared to DNS data to very good agreement, provided we restrict the comparison to scales small enough to be well resolved in our simulations. This work has made use of the resources provided by the UK supercomputing service HECToR, made available through the Edinburgh Compute and Data Facility (ECDF). A.B. is supported by STFC, S.R.Y. and M.F.L. are funded by EPSRC.
NASA Technical Reports Server (NTRS)
Haslach, Henry W., Jr.; Freed, Alan D.; Walker, Kevin P.
1994-01-01
Nonlinear asymptotic integrators are applied to one-dimensional, nonlinear, autonomous, dissipative, ordinary differential equations. These integrators, including a one-step explicit, a one-step implicit, and a one- and two-step midpoint algorithm, are designed to follow the asymptotic behavior of a system approaching a steady state. The methods require that the differential equation be written in a particular asymptotic form. This is always possible for a one-dimensional equation with a globally asymptotic steady state. In this case, conditions are obtained to guarantee that the implicit algorithms are well defined. Further conditions are determined for the implicit methods to be contractive. These methods are all first order accurate, while under certain conditions the midpoint algorithms may also become second order accurate. The stability of each method is investigated and an estimate of the local error is provided.
NASA Astrophysics Data System (ADS)
Lenarčič, Zala; Prosen, Tomaž
2015-03-01
A boundary-driven quantum master equation for a general inhomogeneous (nonintegrable) anisotropic Heisenberg spin-1 /2 chain, or an equivalent nearest neighbor interacting spinless fermion chain, is considered in the presence of a strong external field f . We present an exact closed form expression for large f asymptotics of the current in the presence of a pure incoherent source and sink dissipation at the boundaries. In application, we demonstrate an arbitrary large current rectification in the presence of the interaction.
Ubiquitous mechanisms of energy dissipation in noncontact atomic force microscopy.
Ghasemi, S Alireza; Goedecker, Stefan; Baratoff, Alexis; Lenosky, Thomas; Meyer, Ernst; Hug, Hans J
2008-06-13
Atomistic simulations considering larger tip structures than hitherto assumed reveal novel dissipation mechanisms in noncontact atomic force microscopy. The potential energy surfaces of realistic silicon tips exhibit many energetically close local minima that correspond to different structures. Most of them easily deform, thus causing dissipation arising from hysteresis in force versus distance characteristics. Furthermore, saddle points which connect local minima can suddenly switch to connect different minima. Configurations driven into metastability by the tip motion can thus suddenly access lower energy structures when thermal activation becomes allowed within the time required to detect the resulting average dissipation.
Dynamo action in dissipative, forced, rotating MHD turbulence
NASA Astrophysics Data System (ADS)
Shebalin, John V.
2016-06-01
Magnetohydrodynamic (MHD) turbulence is an inherent feature of large-scale, energetic astrophysical and geophysical magnetofluids. In general, these are rotating and are energized through buoyancy and shear, while viscosity and resistivity provide a means of dissipation of kinetic and magnetic energy. Studies of unforced, rotating, ideal (i.e., non-dissipative) MHD turbulence have produced interesting results, but it is important to determine how these results are affected by dissipation and forcing. Here, we extend our previous work and examine dissipative, forced, and rotating MHD turbulence. Incompressibility is assumed, and finite Fourier series represent turbulent velocity and magnetic field on a 643 grid. Forcing occurs at an intermediate wave number by a method that keeps total energy relatively constant and allows for injection of kinetic and magnetic helicity. We find that 3-D energy spectra are asymmetric when forcing is present. We also find that dynamo action occurs when forcing has either kinetic or magnetic helicity, with magnetic helicity injection being more important. In forced, dissipative MHD turbulence, the dynamo manifests itself as a large-scale coherent structure that is similar to that seen in the ideal case. These results imply that MHD turbulence, per se, may play a fundamental role in the creation and maintenance of large-scale (i.e., dipolar) stellar and planetary magnetic fields.
Dynamo action in dissipative, forced, rotating MHD turbulence
Shebalin, John V.
2016-06-15
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 64{sup 3} grid. Forcing occurs at an intermediate wave number by a method that keeps total energy relatively constant and allows for injection of kinetic and magnetic helicity. We find that 3-D energy spectra are asymmetric when forcing is present. We also find that dynamo action occurs when forcing has either kinetic or magnetic helicity, with magnetic helicity injection being more important. In forced, dissipative MHD turbulence, the dynamo manifests itself as a large-scale coherent structure that is similar to that seen in the ideal case. These results imply that MHD turbulence, per se, may play a fundamental role in the creation and maintenance of large-scale (i.e., dipolar) stellar and planetary magnetic fields.
Collision of viscoelastic bodies: Rigorous derivation of dissipative force.
Goldobin, Denis S; Susloparov, Eugeniy A; Pimenova, Anastasiya V; Brilliantov, Nikolai V
2015-06-01
We report a new theory of dissipative forces acting between colliding viscoelastic bodies. The impact velocity is assumed not to be large to neglect plastic deformations in the material and propagation of sound waves. We consider the general case of bodies of an arbitrary convex shape and of different materials. We develop a mathematically rigorous perturbation scheme to solve the continuum mechanics equations that deal with both displacement and displacement rate fields and accounts for the dissipation in the bulk of the material. The perturbative solution of these equations allows to go beyond the previously used quasi-static approximation and obtain the dissipative force. The derived force does not suffer from the inconsistencies of the quasi-static approximation, like the violation of the third Newton's law for the case of different materials, and depends on particle deformation and deformation rate.
Asymptotic stability for force reflecting teleoperators with time delay
Anderson, R.J. ); Spong, M.W. )
1992-04-01
A bilateral system consists of a local master manipulator and a remotely located slave manipulator. Velocity commands are sent forward from the master to the slave, and force information is reflected back from the slave to the master. Often, there is a transmission delay when communicating between the two subsystems, which causes instability in the force-reflecting teleoperator. Recently, a solution for this problem was found, based on mimicking the behavior of a lossless transmission line. Although the resulting control law was shown to stabilize an actual single-DOF teleoperator system, and although the control law is intuitively stable because of its passivity properties, stability for the system has not yet been proven. In this article the authors extend these results to a nonlinear n-DOF system and prove its stability. Nonlinear, multidimensional networks are used to characterize the nonlinear equations for the master and slave manipulators, the time-delayed communication systems, the human operator, and the environment. Tellegen's theorem and the Lyapunov theory are then applied to prove that the master and slave subsystems have asymptotically stable velocities. In addition, they show how gain scaling can be used without disturbing the stability of the system.
NASA Astrophysics Data System (ADS)
Butuzov, V. F.
2016-08-01
Asymptotic formulae for the solution of the initial-boundary value problem for a singularly perturbed partially dissipative system of reaction-diffusion type are constructed and justified. The system consists of a parabolic and an ordinary differential equation in the case when the corresponding degenerate equation has a root of multiplicity two. The behaviour of the boundary layer functions and the algorithm for constructing them are significantly distinct from the case of a simple (multiplicity-one) root of the degenerate equation. Bibliography: 8 titles.
Forcing of oceanic mean flows by dissipating internal tides
NASA Astrophysics Data System (ADS)
Grisouard, Nicolas; Buhler, Oliver
2012-11-01
We present a theoretical study of the effective mean force exerted on an oceanic mean flow due to the presence of small-amplitude internal waves that are forced by a barotropic tide flowing over a topography and are also subject to dissipation. Although the details of our computation are quite different, we recover the main action-at-a-distance result familiar from atmospheric wave-mean interaction theory, namely that the effective mean force that is felt by the mean flow is located in regions of wave dissipation, and not necessarily near the topographic wave source. Specifically, using a perturbation series in small wave amplitude, we compute the three-dimensional leading-order wave field using a Green's function approach, derive an explicit expression for the leading-order effective mean force at the next order within the framework of generalized Lagrangian-mean theory, discuss in detail the range of situations in which a strong, secularly growing mean-flow response can be expected, and finally compute the effective mean force numerically in a number of illustrative examples with simple topographies. Financial support under the United States National Science Foundation grants NSF/OCE 1024180 and NSF/DMS 1009213 is gratefully acknowledged.
A stochastic boundary forcing for dissipative particle dynamics
NASA Astrophysics Data System (ADS)
Altenhoff, Adrian M.; Walther, Jens H.; Koumoutsakos, Petros
2007-07-01
The method of dissipative particle dynamics (DPD) is an effective, coarse grained model of the hydrodynamics of complex fluids. DPD simulations of wall-bounded flows are however often associated with spurious fluctuations of the fluid properties near the wall. We present a novel stochastic boundary forcing for DPD simulations of wall-bounded flows, based on the identification of fluctuations in simulations of the corresponding homogeneous system at equilibrium. The present method is shown to enforce accurately the no-slip boundary condition, while minimizing spurious fluctuations of material properties, in a number of benchmark problems.
Dissipation of contractile forces: the missing piece in cell mechanics
Kurzawa, Laetitia; Vianay, Benoit; Senger, Fabrice; Vignaud, Timothée; Blanchoin, Laurent; Théry, Manuel
2017-01-01
Mechanical forces are key regulators of cell and tissue physiology. The basic molecular mechanism of fiber contraction by the sliding of actin filament upon myosin leading to conformational change has been known for decades. The regulation of force generation at the level of the cell, however, is still far from elucidated. Indeed, the magnitude of cell traction forces on the underlying extracellular matrix in culture is almost impossible to predict or experimentally control. The considerable variability in measurements of cell-traction forces indicates that they may not be the optimal readout to properly characterize cell contractile state and that a significant part of the contractile energy is not transferred to cell anchorage but instead is involved in actin network dynamics. Here we discuss the experimental, numerical, and biological parameters that may be responsible for the variability in traction force production. We argue that limiting these sources of variability and investigating the dissipation of mechanical work that occurs with structural rearrangements and the disengagement of force transmission is key for further understanding of cell mechanics. PMID:28684608
Forte, Giuseppe; Cecconi, Fabio; Vulpiani, Angelo
2014-12-01
We study the asymptotic and preasymptotic diffusive properties of Brownian particles in channels whose section varies periodically in space. The effective diffusion coefficient D(eff) is numerically determined by the asymptotic behavior of the root mean square displacement in different geometries, considering even cases of steep variations of the channel boundaries. Moreover, we compared the numerical results to the predictions from the various corrections proposed in the literature to the well known Fick-Jacobs approximation. Building an effective one-dimensional equation for the longitudinal diffusion, we obtain an approximation for the effective diffusion coefficient. Such a result goes beyond a perturbation approach, and it is in good agreement with the actual values obtained by the numerical simulations. We discuss also the preasymptotic diffusion which is observed up to a crossover time whose value, in the presence of strong spatial variation of the channel cross section, can be very large. In addition, we show how the Einstein's relation between the mean drift induced by a small external field and the mean square displacement of the unperturbed system is valid in both asymptotic and preasymptotic regimes.
NASA Astrophysics Data System (ADS)
Forte, Giuseppe; Cecconi, Fabio; Vulpiani, Angelo
2014-12-01
We study the asymptotic and preasymptotic diffusive properties of Brownian particles in channels whose section varies periodically in space. The effective diffusion coefficient Deff is numerically determined by the asymptotic behavior of the root mean square displacement in different geometries, considering even cases of steep variations of the channel boundaries. Moreover, we compared the numerical results to the predictions from the various corrections proposed in the literature to the well known Fick-Jacobs approximation. Building an effective one-dimensional equation for the longitudinal diffusion, we obtain an approximation for the effective diffusion coefficient. Such a result goes beyond a perturbation approach, and it is in good agreement with the actual values obtained by the numerical simulations. We discuss also the preasymptotic diffusion which is observed up to a crossover time whose value, in the presence of strong spatial variation of the channel cross section, can be very large. In addition, we show how the Einstein's relation between the mean drift induced by a small external field and the mean square displacement of the unperturbed system is valid in both asymptotic and preasymptotic regimes.
NASA Astrophysics Data System (ADS)
Sadiek, G.
2017-07-01
We consider a finite one-dimensional Ising spin chain under the influence of a dissipative Lindblad environment obeying the Born-Markovian constrain in presence of an external magnetic field with open boundary conditions. We study the effect of a single impurity, located at the terminal or center of the chain, on the time evolution and asymptotic steady state of the bipartite entanglement in the chain starting from a maximally entangled initial state. We found that the impurity has a significant effect on the bipartite entanglement of its nearest spins and can be used to tune their steady state value but has almost no noticeable impact on the far ones. At finite temperature, the thermal excitations suppress the dynamics of the system and reduce the value of the steady state and may completely wipe it out as the temperature is increased, which eliminates the effect of the impurity in that case.
NASA Astrophysics Data System (ADS)
Zhijian, Yang
The paper studies the global existence, asymptotic behavior and blowup of solutions to the initial boundary value problem for a class of nonlinear wave equations with dissipative term. It proves that under rather mild conditions on nonlinear terms and initial data the above-mentioned problem admits a global weak solution and the solution decays exponentially to zero as t→+∞, respectively, in the states of large initial data and small initial energy. In particular, in the case of space dimension N=1, the weak solution is regularized to be a unique generalized solution. And if the conditions guaranteeing the global existence of weak solutions are not valid, then under the opposite conditions, the solutions of above-mentioned problem blow up in finite time. And an example is given.
NASA Astrophysics Data System (ADS)
Paulo, Álvaro San; García, Ricardo
2001-11-01
Amplitude-modulation (tapping mode) atomic force microscopy is a technique for high resolution imaging of a wide variety of surfaces in air and liquid environments. Here by using the virial theorem and energy conservation principles we have derived analytical relationships between the oscillation amplitude, phase shift, and average tip-surface forces. We find that the average value of the interaction force and oscillation and the average power dissipated by the tip-surface interaction are the quantities that control the amplitude reduction. The agreement obtained between analytical and numerical results supports the analytical method.
Asymptotic approximation method of force reconstruction: Proof of concept
NASA Astrophysics Data System (ADS)
Sanchez, J.; Benaroya, H.
2017-08-01
An important problem in engineering is the determination of the system input based on the system response. This type of problem is difficult to solve as it is often ill-defined, and produces inaccurate or non-unique results. Current reconstruction techniques typically involve the employment of optimization methods or additional constraints to regularize the problem, but these methods are not without their flaws as they may be sub-optimally applied and produce inadequate results. An alternative approach is developed that draws upon concepts from control systems theory, the equilibrium analysis of linear dynamical systems with time-dependent inputs, and asymptotic approximation analysis. This paper presents the theoretical development of the proposed method. A simple application of the method is presented to demonstrate the procedure. A more complex application to a continuous system is performed to demonstrate the applicability of the method.
NASA Astrophysics Data System (ADS)
Filipovic, N.; Haber, S.; Kojic, M.; Tsuda, A.
2008-02-01
Traditional DPD methods address dissipative and random forces exerted along the line connecting neighbouring particles. Espanol (1998 Phys. Rev. E 57 2930-48) suggested adding dissipative and random force components in a direction perpendicular to this line. This paper focuses on the advantages and disadvantages of such an addition as compared with the traditional DPD method. Our benchmark system comprises fluid initially at rest occupying the space between two concentric cylinders rotating with various angular velocities. The effect of the lateral force components on the time evolution of the simulated velocity profile was also compared with that of the known analytical solution. The results show that (i) the solution accuracy at steady state has improved and the error has been reduced by at least 30% (in one case by 75%), (ii) the DPD time to reach steady state has been halved, (iii) the CPU time has increased by only 30%, and (iv) no significant differences exist in density and temperature distributions.
Magnetic energy dissipation in force-free jets
NASA Technical Reports Server (NTRS)
Choudhuri, Arnab Rai; Konigl, Arieh
1986-01-01
It is shown that a magnetic pressure-dominated, supersonic jet which expands or contracts in response to variations in the confining external pressure can dissipate magnetic energy through field-line reconnection as it relaxes to a minimum-energy configuration. In order for a continuous dissipation to occur, the effective reconnection time must be a fraction of the expansion time. The dissipation rate for the axisymmetric minimum-energy field configuration is analytically derived. The results indicate that the field relaxation process could be a viable mechanism for powering the synchrotron emission in extragalactic jets if the reconnection time is substantially shorter than the nominal resistive tearing time in the jet.
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.
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
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.
Metal Dissipation and Inefficient Recycling Intensify Climate Forcing.
Ciacci, Luca; Harper, E M; Nassar, N T; Reck, Barbara K; Graedel, T E
2016-10-07
In the metals industry, recycling is commonly included among the most viable options for climate change mitigation, because using secondary (recycled) instead of primary sources in metal production carries both the potential for significant energy savings and for greenhouse gas emissions reduction. Secondary metal production is, however, limited by the relative quantity of scrap available at end-of-life for two reasons: long product lifespans during use delay the availability of the material for reuse and recycling; and end-of-life recycling rates are low, a result of inefficient collection, separation, and processing. For a few metals, additional losses exist in the form of in-use dissipation. The sum of these lost material flows forms the theoretical maximum potential for future efficiency improvements. Based on a dynamic material flow analysis, we have evaluated these factors from an energy perspective for 50 metals and calculated the corresponding greenhouse gas emissions associated with the supply of lost material from primary sources that would otherwise be used to satisfy demand. A use-by-use examination demonstrates the potential emission gains associated with major application sectors. The results show that minimizing in-use dissipation and constraints to metal recycling have the potential to reduce greenhouse gas emissions from the metal industry by about 13-23%, corresponding to 1% of global anthropogenic greenhouse gas emissions.
Drag forces on inclusions in classical fields with dissipative dynamics.
Démery, V; Dean, D S
2010-08-01
We study the drag force on uniformly moving inclusions which interact linearly with dynamical free field theories commonly used to study soft condensed matter systems. Drag forces are shown to be nonlinear functions of the inclusion velocity and depend strongly on the field dynamics. The general results obtained can be used to explain drag forces in Ising systems and also predict the existence of drag forces on proteins in membranes due to couplings to various physical parameters of the membrane such as composition, phase and height fluctuations.
Dissipative, forced turbulence in two-dimensional magnetohydrodynamics
NASA Technical Reports Server (NTRS)
Fyfe, D.; Montgomery, D.; Joyce, G.
1976-01-01
The equations of motion for turbulent two-dimensional magnetohydrodynamic flows are solved in the presence of finite viscosity and resistivity, for the case in which external forces (mechanical and/or magnetic) act on the fluid. The goal is to verify the existence of a magnetohydrodynamic dynamo effect which is represented mathematically by a substantial back-transfer of mean square vector potential to the longest allowed Fourier wavelengths. External forces consisting of a random part plus a fraction of the value at the previous time step are employed, after the manner of Lilly for the Navier-Stokes case. The regime explored is that for which the mechanical and magnetic Reynolds numbers are in the region of 100 to 1000. The conclusions are that mechanical forcing terms alone cannot lead to dynamo action, but that dynamo action can result from either magnetic forcing terms or from both mechanical and magnetic forcing terms simultaneously.
Computational model for noncontact atomic force microscopy: energy dissipation of cantilever.
Senda, Yasuhiro; Blomqvist, Janne; Nieminen, Risto M
2016-09-21
We propose a computational model for noncontact atomic force microscopy (AFM) in which the atomic force between the cantilever tip and the surface is calculated using a molecular dynamics method, and the macroscopic motion of the cantilever is modeled by an oscillating spring. The movement of atoms in the tip and surface is connected with the oscillating spring using a recently developed coupling method. In this computational model, the oscillation energy is dissipated, as observed in AFM experiments. We attribute this dissipation to the hysteresis and nonconservative properties of the interatomic force that acts between the atoms in the tip and sample surface. The dissipation rate strongly depends on the parameters used in the computational model.
NASA Astrophysics Data System (ADS)
Grannan, Alex; Favier, Benjamin; Bills, Bruce; Lemasquerier, Daphne; Le Bars, Michael; Aurnou, Jonathan
2016-10-01
The turbulent fluid motions generated in the liquid metal cores and oceans of planetary bodies can have profound effects on energy dissipation and magnetic field generation. An important driver of such fluid motions is mechanical forcing from precession, libration, and tidal forcing. On Earth, the dissipation of energy through tidal forcing occurs primarily in the oceans and may be due, in part, to nonlinear tidally forced resonances. However, the role that such nonlinear resonances play are not generally considered for other planetary bodies also possessing oceans and liquid metal cores.Recent laboratory experimental and numerical studies of Grannan et al. 2014 and Favier et al. 2015 have shown that nonlinear fluid resonances generated by sufficiently strong librational forcing can drive turbulent flows in ellipsoidal containers that mimic gravitational deformations. In Grannan et al. 2016, similar results were found for strong tidal forcing. Thus, a generalized scaling law for the turbulent r.m.s. velocity is derived, U~ɛβE-α, where ɛ is the dimensionless amplitude of the tidal or librational forcing, β is the dimensionless tidal deformation of the body, E is the dimensionless Ekman number characterizing the ratio of viscous to Coriolis forces, and α is a varying exponent.Using planetary values for tidal and librational forcing parameters, the turbulent dissipation is estimated for multiple bodies. For the subsurface oceans of Europa and Enceladus, the amount of nonlinear dissipation is comparable to the dissipation generated from linear resonances of the fluid layer and from upper bounding estimates of the tidal dissipation in the solid icy shell. In addition, our estimates of this turbulent dissipation provide bounds for the stratification in these subsurface oceans. Finally we find that dissipation from these nonlinear resonances in the liquid metal cores of the the early and present Earth, Io, and several exoplanets may help drive the dynamos in these
Dissipative, forced turbulence in two-dimensional magnetohydrodynamics
NASA Technical Reports Server (NTRS)
Fyfe, D.; Montgomery, D.; Joyce, G.
1977-01-01
The equations of motion of a turbulent two-dimensional MHD flow are solved in the presence of finite viscosity and resistivity for the case when external mechanical and/or magnetic forces act on the fluid, the goal of the study being to verify the existence of a MHD dynamo effect which is represented by a substantial back-transfer of mean square vector potential to the longest allowed Fourier wavelengths. The regime explored is that for which the mechanical and magnetic Reynolds numbers are in the range 100 to 1000. It is concluded that mechanical forcing terms alone cannot lead to dynamo action, but that dynamo action can result from either magnetic forcing terms or from both mechanical and magnetic forcing terms simultaneously.
NASA Astrophysics Data System (ADS)
Fendt, C.
1997-07-01
Highly collimated jets are observed in various astronomical objects, as active galactic nuclei, galactic high energy sources, and also young stellar objects. There is observational indication that these jets originate in accretion disks, and that magnetic fields play an important role for the jet collimation and plasma acceleration. The rapid disk rotation close to the central object leads to relativistic rotational velocities of the magnetic field lines. The structure of these axisymmetric magnetic flux surfaces follows from the trans-field force-balance described by the Grad-Schlueter-Shafranov equation. In this paper, we investigate the asymptotic field structure of differentially rotating magnetic jets, widening the study by Appl & Camenzind (1993A&A...270...71A, 1993A&A...274..699A). In general, our results show that, with the same current distribution, differentially rotating jets are collimated to smaller jet radii as compared with jets with rigidly rotating field. Differentially rotating jets need a stronger net poloidal current in order to collimate to the same asymptotic radius. Current-free solutions are not possible for differentially rotating disk-jet magnetospheres with cylindrical asymptotics. We present a simple analytical relation between the poloidal current distribution and magnetic field rotation law. A general relation is derived for the current strength for jets with maximum differential rotation and minimum differential rotation. Analytical solutions are also given in the case of a field rotation leading to a degeneration of the light cylinder. By linking the asymptotic solution to a Keplerian accretion disk, 'total expansion rates' for the jets, and also the flux distribution at the foot points of the flux surfaces are derived. Large poloidal currents imply a strong opening of flux surfaces, a stronger gradient of field rotation leads to smaller expansion rates. There is indication that AGN jet expansion rates are less than in the case of
NASA Astrophysics Data System (ADS)
Yasumura, Kevin Youl
In 1986 the atomic force microscope (AFM) was invented by Binnig, Quate, and Gerber. Cantilever based force microscopy has been used in a wide range of fields including the study of biological samples, data storage media, and microelectronics. These AFM-based imaging techniques typically measure forces in the piconewton (10-12 N) range. Recent developments in microcantilever fabrication and optical fiber displacement sensors have allowed for the construction of force microscope systems that are capable of measuring forces in the attonewton (10-18 N) range. Applications such as magnetic resonance force microscopy (MRFM) require the cantilevers used to have subattonewton force resolution in order to eventually detect single nuclear spins. It is believed that improvements in cantilever and experimental design will allow for improved force resolution. A fundamental limit to the detection of small forces is thermomechanical noise. The thermal noise force limit, via the fluctuation dissipation theorem, is directly related to the amount of mechanical energy dissipation in the cantilever-based force sensor. Work has therefore been focused on developing an understanding of which mechanisms are limiting the force resolution of these microcantilever oscillators. Arrays of silicon nitride, single-crystal silicon, and polysilicon cantilevers have been fabricated and studied. By measuring the dependence of Q on cantilever material, geometry, and surface treatments, significant insight into the dissipation mechanisms has been obtained. For submicron thick cantilevers, Q is found to decrease with decreasing cantilever thickness, indicative of surface loss mechanisms. For single-crystal silicon cantilevers, significant increase in room temperature Q is obtained after 700 C heat treatment in either N 2 or forming gas. Thermoelastic dissipation is not a factor for submicron thick cantilevers, but is shown to be significant for silicon nitride cantilevers as thin as 2.3 um. At low
On the importance of shear dissipative forces in coarse-grained dynamics of molecular liquids.
Izvekov, Sergei; Rice, Betsy M
2015-04-28
In this work we demonstrate from first principles that the shear frictions describing dissipative forces in the direction normal to the vector connecting the coarse-grained (CG) particles in dissipative particle dynamics (DPD) could be dominant for certain real molecular liquids at high-resolution coarse-graining. This is in contrast to previous works on bottom-up DPD modeling and indicates that such liquids cannot be simulated accurately using the conventional form of DPD which relies only on frictions in the radial direction. Specifically, we describe the development of fully bottom-up CG models for liquid hexahydro-1,3,5-trinitro-s-triazine (RDX) which are incorporated into the DPD method. Consistent with the microscopic foundation of DPD dynamics, the conservative part of the DPD models is obtained by the multi-scale coarse-graining (MS-CG) approach, which implements the pairwise decomposition of the atomistic potential of mean force (PMF) in CG coordinates. The radial and shear distant-dependent friction coefficients in a parameter-free form are derived systematically from microscopic velocity and force correlation data along system trajectories using a recently proposed approach [J. Chem. Phys., 2014, 140, 104104]. The shear dissipative forces for the reported system appear to be dominant. We discuss the implications of dominant shear dissipation on dynamical and transport properties of CG liquids such as diffusion and viscosity as revealed by simulations of liquid RDX using the new MS-CG/DPD models.
Vasic, Borislav; Matkovic, Aleksandar; Gajic, Rados
2017-09-21
We investigate phase imaging of supported graphene using amplitude modulation atomic force microscopy (AFM), so called, tapping mode. The phase contrast between graphene and neighbouring substrate grows at hard tapping conditions and the contrast is enhanced compared to the topographic one. Therefore, the phase measurements could enable a high contrast imaging of graphene and related two dimensional materials and heterostructures, not achievable with conventional AFM based topographic measurements. Obtained phase maps are then transformed into energy dissipation maps which are important for graphene applications in various mechanical systems. From fundamental point of view, the energy dissipation gives further insights into mechanical properties. Reliable measurements, obtained in the repulsive regime, show that the energy dissipation on graphene covered substrate is lower than on bare one, so graphene provides a certain shielding in tip-substrate interaction. According to obtained phase curves and their derivatives, as well as according to correlation measurements based on AFM nanoindentation and force modulation microscopy, we conclude that the main dissipation channels in graphene-substrate systems are short range hysteresis and long range interfacial forces. © 2017 IOP Publishing Ltd.
Kiracofe, Daniel; Raman, Arvind
2011-12-02
The use of a piezoelectric element (acoustic excitation) to vibrate the base of microcantilevers is a popular method for dynamic atomic force microscopy. In air or vacuum, the base motion is so small (relative to tip motion) that it can be neglected. However, in liquid environments the base motion can be large and cannot be neglected. Yet it cannot be directly observed in most AFMs. Therefore, in liquids, quantitative force and energy dissipation spectroscopy with acoustic AFM relies on theoretical formulae and models to estimate the magnitude of the base motion. However, such formulae can be inaccurate due to several effects. For example, a significant component of the piezo excitation does not mechanically excite the cantilever but rather transmits acoustic waves through the surrounding liquid, which in turn indirectly excites the cantilever. Moreover, resonances of the piezo, chip and holder can obscure the true cantilever dynamics even in well-designed liquid cells. Although some groups have tried to overcome these limitations (either by theory modification or better design of piezos and liquid cells), it is generally accepted that acoustic excitation is unsuitable for quantitative force and dissipation spectroscopy in liquids. In this paper the authors present a careful study of the base motion and excitation forces and propose a method by which quantitative analysis is in fact possible, thus opening this popular method for quantitative force and dissipation spectroscopy using dynamic AFM in liquids. This method is validated by experiments in water on mica using a scanning laser Doppler vibrometer, which can measure the actual base motion. Finally, the method is demonstrated by using small-amplitude dynamic AFM to extract the force gradients and dissipation on solvation shells of octamethylcyclotetrasiloxane (OMCTS) molecules on mica.
Ledezma, G.A.; Campo, A.
1999-04-01
The utilization of internal longitudinal finned tubes has received unparallel attention in the heat transfer literature over the years as a result of its imminent application in high performance compact heat exchangers to enhance the heat transfer between laminar streams of viscous fluids and tube walls. Here, the central goal of this paper is to report a simple approximate way for the prediction of the two asymptotes for the local Nusselt number in laminar forced convection flows inside internal longitudinal finned tubes. The computational attributes of the Method Of Lines (MOL) are propitious for the determination of asymptotic temperature solutions and corresponding heat transfer rates (one for Z {r_arrow} 0 and the other for z {r_arrow} {infinity}). The two local Nusselt number sub-distributions, namely Nu{sub z{r_arrow}0} and Nu{sub z{r_arrow}{infinity}}, blend themselves into an approximate Nusselt number distribution that covers the entire z-domain in a natural way.
Laminar forced convection with viscous dissipation in a concentric annular duct
NASA Astrophysics Data System (ADS)
Avcı, Mete; Aydın, Orhan
2006-03-01
Forced convection heat transfer in fully developed flows of viscous dissipating fluids in concentric annular ducts is analyzed analytically. Special attention has been paid to the effect of the viscous dissipation. Two different cases of the thermal boundary conditions are considered: uniform heat flux at the outer wall and adiabatic inner wall (Case A) and uniform heat flux at the inner wall and adiabatic outer wall (Case B). Solutions for the velocity and temperature distributions and the Nusselt number are obtained for different values of the aspect ratio and the Brinkman number. The present analytical results for the case without the viscous dissipation effect are compared with those available in the literature and an excellent agreement is observed. To cite this article: M. Avcı, O. Aydın, C. R. Mecanique 334 (2006).
Effects of gas interparticle interaction on dissipative wake-mediated forces.
Kliushnychenko, O V; Lukyanets, S P
2017-01-01
We examine how the short-range repulsive interaction in a gas of Brownian particles affects behavior of the nonequilibrium depletion forces between obstacles embedded into the gas flow. It is shown that for an ensemble of small and widely separated obstacles the dissipative wake-mediated interaction belongs to the type of induced dipole-dipole interaction governed by an anisotropic screened Coulomb-like potential. For closely located obstacles, formation of a common density perturbation "coat" around them leads to enhancement of dissipative interaction, manifested by characteristic peaks in its dependence on both the bath fraction and the external driving field. Moreover, additional screening of the gas flow due to nonlinear blockade effect gives rise to generation of a pronounced step-like profile of gas density distribution around the obstacles. This can lead to additional enhancement of dissipative interaction between obstacles. The possibility of the dissipative pairing effect and dissipative interaction switching provoked by wake inversion is briefly discussed. All the results are obtained within the classical lattice-gas model.
Effects of gas interparticle interaction on dissipative wake-mediated forces
NASA Astrophysics Data System (ADS)
Kliushnychenko, O. V.; Lukyanets, S. P.
2017-01-01
We examine how the short-range repulsive interaction in a gas of Brownian particles affects behavior of the nonequilibrium depletion forces between obstacles embedded into the gas flow. It is shown that for an ensemble of small and widely separated obstacles the dissipative wake-mediated interaction belongs to the type of induced dipole-dipole interaction governed by an anisotropic screened Coulomb-like potential. For closely located obstacles, formation of a common density perturbation "coat" around them leads to enhancement of dissipative interaction, manifested by characteristic peaks in its dependence on both the bath fraction and the external driving field. Moreover, additional screening of the gas flow due to nonlinear blockade effect gives rise to generation of a pronounced step-like profile of gas density distribution around the obstacles. This can lead to additional enhancement of dissipative interaction between obstacles. The possibility of the dissipative pairing effect and dissipative interaction switching provoked by wake inversion is briefly discussed. All the results are obtained within the classical lattice-gas model.
Can Dissipative Properties of Single Molecules Be Extracted from a Force Spectroscopy Experiment?
Benedetti, Fabrizio; Gazizova, Yulia; Kulik, Andrzej J; Marszalek, Piotr E; Klinov, Dmitry V; Dietler, Giovanni; Sekatskii, Sergey K
2016-09-20
We performed dynamic force spectroscopy of single dextran and titin I27 molecules using small-amplitude and low-frequency (40-240 Hz) dithering of an atomic force microscope tip excited by a sine wave voltage fed onto the tip-carrying piezo. We show that for such low-frequency dithering experiments, recorded phase information can be unambiguously interpreted within the framework of a transparent theoretical model that starts from a well-known partial differential equation to describe the dithering of an atomic force microscope cantilever and a single molecule attached to its end system, uses an appropriate set of initial and boundary conditions, and does not exploit any implicit suggestions. We conclude that the observed phase (dissipation) signal is due completely to the dissipation related to the dithering of the cantilever itself (i.e., to the change of boundary conditions in the course of stretching). For both cases, only the upper bound of the dissipation of a single molecule has been established as not exceeding 3⋅10(-7)kg/s. We compare our results with previously reported measurements of the viscoelastic properties of single molecules, and we emphasize that extreme caution must be taken in distinguishing between the dissipation related to the stretched molecule and the dissipation that originates from the viscous damping of the dithered cantilever. We also present the results of an amplitude channel data analysis, which reveal that the typical values of the spring constant of a I27 molecule at the moment of module unfolding are equal to 4±1.5mN/m, and the typical values of the spring constant of dextran at the moment of chair-boat transition are equal to 30-50mN/m.
Thermal dissipation force modeling with preliminary results for Pioneer 10/11
NASA Astrophysics Data System (ADS)
Rievers, Benny; Bremer, Stefanie; List, Meike; Lämmerzahl, Claus; Dittus, Hansjörg
2010-02-01
The dissipation of thermal energy can produce disturbance forces on spacecraft surfaces if the energy is not dissipated in a symmetric pattern. This force can be computed as the quotient of the radiated power and the speed of light for a plate surface element. Depending on mission and spacecraft design the resulting surface forces have to be included into the disturbance budget. At ZARM (Center of Applied Space Technology and Microgravity) a raytracing algorithm was developed that allows the computation of the resulting force for complex spacecraft geometries. The method is based on the modeling of the spacecraft geometry in finite elements (FEs). Using an FE-solver the surface temperatures of the satellite can be derived with geometry and material parameters using heat sources/sinks as constraints. The outgoing radiation force is computed including reflectivity and absorption between all elements of the model. As an example for the method a test case model of the radio isotope thermal generators (RTGs) of Pioneer 11 is processed with this force computing method. The results show that detailed thermal modeling for the whole craft is necessary as the simplified test case results in a force that is non-negligible with respect to the pioneer anomaly.
Casimir forces in transmission-line circuits: QED and fluctuation-dissipation formalisms
NASA Astrophysics Data System (ADS)
Shahmoon, Ephraim
2017-06-01
It was recently shown that transmission-line waveguides can mediate long-range fluctuation forces between neutral objects, potentially leading to novel Casimir forces in electric circuits. Here we present two approaches for the general description of these forces between electric components embedded in transmission-line circuits. The first, following ordinary quantum electrodynamics (QED), consists of the quantization and scattering theory of voltage and current waves inside transmission lines. The second approach relies on a simple circuit analysis with additional noisy current sources due to resistors in the circuit, as per the fluctuation-dissipation theorem (FDT). We apply the latter approach to derive a general formula for the Casimir force induced by circuit fluctuations between any two impedances. The application of this formula, considering the sign of the resulting force, is discussed. While both QED and FDT approaches are equivalent, we conclude that the latter is simpler to generalize and solve.
Casimir-Polder force fluctuations as spatial probes of dissipation in metals
NASA Astrophysics Data System (ADS)
Cherroret, Nicolas; Crépin, Pierre-Philippe; Guérout, Romain; Lambrecht, Astrid; Reynaud, Serge
2017-03-01
We study the spatial fluctuations of the Casimir-Polder force experienced by an atom or a small sphere moved above a metallic plate at fixed separation distance. We demonstrate that unlike the mean force, the magnitude of these fluctuations crucially relies on the relaxation of conduction electron in the metallic bulk, and even achieves values that differ by orders of magnitude depending on the amount of dissipation. We also discover that fluctuations suffer a spectacular decrease at large distances in the case of nonzero temperature.
The effect of dissipation on the torque and force experienced by nanoparticles in an AC field
NASA Astrophysics Data System (ADS)
Claro, F.; Fuchs, R.; Robles, P.; Rojas, R.
2015-09-01
We discuss the force and torque acting on spherical particles in an ensemble in the presence of a uniform AC electric field. We show that for a torque causing particle rotation to appear the particle must be absorptive. Our proof includes all electromagnetic excitations, which in the case of two or more particles gives rise to one or more resonances in the spectrum of force and torque depending on interparticle distance. Several peaks are found in the force and torque between two spheres at small interparticle distances, which coalesce to just one as the separation grows beyond three particle radii. We also show that in the presence of dissipation the force on each particle is nonconservative and may not be derived from the classical interaction potential energy as has been done in the past.
NASA Astrophysics Data System (ADS)
Huang, Sumei; Agarwal, G. S.
2017-02-01
We theoretically investigate optical detection of a weak classical force acting on a free particle in a dissipative coupling optomechanical system with a degenerate parametric amplifier (PA). We show that the PA allows one to achieve the force sensitivity far better than the standard quantum limit (SQL) over a broad range of the detection frequencies. The improvement depends on the parametric gain and the driving power. Moreover, we discuss the effects of the mechanical damping and the thermal noise on the force sensitivity. We find that the robustness of the force sensitivity is much better than the SQL against the mechanical damping and the thermal noise is achievable in the presence of the PA with a high parametric gain. For the temperature T =1 K, the improvement in sensitivity is better by a factor of about 7 when the driving power is set at a value corresponding to the SQL with no PA.
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.
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.
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.
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)
Cooper, Fenwick; Haynes, Peter
2013-04-01
The Fluctuation-Dissipation Theorem (FDT) predicts the response of a stochastic dynamical system to a small applied forcing given data on the unforced behaviour of the system. The applicability of the FDT to predicting the zonally averaged response of the tropospheric circulation to an external forcing is investigated, with particular emphasis on quantitative accuracy. The latter requires consideration of the statistical problem of estimating the linear operator, expressing the response in terms of the applied forcing, from the available data. Two different forms of this estimated operator are considered, one (the Gaussian FDT) resulting from a quasi-Gaussian assumption and the other (the linear FDT) resulting from a linear inverse modelling approach. Both forms include a parameter that needs to be chosen on practical grounds. Analysis of the behaviour of a simple two-dimensional stochastic model shows how statistical uncertainty needs to be taken into account in choosing the optimal form for the estimated operator. The same principles are shown to be relevant when applying the FDT to a simple general circulation model. The additional question of how many spatial degrees of freedom it is useful to include in the calculation is also considered. Other aspects of the application of the FDT which are also important to consider include whether or not a linearised approach valid for small forcing is justified and also the calculation of an 'effective forcing' that is required when the FDT is applied to a reduced system in which some of the degrees of freedom of the original system have been discarded. Having taken all these aspects into account, it is concluded that the Gaussian FDT and linear FDT are not useful quantitative estimators of the zonally symmetric circulation response.
Mori-Zwanzig theory for dissipative forces in coarse-grained dynamics in the Markov limit
NASA Astrophysics Data System (ADS)
Izvekov, Sergei
2017-01-01
We derive alternative Markov approximations for the projected (stochastic) force and memory function in the coarse-grained (CG) generalized Langevin equation, which describes the time evolution of the center-of-mass coordinates of clusters of particles in the microscopic ensemble. This is done with the aid of the Mori-Zwanzig projection operator method based on the recently introduced projection operator [S. Izvekov, J. Chem. Phys. 138, 134106 (2013), 10.1063/1.4795091]. The derivation exploits the "generalized additive fluctuating force" representation to which the projected force reduces in the adopted projection operator formalism. For the projected force, we present a first-order time expansion which correctly extends the static fluctuating force ansatz with the terms necessary to maintain the required orthogonality of the projected dynamics in the Markov limit to the space of CG phase variables. The approximant of the memory function correctly accounts for the momentum dependence in the lowest (second) order and indicates that such a dependence may be important in the CG dynamics approaching the Markov limit. In the case of CG dynamics with a weak dependence of the memory effects on the particle momenta, the expression for the memory function presented in this work is applicable to non-Markov systems. The approximations are formulated in a propagator-free form allowing their efficient evaluation from the microscopic data sampled by standard molecular dynamics simulations. A numerical application is presented for a molecular liquid (nitromethane). With our formalism we do not observe the "plateau-value problem" if the friction tensors for dissipative particle dynamics (DPD) are computed using the Green-Kubo relation. Our formalism provides a consistent bottom-up route for hierarchical parametrization of DPD models from atomistic simulations.
Mori-Zwanzig theory for dissipative forces in coarse-grained dynamics in the Markov limit.
Izvekov, Sergei
2017-01-01
We derive alternative Markov approximations for the projected (stochastic) force and memory function in the coarse-grained (CG) generalized Langevin equation, which describes the time evolution of the center-of-mass coordinates of clusters of particles in the microscopic ensemble. This is done with the aid of the Mori-Zwanzig projection operator method based on the recently introduced projection operator [S. Izvekov, J. Chem. Phys. 138, 134106 (2013)10.1063/1.4795091]. The derivation exploits the "generalized additive fluctuating force" representation to which the projected force reduces in the adopted projection operator formalism. For the projected force, we present a first-order time expansion which correctly extends the static fluctuating force ansatz with the terms necessary to maintain the required orthogonality of the projected dynamics in the Markov limit to the space of CG phase variables. The approximant of the memory function correctly accounts for the momentum dependence in the lowest (second) order and indicates that such a dependence may be important in the CG dynamics approaching the Markov limit. In the case of CG dynamics with a weak dependence of the memory effects on the particle momenta, the expression for the memory function presented in this work is applicable to non-Markov systems. The approximations are formulated in a propagator-free form allowing their efficient evaluation from the microscopic data sampled by standard molecular dynamics simulations. A numerical application is presented for a molecular liquid (nitromethane). With our formalism we do not observe the "plateau-value problem" if the friction tensors for dissipative particle dynamics (DPD) are computed using the Green-Kubo relation. Our formalism provides a consistent bottom-up route for hierarchical parametrization of DPD models from atomistic simulations.
Forced cubic Schrödinger equation with Robin boundary data: large-time asymptotics.
Kaikina, Elena I
2013-11-08
We consider the initial-boundary-value problem for the cubic nonlinear Schrödinger equation, formulated on a half-line with inhomogeneous Robin boundary data. We study traditionally important problems of the theory of nonlinear partial differential equations, such as the global-in-time existence of solutions to the initial-boundary-value problem and the asymptotic behaviour of solutions for large time.
Forced cubic Schrödinger equation with Robin boundary data: large-time asymptotics
Kaikina, Elena I.
2013-01-01
We consider the initial-boundary-value problem for the cubic nonlinear Schrödinger equation, formulated on a half-line with inhomogeneous Robin boundary data. We study traditionally important problems of the theory of nonlinear partial differential equations, such as the global-in-time existence of solutions to the initial-boundary-value problem and the asymptotic behaviour of solutions for large time. PMID:24204185
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.
Kisiel, M; Pellegrini, F; Santoro, G E; Samadashvili, M; Pawlak, R; Benassi, A; Gysin, U; Buzio, R; Gerbi, A; Meyer, E; Tosatti, E
2015-07-24
The critical fluctuations at second order structural transitions in a bulk crystal may affect the dissipation of mechanical probes even if completely external to the crystal surface. Here, we show that noncontact force microscope dissipation bears clear evidence of the antiferrodistortive phase transition of SrTiO_{3}, known for a long time to exhibit a unique, extremely narrow neutron scattering "central peak." The noncontact geometry suggests a central peak linear response coupling connected with strain. The detailed temperature dependence reveals for the first time the intrinsic central peak width of order 80 kHz, 2 orders of magnitude below the established neutron upper bound.
NASA Astrophysics Data System (ADS)
Cyranka, Jacek; Zgliczyński, Piotr
2016-10-01
We describe a topological method to study the dynamics of dissipative PDEs on a torus with rapidly oscillating forcing terms. We show that a dissipative PDE, which is invariant with respect to the Galilean transformations, with a large average initial velocity can be reduced to a problem with rapidly oscillating forcing terms. We apply the technique to the viscous Burgers' equation, and the incompressible 2D Navier-Stokes equations with a time-dependent forcing. We prove that for a large initial average speed the equation admits a bounded eternal solution, which attracts all other solutions forward in time. For the incompressible 3D Navier-Stokes equations we establish the existence of a locally attracting solution.
NASA Astrophysics Data System (ADS)
Brancati, Renato; Strano, Salvatore; Timpone, Francesco
2011-10-01
When in use, a tire dissipates energy according to various mechanisms: rolling resistance, viscosity, hysteresis, friction energy, etc. This dissipation of energy contributes to influencing tire temperature, contact conditions and the resulting friction coefficient. This research project deals with viscoelastic and hysteretic mechanisms, and presents an explicit expression of the energy dissipated by tire-road interactions caused by these mechanisms. It is based on the Dahl model with regard to the hysteretic force together with a spring and a frequency variable damping coefficient with regard to the viscoelastic one. The energy expression found in this way can be used in tire thermal models to determine one of the heat flows needed to estimate the contact temperature and to find out the actual friction coefficient to be used in real time tire-road interaction models. Experimental tests were carried out, for longitudinal interaction only, in order to evaluate the effectiveness of the proposed expression by identifying the parameters and validating the results.
Two-photon exchange force in scalar quantum electrodynamics: The asymptotic story
NASA Astrophysics Data System (ADS)
Sucher, J.
1994-04-01
The dependence of the potential V2γ arising from two-photon exchange between charged spinless systems on the one-photon exchange potential V1γ is examined. It is found that, unlike the case when at least one of the two systems is neutral, the form of V1γ can play a key role in determining the large-r behavior of V2γ. It is shown that if V1γ is defined in a way inspired by the use of the Coulomb gauge rather than the Feynman gauge, V2γ falls off as r-3, rather than as r-2. This result, which removes an apparent cognitive dissonance with the related work of Spruch, does not mean that the effective potential is inherently gauge dependent. Instead it highlights the fact that in this case the concept of the asymptotic behavior of V2γ is not as sharp as one might have thought. The relation of this result to an analogous one expected to hold for spinor QED and to the nonrelativistic form of the orbit-orbit interaction is also discussed.
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.
Diaz, Alfredo J.; Eslami, Babak; López-Guerra, Enrique A.; Solares, Santiago D.
2014-09-14
This paper explores the effect of the amplitude ratio of the higher to the fundamental eigenmode in bimodal atomic force microscopy (AFM) on the phase contrast and the dissipated power contrast of the higher eigenmode. We explore the optimization of the amplitude ratio in order to maximize the type of contrast that is most relevant to the particular study. Specifically, we show that the trends in the contrast range behave differently for different quantities, especially the dissipated power and the phase, with the former being more meaningful than the latter (a similar analysis can be carried out using the virial, for which we also provide a brief example). Our work is based on numerical simulations using two different conservative-dissipative tip-sample models, including the standard linear solid and the combination of a dissipation coefficient with a conservative model, as well as experimental images of thin film Nafion{sup ®} proton exchange polymers. We focus on the original bimodal AFM method, where the higher eigenmode is driven with constant amplitude and frequency (i.e., in “open loop”).
ERIC Educational Resources Information Center
Dobbs, David E.
2010-01-01
This note develops and implements the theory of polynomial asymptotes to (graphs of) rational functions, as a generalization of the classical topics of horizontal asymptotes and oblique/slant asymptotes. Applications are given to hyperbolic asymptotes. Prerequisites include the division algorithm for polynomials with coefficients in the field of…
ERIC Educational Resources Information Center
Dobbs, David E.
2010-01-01
This note develops and implements the theory of polynomial asymptotes to (graphs of) rational functions, as a generalization of the classical topics of horizontal asymptotes and oblique/slant asymptotes. Applications are given to hyperbolic asymptotes. Prerequisites include the division algorithm for polynomials with coefficients in the field of…
NASA Astrophysics Data System (ADS)
Cho, Yeunwoo
2014-11-01
The shedding phenomena of 3-D viscous gravity-capillary solitary waves generated by a moving air-forcing on the surface of deep water are investigated. Near the resonance where the forcing speed is close to 23 cm/s, two kinds of shedding modes are possible; Anti-symmetric and symmetric modes. A relevant theoretical model equation is numerically solved for the identification of shedding of solitary waves, and is analytically studied in terms of their linear stability to transverse perturbations. Furthermore, by tracing trajectories of shed solitary waves, the decay rate of a 3-D solitary wave due to viscous dissipation is estimated. This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (NRF-2014R1A1A1002441).
NASA Astrophysics Data System (ADS)
Yazdani, Alireza; Deng, Mingge; Caswell, Bruce; Karniadakis, George Em
2016-01-01
We demonstrate how the quality of simulations by Dissipative Particle Dynamics (DPD) of flows in complex geometries is greatly enhanced when driven by body forces suitably tailored to the geometry. In practice, the body force fields are most conveniently chosen to be the pressure gradient of the corresponding Navier-Stokes (N-S) flow. In the first of three examples, the driving-force required to yield a stagnation-point flow is derived from the pressure field of the potential flow for a lattice of counter-rotating line vortices. Such a lattice contains periodic squares bounded by streamlines with four vortices within them. Hence, the DPD simulation can be performed with periodic boundary conditions to demonstrate the value of a non-uniform driving-force without the need to model real boundaries. The second example is an irregular geometry consisting of a 2D rectangular cavity on one side of an otherwise uniform channel. The Navier-Stokes pressure field for the same geometry is obtained numerically, and its interpolated gradient is then employed as the driving-force for the DPD simulation. Finally, we present a third example, where the proposed method is applied to a complex 3D geometry of an asymmetric constriction. It is shown that in each case the DPD simulations closely reproduce the Navier-Stokes solutions. Convergence rates are found to be much superior to alternative methods; in addition, the range of convergence with respect to Reynolds number and Mach number is greatly extended.
Wang, Chao; Kittle, Joshua D; Qian, Chen; Roman, Maren; Esker, Alan R
2013-08-12
Chitinases are widely distributed in nature and have wide-ranging pharmaceutical and biotechnological applications. This work highlights a real-time and label-free method to assay Chitinase activity via a quartz crystal microbalance with dissipation monitoring (QCM-D) and atomic force microscopy (AFM). The chitin substrate was prepared by spincoating a trimethylsilyl chitin solution onto a silica substrate, followed by regeneration to amorphous chitin (RChi). The QCM-D and AFM results clearly showed that the hydrolysis rate of RChi films increased as Chitinase (from Streptomyces griseus) concentrations increased, and the optimal temperature and pH for Chitinase activity were around 37 °C and 6-8, respectively. The Chitinase showed greater activity on chitin substrates, having a high degree of acetylation, than on chitosan substrates, having a low degree of acetylation.
NASA Astrophysics Data System (ADS)
Charan, Harish; Ganesh, Rajaraman
2016-10-01
Systems with excess of average potential energy per particle than its kinetic energy develop strong correlations. It is well known that such systems are not amenable to standard procedures of BBGKY hierarchy. This results in failure of both kinetic and fluid models. Phenomenology is the normal way out. If such a strongly correlated system is further subjected to strong drive and/or dissipation, “near first principles” computational methods such as Molecular Dynamics become necessary. Formation of Rayleigh-Bénnard convection cells (RBCC), where a liquid is under the action of external gravity and external temperature gradient, is one such phenomena. We report here, the formation of RBCC in 2-dimensional strongly coupled Yukawa liquids, characterized by coupling strength Γ (ratio of average potential energy to kinetic energy per particle) and screening parameter κ (ratio of average inter particle distance to Debye length). We observe the existence of a critical external temperature difference, beyond which RBCC are seen to emerge. Beyond this critical external temperature difference, the strength of the maximum convective flow velocity is shown to exhibit a new, linear relationship with external temperature difference and with a slope independent of (Γ, κ). The time taken for the transients to settle down (ts ) is found to be 10,000 to 20,000 ωpd -1, where ωpd is dust plasma frequency. At very high values of Γ and/or low values of κ, RBCC are seen to get suppressed.
Casimir friction force and energy dissipation for moving harmonic oscillators. II
NASA Astrophysics Data System (ADS)
Høye, J. S.; Brevik, I.
2011-01-01
This paper is a second in a series devoted to the study of a two-oscillator system in linear relative motion (the first one published as a letter in [J.S. Høye, I. Brevik, Europhys. Lett. 91, 60003 (2010)]). The main idea behind considering this kind of system is to use it as a simple model for Casimir friction. In the present paper we extend our previous theory so as to obtain the change in the oscillator energy to second order in the perturbation, even though we employ first order perturbation theory only. The results agree with, and confirm, our earlier results obtained via different routes. The friction force is finite at finite temperatures, whereas in the case of two oscillators moving with constant relative velocity the force becomes zero at zero temperature, due to slowly varying coupling.
Asymptotic solutions in asymptotic safety
NASA Astrophysics Data System (ADS)
Gonzalez-Martin, Sergio; Morris, Tim R.; Slade, Zoë H.
2017-05-01
We explain how to find the asymptotic form of fixed point solutions in functional truncations, in particular f (R ) approximations. We find that quantum fluctuations do not decouple at large R , typically leading to elaborate asymptotic solutions containing several free parameters. By a counting argument, these can be used to map out the dimension of the fixed point solution spaces. They are also necessary to validate the numerical solution and provide the physical part in the limit that the cutoff is removed: the fixed point equation of state. As an example, we apply the techniques to a recent f (R ) approximation by Demmel et al., finding asymptotic matches to their numerical solution. Depending on the value of the endomorphism parameter, we find many other asymptotic solutions and fixed point solution spaces of differing dimensions, yielding several alternative scenarios for the equation of state. Asymptotic studies of other f (R ) approximations are needed to clarify the picture.
NASA Technical Reports Server (NTRS)
Thompson, P. M.; Stein, G.
1980-01-01
The behavior of the closed loop eigenstructure of a linear system with output feedback is analyzed as a single parameter multiplying the feedback gain is varied. An algorithm is presented that computes the asymptotically infinite eigenstructure, and it is shown how a system with high gain feedback decouples into single input single ouput systems. Then a synthesis algorithm is presented which uses full state feedback to achieve a desired asymptotic eigenstructure.
NASA Technical Reports Server (NTRS)
Thompson, P. M.; Stein, G.
1980-01-01
The behavior of the closed loop eigenstructure of a linear system with output feedback is analyzed as a single parameter multiplying the feedback gain is varied. An algorithm is presented that computes the asymptotically infinite eigenstructure, and it is shown how a system with high gain, feedback decouples into single input, single output systems. Then a synthesis algorithm is presented which uses full state feedback to achieve a desired asymptotic eigenstructure.
Engl, Christoph; Beek, Alex Ter; Bekker, Martijn; de Mattos, Joost Teixeira; Jovanovic, Goran; Buck, Martin
2011-05-01
Phage shock proteins (Psp) and their homologues are found in species from the three domains of life: Bacteria, Archaea and Eukarya (e.g. higher plants). In enterobacteria, the Psp response helps to maintain the proton motive force (PMF) of the cell when the inner membrane integrity is impaired. The presumed ability of ArcB to sense redox changes in the cellular quinone pool and the strong decrease of psp induction in ΔubiG or ΔarcAB backgrounds suggest a link between the Psp response and the quinone pool. The authors now provide evidence indicating that the physiological signal for inducing psp by secretin-induced stress is neither the quinone redox state nor a drop in PMF. Neither the loss of the H(+)-gradient nor the dissipation of the electrical potential alone is sufficient to induce the Psp response. A set of electron transport mutants differing in their redox states due to the lack of a NADH dehydrogenase and a quinol oxidase, but retaining a normal PMF displayed low levels of psp induction inversely related to oxidised ubiquinone levels under microaerobic growth and independent of PMF. In contrast, cells displaying higher secretin induced psp expression showed increased levels of ubiquinone. Taken together, this study suggests that not a single but likely multiple signals are needed to be integrated to induce the Psp response.
Wang, Chao; Qian, Chen; Roman, Maren; Glasser, Wolfgang G; Esker, Alan R
2013-11-11
This work highlights a real-time and label-free method to monitor the dehydrogenative polymerization of monolignols initiated by horseradish peroxidase (HRP) physically immobilized on surfaces using a quartz crystal microbalance with dissipation monitoring (QCM-D). The dehydrogenative polymer (DHP) films are expected to provide good model substrates for studying ligninolytic enzymes. The HRP was adsorbed onto gold or silica surfaces or onto and within porous desulfated nanocrystalline cellulose films from an aqueous solution. Surface-immobilized HRP retained its activity and selectivity for monolignols as coniferyl and p-coumaryl alcohol underwent dehydrogenative polymerization in the presence of hydrogen peroxide, whereas sinapyl alcohol polymerization required the addition of a nucleophile. The morphologies of the DHP layers on the surfaces were investigated via atomic force microscopy (AFM). Data from QCM-D and AFM showed that the surface-immobilized HRP-initiated dehydrogenative polymerization of monolignols was greatly affected by the support surface, monolignol concentration, hydrogen peroxide concentration, and temperature.
NASA Astrophysics Data System (ADS)
Berry, M. V.
2005-01-01
By applying the technique of uniform asymptotic approximation to the oscillatory integrals representing tsunami wave profiles, the form of the travelling wave far from the source is calculated for arbitrary initial disturbances. The approximations reproduce the entire profiles very accurately, from the front to the tail, and their numerical computation is much faster than that of the oscillatory integrals. For one-dimensional propagation, the uniform asymptotics involve Airy functions and their derivatives; for two-dimensional propagation, the uniform asymptotics involve products of these functions. Separate analyses are required when the initial disturbance is specified as surface elevation or surface velocity as functions of position, and when these functions are even or odd. 'There was an awful rainbow once in heaven' (John Keats, 1820)
NASA Astrophysics Data System (ADS)
Rajabpour, M. A.
2016-11-01
We classify the sign of the critical Casimir force between two finite objects separated by a large distance in the two-dimensional systems that can be described by conformal field theory (CFT). Specifically, we show that, as long as the smallest scaling dimension present in the spectrum of the system is smaller than one, the sign of the force is independent of the shape of the objects and can be determined by the elements of the modular S matrix of the CFT. The provided formula for the sign of the force indicates that the force is always attractive for equal boundary conditions, independent of the shape of the objects. However, different boundary conditions can lead to attractive or repulsive forces. Using the derived formula, we prove the known results regarding the Ising model and the free bosons. As new examples, we give detailed results regarding the Q =3 state Potts model and the compactified bosons. For example, for the latter model we show that the Dirichlet boundary condition does not always lead to an attractive force.
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)
Li, Yan Jun; Kobayashi, Naritaka; Nomura, Hikaru; Naitoh, Yoshitaka; Kageshima, Masami; Sugawara, Yasuhiro
2008-07-01
We have developed high-speed phase-modulation atomic force microscopy (PM-AFM) in a constant-amplitude (CA) mode. Using this imaging mode, we have theoretically demonstrated that energy dissipation due to tip-sample interaction can be obtained from the excitation amplitude of a cantilever. Moreover, we have found that the photothermal excitation method is better than the acoustic excitation method for cantilever oscillation in liquids. For the first time, we have demonstrated that a homebuilt high-speed PM-AFM in the CA mode has the capability to simultaneously measure the topography and energy dissipation with a material-specific contrast for a PS/PIB polymer-blend film.
Dissipative Solitons that Cannot be Trapped
Pardo, Rosa; Perez-Garcia, Victor M.
2006-12-22
We show that dissipative solitons in systems with high-order nonlinear dissipation cannot survive in the presence of trapping potentials of the rigid wall or asymptotically increasing type. Solitons in such systems can survive in the presence of a weak potential but only with energies out of the interval of existence of linear quantum mechanical stationary states.
NASA Astrophysics Data System (ADS)
Aschwanden, Markus J.
2016-06-01
In this work we provide an updated description of the Vertical-Current Approximation Nonlinear Force-Free Field (VCA-NLFFF) code, which is designed to measure the evolution of the potential, non-potential, free energies, and the dissipated magnetic energies during solar flares. This code provides a complementary and alternative method to existing traditional NLFFF codes. The chief advantages of the VCA-NLFFF code over traditional NLFFF codes are the circumvention of the unrealistic assumption of a force-free photosphere in the magnetic field extrapolation method, the capability to minimize the misalignment angles between observed coronal loops (or chromospheric fibril structures) and theoretical model field lines, as well as computational speed. In performance tests of the VCA-NLFFF code, by comparing with the NLFFF code of Wiegelmann, we find agreement in the potential, non-potential, and free energy within a factor of ≲ 1.3, but the Wiegelmann code yields in the average a factor of 2 lower flare energies. The VCA-NLFFF code is found to detect decreases in flare energies in most X, M, and C-class flares. The successful detection of energy decreases during a variety of flares with the VCA-NLFFF code indicates that current-driven twisting and untwisting of the magnetic field is an adequate model to quantify the storage of magnetic energies in active regions and their dissipation during flares. The VCA-NLFFF code is also publicly available in the Solar SoftWare.
Tidal waves within the thermosphere. [emphasizing wave dissipation and diffusion
NASA Technical Reports Server (NTRS)
Volland, H.; Mayr, H. G.
1974-01-01
The eigenfunctions of the atmosphere (the Hough functions within the lower atmosphere below about 100 km) change their structure and their propagation characteristics within the thermosphere due to dissipation effects such as heat conduction, viscosity, and ion drag. Wave dissipation can be parameterized to a first-order approximation by a complex frequency, the imaginary term of which simulates an effective ion drag force. It is shown how the equivalent depth, the attenuation, and the vertical wavelength of the predominant symmetric diurnal tidal modes change with height as functions of effective ion drag. The boundary conditions of tidal waves are discussed, and asymptotic solutions for the wave parameters like pressure, density, temperature, and wind generated by a heat input proportional to the mean pressure are given. Finally, diffusion effects upon the minor constituents within the thermosphere are described.
Tidal Dissipation in Rotating Giant Planets
NASA Astrophysics Data System (ADS)
Ogilvie, G. I.; Lin, D. N. C.
2004-07-01
present a set of illustrative numerical calculations of the tidal dissipation rate. We argue that inertial waves provide a natural avenue for efficient tidal dissipation in most cases of interest. In the presence of a solid core, the excited disturbance tends to be localized on a web of rays rather than resembling a smooth eigenfunction. The resulting value of Q depends, in principle, in a highly erratic way on the forcing frequency, but we provide analytical and numerical evidence that the frequency-averaged dissipation rate may be asymptotically independent of the viscosity in the limit of small Ekman number. For a smaller viscosity, the tidal disturbance has a finer spatial structure and individual resonances are more pronounced. In short-period extrasolar planets, tidal dissipation via inertial waves becomes somewhat less efficient once they are spun down to a synchronous state. However, if the stellar irradiation of the planet leads to the formation of a radiative outer layer that supports generalized Hough modes, the tidal dissipation rate can be enhanced, albeit with significant uncertainty, through the excitation and damping of these waves. The dissipative mechanisms that we describe offer a promising explanation of the historical evolution and current state of the Galilean satellites, as well as the observed circularization of the orbits of short-period extrasolar planets.
NASA Astrophysics Data System (ADS)
Vysotskii, V. I.; Vysotskyy, M. V.
2014-04-01
The features of the formation of correlated coherent states of a particle in a parabolic potential well at its monotonic deformation (expansion or compression) in finite limits have been considered in the presence of dissipation and a stochastic force. It has been shown that, in both deformation regimes, a correlated coherent state is rapidly formed with a large correlation coefficient | r| → 1, which corresponds at a low energy of the particle to a very significant (by a factor of 1050-10100 or larger) increase in the transparency of the potential barrier at its interaction with atoms (nuclei) forming the "walls" of the potential well or other atoms located in the same well. The efficiency of the formation of correlated coherent states, as well as | r|, increases with an increase in the deformation interval and with a decrease in the deformation time. The presence of the stochastic force acting on the particle can significantly reduce the maximum | r| value and result in the fast relaxation of correlated coherent states with | r| → 0. The effect of dissipation in real systems is weaker than the action of the stochastic force. It has been shown that the formation of correlated coherent states at the fast expansion of the well can underlie the mechanism of nuclear reactions at a low energy, e.g., in microcracks developing in the bulk of metal hydrides loaded with hydrogen or deuterium, as well as in a low-pressure plasma in a variable magnetic field in which the motion of ions is similar to a harmonic oscillator with a variable frequency.
NASA Astrophysics Data System (ADS)
Gentile, Guido; Bartuccelli, Michele V.; Deane, Jonathan H. B.
2005-06-01
We consider a class of second order ordinary differential equations describing one-dimensional systems with a quasiperiodic analytic forcing term and in the presence of damping. As a physical application one can think of a resistor-inductor-varactor circuit with a periodic (or quasiperiodic) forcing function, even if the range of applicability of the theory is much wider. In the limit of large damping we look for quasiperiodic solutions which have the same frequency vector of the forcing term, and we study their analyticity properties in the inverse of the damping coefficient. We find that even the case of periodic forcing terms is nontrivial, as the solution is not analytic in a neighborhood of the origin: it turns out to be Borel summable. In the case of quasiperiodic forcing terms we need renormalization group techniques in order to control the small divisors arising in the perturbation series. We show the existence of a summation criterion of the series in this case also; however, this cannot be interpreted as Borel summability.
NASA Astrophysics Data System (ADS)
Puzyrev, V. E.
Sufficient conditions are obtained for the asymptotic stability of nonuniform rotations of a symmetric heavy rigid body about the principal inertia axis in the presence of medium resistance forces. In contrast to the case previously investigated by Matrosov (1962), the dissipation function is not necessarily positive definite.
NASA Technical Reports Server (NTRS)
Lasalle, J. P.
1972-01-01
A theory is presented that shows how the concept of dissipative systems of ordinary differential equations can be extended to include a broad class of functional and partial differential equations, such as retarded functional differential equations and parabolic partial differential equations. Since the basic hypotheses are all in terms of boundedness, finding sufficient conditions in terms of Liapunov functions would not be too difficult.
Fixed point theorems and dissipative processes
NASA Technical Reports Server (NTRS)
Hale, J. K.; Lopes, O.
1972-01-01
The deficiencies of the theories that characterize the maximal compact invariant set of T as asymptotically stable, and that some iterate of T has a fixed point are discussed. It is shown that this fixed point condition is always satisfied for condensing and local dissipative T. Applications are given to a class of neutral functional differential equations.
NASA Technical Reports Server (NTRS)
Lasalle, J. P.
1971-01-01
The abstract theory presented shows how the theory of dissipative systems of ordinary differential equations can be extended to include a wide class of functional and partial differential equations. Since the basic hypotheses are all in terms of boundedness, finding sufficient conditions in terms of Liapunov functions was not difficult. Work is being undertaken to solve some nontrivial examples to illustrate how the theory can applied.
An asymptotic model of the F layer
NASA Astrophysics Data System (ADS)
Oliver, W. L.
2012-01-01
A model of the F layer of the ionosphere is presented that consists of a bottomside asymptote that ignores transport and a topside asymptote that ignores chemistry. The asymptotes connect at the balance height dividing the chemistry and transport regimes. A combination of these two asymptotes produces a good approximation to the true F layer. Analogously, a model of F layer response to an applied vertical drift is presented that consists of two asymptotic responses, one that ignores transport and one that ignores chemistry. The combination of these asymptotic responses produces a good approximation to the response of the true F layer. This latter response is identical to the “servo” response of Rishbeth et al. (1978), derived from the continuity equation. The asymptotic approach bypasses the continuity equation in favor of “force balance” arguments and so replaces a differential equation with simpler algebraic equations. This new approach provides a convenient and intuitive mean for first-order estimates of the change in F layer peak height and density in terms of changes in neutral density, composition, temperature, winds, and electric fields. It is applicable at midlatitudes and at magnetically quiet times at high latitudes. Forensic inverse relations are possible but are not unique. The validity of the asymptotic relations is shown through numerical simulation.
NASA Astrophysics Data System (ADS)
Shargel, Benjamin Hertz; Chou, Tom
2009-10-01
Asymptotic fluctuation theorems are statements of a Gallavotti-Cohen symmetry in the rate function of either the time-averaged entropy production or heat dissipation of a process. Such theorems have been proved for various general classes of continuous-time deterministic and stochastic processes, but always under the assumption that the forces driving the system are time independent, and often relying on the existence of a limiting ergodic distribution. In this paper we extend the asymptotic fluctuation theorem for the first time to inhomogeneous continuous-time processes without a stationary distribution, considering specifically a finite state Markov chain driven by periodic transition rates. We find that for both entropy production and heat dissipation, the usual Gallavotti-Cohen symmetry of the rate function is generalized to an analogous relation between the rate functions of the original process and its corresponding backward process, in which the trajectory and the driving protocol have been time-reversed. The effect is that spontaneous positive fluctuations in the long time average of each quantity in the forward process are exponentially more likely than spontaneous negative fluctuations in the backward process, and vice-versa, revealing that the distributions of fluctuations in universes in which time moves forward and backward are related. As an additional result, the asymptotic time-averaged entropy production is obtained as the integral of a periodic entropy production rate that generalizes the constant rate pertaining to homogeneous dynamics.
Dissipative structures and related methods
Langhorst, Benjamin R; Chu, Henry S
2013-11-05
Dissipative structures include at least one panel and a cell structure disposed adjacent to the at least one panel having interconnected cells. A deformable material, which may comprise at least one hydrogel, is disposed within at least one interconnected cell proximate to the at least one panel. Dissipative structures may also include a cell structure having interconnected cells formed by wall elements. The wall elements may include a mesh formed by overlapping fibers having apertures formed therebetween. The apertures may form passageways between the interconnected cells. Methods of dissipating a force include disposing at least one hydrogel in a cell structure proximate to at least one panel, applying a force to the at least one panel, and forcing at least a portion of the at least one hydrogel through apertures formed in the cell structure.
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.
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.
Dissipation effects in mechanics and thermodynamics
NASA Astrophysics Data System (ADS)
Güémez, J.; Fiolhais, M.
2016-07-01
With the discussion of three examples, we aim at clarifying the concept of energy transfer associated with dissipation in mechanics and in thermodynamics. The dissipation effects due to dissipative forces, such as the friction force between solids or the drag force in motions in fluids, lead to an internal energy increase of the system and/or to heat transfer to the surroundings. This heat flow is consistent with the second law, which states that the entropy of the universe should increase when those forces are present because of the irreversibility always associated with their actions. As far as mechanics is concerned, the effects of the dissipative forces are included in Newton’s equations as impulses and pseudo-works.
Large Time Asymptotics for Partially Dissipative Hyperbolic Systems
NASA Astrophysics Data System (ADS)
Beauchard, Karine; Zuazua, Enrique
2011-01-01
This work is concerned with ( n-component) hyperbolic systems of balance laws in m space dimensions. First, we consider linear systems with constant coefficients and analyze the possible behavior of solutions as t → ∞. Using the Fourier transform, we examine the role that control theoretical tools, such as the classical Kalman rank condition, play. We build Lyapunov functionals allowing us to establish explicit decay rates depending on the frequency variable. In this way we extend the previous analysis by Shizuta and Kawashima under the so-called algebraic condition (SK). In particular, we show the existence of systems exhibiting more complex behavior than the one that the (SK) condition allows. We also discuss links between this analysis and previous literature in the context of damped wave equations, hypoellipticity and hypocoercivity. To conclude, we analyze the existence of global solutions around constant equilibria for nonlinear systems of balance laws. Our analysis of the linear case allows proving existence results in situations that the previously existing theory does not cover.
Dissipative Boltzmann-Robertson-Walker cosmologies
Hiscock, W.A.; Salmonson, J. )
1991-05-15
The equations governing a flat Robertson-Walker cosmological model containing a dissipative Boltzmann gas are integrated numerically. The bulk viscous stress is modeled using the Eckart and Israel-Stewart theories of dissipative relativistic fluids; the resulting cosmologies are compared and contrasted. The Eckart models are shown to always differ in a significant quantitative way from the Israel-Stewart models. It thus appears inappropriate to use the pathological (nonhyperbolic) Eckart theory for cosmological applications. For large bulk viscosities, both cosmological models approach asymptotic nonequilibrium states; in the Eckart model the total pressure is negative, while in the Israel-Stewart model the total pressure is asymptotically zero. The Eckart model also expands more rapidly than the Israel-Stewart models. These results suggest that bulk-viscous'' inflation may be an artifact of using a pathological fluid theory such as the Eckart theory.
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.
Apertet, Y; Ouerdane, H; Goupil, C; Lecoeur, Ph
2013-08-01
We present an in-depth analysis of the sometimes understated role of the principle of energy conservation in linear irreversible thermodynamics. Our case study is that of a thermoelectric generator (TEG), which is a heat engine of choice in irreversible thermodynamics, owing to the coupling between the electrical and heat fluxes. We show why Onsager's reciprocal relations must be considered locally and how internal dissipative processes emerge from the extension of these relations to a global scale: The linear behavior of a heat engine at the local scale is associated with a dissipation process that must partake in the global energy balance. We discuss the consequences of internal dissipations on the so-called efficiency at maximum power, in the light of our comparative analyses of exoreversibility and endoreversibility on the one hand and of two classes of heat engines, autonomous and periodically driven, on the other hand. Finally, basing our analysis on energy conservation, we also discuss recent works which claim the possibility to overcome the traditional boundaries on efficiency imposed by finite-time thermodynamics in thermoelectric systems with broken time-reversal symmetry; this we do by introducing a "thermal" thermopower and an "electrical" thermopower which permits an analysis of the thermoelectric response of the TEG considering a possible dissymmetry between the electrical/thermal and the thermal/electrical couplings.
Material Systems for Blast-Energy Dissipation
James Schondel; Henry S. Chu
2010-10-01
Lightweight panels have been designed to protect buildings and vehicles from blast pressures by activating energy dissipation mechanisms under the influence of blast loading. Panels were fabricated which featured a variety of granular materials and hydraulic dissipative deformation mechanisms and the test articles were subjected to full-scale blast loading. The force time-histories transmitted by each technology were measured by a novel method that utilized inexpensive custom-designed force sensors. The array of tests revealed that granular materials can effectively dissipate blast energy if they are employed in a way that they easily crush and rearrange. Similarly, hydraulic dissipation can effectively dissipate energy if the panel features a high fraction of porosity and the panel encasement features low compressive stiffness.
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.
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.
Tidal Dissipation in Exoplanetary Systems
NASA Astrophysics Data System (ADS)
Lai, Dong
Observations of exoplanetary systems containing hot Jupiters have provided strong hints that tidal dissipation plays an important role in shaping the property, formation and evolution of these systems. However, most previous studies and discussions of tidal effects in hot Jupiter systems have relied on parameterized equilibrium ("weak friction") tidal theory, which does not capture the underlying physics of tidal dissipation. We propose a multifaceted theoretical/computational program devoted to understanding the physics of tidal dissipation in hot Jupiter systems, including tides in the planets and in the host stars. For the planets, we will study dynamical tides in the liquid envelope, taking account of the rotational effect, periodic thermal forcing, and the possible role of composition gradient. We will also explore viscoelastic dissipation in the solid core which may exist inside the planet. We will apply the results of our tidal dissipation calculations to the high-eccentricity migration mechanism for the formation of hot Jupiters and examine how tidal dissipation may contribute to the observed planetary radius inflation. For the host stars, we will study dynamical stellar tides raised by planets on eccentric and inclined orbits. We will consider stars of various masses (with and without surface convection zones) and examine how tidal dissipations affect the spin- orbit misalignment angles and planetary orbital decay. The overall goal of our proposed research projects is to significantly increase our understanding of how tidal interactions between stars and planets shape the observed properties of exoplanetary systems. This proposal is relevant to NASA's existing and planned space missions (e.g., HST, SOFIA, Herschel, Kepler, TESS and JWST) to understand the origins of stars and planets. It directly addresses NASA's research objectives of understanding the phenomena and processes associated with planetary system formation and evolution and of measuring the
Asymptotic analysis and symmetry in MHD convection
Alboussiere, T.; Garandet, J.P.
1996-08-01
The motion of an electrically conducting fluid in the presence of a steady magnetic field is analyzed. For any non-uniform magnetic field and any non-electromagnetic driving force, a high Hartmann number asymptotic analysis is developed using curvilinear coordinates based on the magnetic field. This analysis yields the structure of the electric current density and velocity fields. In a second step, orthogonal planar symmetries lead to a significant simplification of the asymptotic structure, depending on the nature of the symmetry. The asymptotic solution is applied to some configurations, some of them corresponding to crystal growth from a melt. In the case of electrically insulating boundaries, the nature of the symmetry is found to govern the magnitude and structure of the damped velocity. {copyright} {ital 1996 American Institute of Physics.}
Asymptotic freedom, asymptotic flatness and cosmology
Kiritsis, Elias
2013-11-01
Holographic RG flows in some cases are known to be related to cosmological solutions. In this paper another example of such correspondence is provided. Holographic RG flows giving rise to asymptotically-free β-functions have been analyzed in connection with holographic models of QCD. They are shown upon Wick rotation to provide a large class of inflationary models with logarithmically-soft inflaton potentials. The scalar spectral index is universal and depends only on the number of e-foldings. The ratio of tensor to scalar power depends on the single extra real parameter that defines this class of models. The Starobinsky inflationary model as well as the recently proposed models of T-inflation are members of this class. The holographic setup gives a completely new (and contrasting) view to the stability, naturalness and other problems of such inflationary models.
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.
Asymptotic expansions in nonlinear rotordynamics
NASA Technical Reports Server (NTRS)
Day, William B.
1987-01-01
This paper is an examination of special nonlinearities of the Jeffcott equations in rotordynamics. The immediate application of this analysis is directed toward understanding the excessive vibrations recorded in the LOX pump of the SSME during hot-firing ground testing. Deadband, side force, and rubbing are three possible sources of inducing nonlinearity in the Jeffcott equations. The present analysis initially reduces these problems to the same mathematical description. A special frequency, named the nonlinear natural frequency, is defined and used to develop the solutions of the nonlinear Jeffcott equations as singular asymptotic expansions. This nonlinear natural frequency, which is the ratio of the cross-stiffness and the damping, plays a major role in determining response frequencies.
Involatile nanodroplets: an asymptotic analysis.
Jarymowycz, Lucien B; Ortoleva, Peter J
2006-06-21
The structure of nanometer-scale droplets of weakly volatile liquids arises through the interplay of strong intermolecular attraction, and core intermolecular repulsion, interfacial forces, and the large, negative chemical potential of the low density vapor with which it is in equilibrium. Using a van der Waals equation of state and a mesoscopic multiphase model, the structure of such nanodroplets is determined via an asymptotic analysis in terms of the ambient to critical temperature ratio. The structure of a spherical droplet is obtained as the solution of a simple "shooting" problem. The intradroplet pressure profile and a minimal droplet size are determined. The high pressure in the core of the droplet gives evidence for the preferred melting there for systems like water with a negative volume of melting. Our methodology can be generalized to multiphase droplets, as well as to composite structures wherein viruses or other nanoparticles are embedded.
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)
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)
Cascade replication of dissipative solitons
NASA Astrophysics Data System (ADS)
Kochetov, Bogdan A.; Tuz, Vladimir R.
2017-07-01
We report a new effect of a cascade replication of dissipative solitons from a single one. It is discussed in the framework of a common model based on the one-dimensional cubic-quintic complex Ginzburg-Landau equation in which an additional linear term is introduced to account the perturbation from a particular potential of externally applied force. The effect is demonstrated on the light beams propagating through a planar waveguide. The waveguide consists of a nonlinear layer able to guide dissipative solitons and a magneto-optic substrate. In the waveguide an externally applied force is considered to be an inhomogeneous magnetic field which is induced by modulated electric currents flowing along a set of conducting wires adjusted on the top of the waveguide.
Energy shaping and dissipation: Underwater vehicle stabilization using internal rotors
NASA Astrophysics Data System (ADS)
Woolsey, Craig Arthur
This dissertation concerns nonlinear feedback stabilization of mechanical systems using energy-based methods. Nonlinear techniques are appealing because they can yield large regions of attraction for feedback-stabilized equilibria. Energy-based methods are particularly attractive for mechanical systems because these methods preserve a physical view of a system's dynamics and because they yield Lyapunov functions. For conservative systems, proof of stability typically requires the existence of a Lyapunov function. For systems with damping, Lyapunov functions can be used to design feedback dissipation to ensure or enhance asymptotic stability and to obtain more global conclusions. Both as a case study of a particular control methodology and as a practical contribution in the area of underwater vehicle control, we consider stabilization of an underwater vehicle using internal rotors as actuators. The methodology used to develop stabilizing control laws consists of three steps. The first step involves shaping the kinetic energy of the conservative dynamics. For the underwater vehicle, the control term in this step may be interpreted as modifying the system inertia. In the second step, feedback dissipation is designed based on a Lyapunov function developed in the first step. In the third step, it is verified that the effect of external damping due to viscous forces does not destroy the stability results. This method is applied first to a vehicle whose centers of gravity and buoyancy coincide and then to a vehicle with noncoincident centers of gravity and buoyancy. The method of controlled Lagrangians, developed in recent years, is a generalization of the idea of kinetic energy shaping. The method applies to underactuated mechanical systems (systems with more degrees of freedom than independent actuators). Motivated by the results of the investigation into the effect of external damping on an underwater vehicle with internal rotors, we study the effect of damping on more
Time in dissipative tunneling: Subtleties and applications
NASA Astrophysics Data System (ADS)
Kelkar, N. G.; Lozano Gómez, D.; Patiño, Edgar J.
2017-07-01
Characteristic features of tunneling times for dissipative tunneling of a particle through a rectangular barrier are studied within a semiclassical model involving dissipation in the form of a velocity dependent frictional force. The average dwell time and traversal time with dissipation are found to be less than those without dissipation. This counter-intuitive behavior is reversed if one evaluates the physically relevant transmission dwell time. Apart from these observations, we find that the percentage of energy lost by the tunneling particle is higher for smaller energies. The above observations are tested and confirmed in a realistic case by applying the dissipation model to study the current-voltage data in a Al/Al2O3/Al solid state junction at various temperatures. The friction coefficient for Al2O3 as a function of temperature is presented. It is found to decrease with increasing temperature.
NASA Astrophysics Data System (ADS)
Linkmann, Moritz; Berera, Arjun; Goldstraw, Erin E.
2017-01-01
This paper examines the behavior of the dimensionless dissipation rate Cɛ for stationary and nonstationary magnetohydrodynamic (MHD) turbulence in the presence of external forces. By combining with previous studies for freely decaying MHD turbulence, we obtain here both the most general model equation for Cɛ applicable to homogeneous MHD turbulence and a comprehensive numerical study of the Reynolds number dependence of the dimensionless total energy dissipation rate at unity magnetic Prandtl number. We carry out a series of medium to high resolution direct numerical simulations of mechanically forced stationary MHD turbulence in order to verify the predictions of the model equation for the stationary case. Furthermore, questions of nonuniversality are discussed in terms of the effect of external forces as well as the level of cross- and magnetic helicity. The measured values of the asymptote Cɛ ,∞ lie between 0.193 ≤Cɛ ,∞≤0.268 for free decay, where the value depends on the initial level of cross- and magnetic helicities. In the stationary case we measure Cɛ ,∞=0.223 .
Linkmann, Moritz; Berera, Arjun; Goldstraw, Erin E
2017-01-01
This paper examines the behavior of the dimensionless dissipation rate C_{ɛ} for stationary and nonstationary magnetohydrodynamic (MHD) turbulence in the presence of external forces. By combining with previous studies for freely decaying MHD turbulence, we obtain here both the most general model equation for C_{ɛ} applicable to homogeneous MHD turbulence and a comprehensive numerical study of the Reynolds number dependence of the dimensionless total energy dissipation rate at unity magnetic Prandtl number. We carry out a series of medium to high resolution direct numerical simulations of mechanically forced stationary MHD turbulence in order to verify the predictions of the model equation for the stationary case. Furthermore, questions of nonuniversality are discussed in terms of the effect of external forces as well as the level of cross- and magnetic helicity. The measured values of the asymptote C_{ɛ,∞} lie between 0.193≤C_{ɛ,∞}≤0.268 for free decay, where the value depends on the initial level of cross- and magnetic helicities. In the stationary case we measure C_{ɛ,∞}=0.223.
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.
Quons in a quantum dissipative system
NASA Astrophysics Data System (ADS)
Lee, Taejin
2016-03-01
String theory proves to be an imperative tool to explore the critical behavior of the quantum dissipative system. We discuss the quantum particles moving in two dimensions, in the presence of a uniform magnetic field, subject to a periodic potential and a dissipative force, which are described by the dissipative Wannier-Azbel-Hofstadter (DWAH) model. Using string theory formulation of the model, we find that the elementary excitations of the system at the generic points of the off-critical regions, in the zero temperature limit are quons, which satisfy q-deformed statistics.
NASA Astrophysics Data System (ADS)
Pucci, Patrizia; Saldi, Sara
2017-09-01
This paper is devoted to the question of global and local asymptotic stability for nonlinear damped Kirchhoff systems, with homogeneous Dirichlet boundary conditions, under fairly natural assumptions on the external force f = f (t , x , u), the distributed damping Q = Q (t , x , u ,ut), the perturbation term μ | u| p - 2 u and the dissipative term ϱ (t) M ([u]sp) |ut| p - 2ut, with ϱ ≥ 0 and in Lloc1 (R0+), when the initial data are in a special region. Here u = (u1 , … ,uN) = u (t , x) represents the vectorial displacement, with N ≥ 1. Particular attention is devoted to the asymptotic behavior of the solutions in the linear case specified in Section 5. Finally, the results are extended to problems where the fractional p-Laplacian is replaced by a more general elliptic nonlocal integro-differential operator. The paper extends in several directions recent theorems and covers also the so-called degenerate case, that is the case in which M is zero at zero.
Kolmogorov turbulence by matched asymptotic expansions
NASA Astrophysics Data System (ADS)
Lundgren, Thomas S.
2003-04-01
The Kolmogorov [Dokl. Akad. Nauk. SSSR 30, 299 (1941), hereafter K41] inertial range theory is derived from first principles by analysis of the Navier-Stokes equation using the method of matched asymptotic expansions without assuming isotropy or homogeneity and the Kolmogorov (K62) [J. Fluid Mech. 13, 82 (1962)] refined theory is analyzed. This paper is an extension of Lundgren [Phys. Fluids 14, 638 (2002)], in which the second- and third-order structure functions were determined from the isotropic Karman-Howarth [Proc. R. Soc. London, Ser. A 164, 192 (1938)] equation. The starting point for the present analysis is an equation for the difference in velocity between two points, one of which is a Lagrangian fluid point and the second, slaved to the first by a fixed separation r, is not Lagrangian. The velocity difference, so defined, satisfies the Navier-Stokes equation with spatial variable r. The analysis is carried out in two parts. In the first part the physical hypothesis is made that the mean dissipation is independent of viscosity as viscosity tends to zero, as assumed in K41. This means that the mean dissipation is finite as Reynolds number tends to infinity and leads to the K41 inertial range results. In the second part this dissipation assumption is relaxed in an attempt to duplicate the K62 theory. While the K62 structure is obtained, there are restrictions, resulting from the analysis which shows that there can be no inertial range intermittency as Reynolds number tends to infinity, and therefore the mean dissipation has to be finite as Reynolds number tends to infinity, as assumed in part one. Reynolds number-dependent corrections to the K41 results are obtained in the form of compensating functions of r/λ, which tend to zero slowly like Rλ-2/3 as Rλ→∞.
NASA Astrophysics Data System (ADS)
Ho, Pei-Ming
2017-04-01
Following earlier works on the KMY model of black-hole formation and evaporation, we construct the metric for a matter sphere in gravitational collapse, with the back-reaction of pre-Hawking radiation taken into consideration. The mass distribution and collapsing velocity of the matter sphere are allowed to have an arbitrary radial dependence. We find that a generic gravitational collapse asymptote to a universal configuration which resembles a black hole but without horizon. This approach clarifies several misunderstandings about black-hole formation and evaporation, and provides a new model for black-hole-like objects in the universe.
Asymptotically flat multiblack lenses
NASA Astrophysics Data System (ADS)
Tomizawa, Shinya; Okuda, Taika
2017-03-01
We present an asymptotically flat and stationary multiblack lens solution with biaxisymmetry of U (1 )×U (1 ) as a supersymmetric solution in the five-dimensional minimal ungauged supergravity. We show that the spatial cross section of each degenerate Killing horizon admits different lens space topologies of L (n ,1 )=S3/Zn as well as a sphere S3. Moreover, we show that, in contrast to the higher-dimensional Majumdar-Papapetrou multiblack hole and multi-Breckenridge-Myers-Peet-Vafa (BMPV) black hole spacetime, the metric is smooth on each horizon even if the horizon topology is spherical.
Asymptotic dynamics on a singular chemotaxis system modeling onset of tumor angiogenesis
NASA Astrophysics Data System (ADS)
Wang, Zhi-An; Xiang, Zhaoyin; Yu, Pei
2016-02-01
The asymptotic behavior of solutions to a singular chemotaxis system modeling the onset of tumor angiogenesis in two and three dimensional whole spaces is investigated in the paper. By a Cole-Hopf type transformation, the singular chemotaxis is converted into a non-singular hyperbolic system. Then we study the transformed system and establish the global existence, asymptotic decay rates and diffusion convergence rate of solutions by the method of energy estimates. The main novelty of our results is the finding of a hidden interactive dissipation structure in the system by which the energy dissipation is established.
Alfven wave absorption in dissipative plasma
NASA Astrophysics Data System (ADS)
Gavrikov, M. B.; Taiurskii, A. A.
2017-01-01
We consider nonlinear absorption of Alfven waves due to dissipative effects in plasma and relaxation of temperatures of electrons and ions. This study is based on an exact solution of the equations of two-fluid electromagnetic hydrodynamics (EMHD) of plasma. It is shown that in order to study the decay of Alfven waves, it suffices to examine the behavior of their amplitudes whose evolution is described by a system of ordinary differential equations (ODEs) obtained in this paper. On finite time intervals, the system of equations on the amplitudes is studied numerically, while asymptotic integration (the Hartman-Grobman theorem) is used to examine its large-time behavior.
Thermodynamics of Asymptotically Conical Geometries.
Cvetič, Mirjam; Gibbons, Gary W; Saleem, Zain H
2015-06-12
We study the thermodynamical properties of a class of asymptotically conical geometries known as "subtracted geometries." We derive the mass and angular momentum from the regulated Komar integral and the Hawking-Horowitz prescription and show that they are equivalent. By deriving the asymptotic charges, we show that the Smarr formula and the first law of thermodynamics hold. We also propose an analog of Christodulou-Ruffini inequality. The analysis can be generalized to other asymptotically conical geometries.
Asymptotic symmetries on Killing horizons
NASA Astrophysics Data System (ADS)
Koga, Jun-Ichirou
2001-12-01
We investigate asymptotic symmetries regularly defined on spherically symmetric Killing horizons in Einstein theory with or without the cosmological constant. These asymptotic symmetries are described by asymptotic Killing vectors, along which the Lie derivatives of perturbed metrics vanish on a Killing horizon. We derive the general form of the asymptotic Killing vectors and find that the group of asymptotic symmetries consists of rigid O(3) rotations of a horizon two-sphere and supertranslations along the null direction on the horizon, which depend arbitrarily on the null coordinate as well as the angular coordinates. By introducing the notion of asymptotic Killing horizons, we also show that local properties of Killing horizons are preserved not only under diffeomorphisms but also under nontrivial transformations generated by the asymptotic symmetry group. Although the asymptotic symmetry group contains the Diff(S1) subgroup, which results from supertranslations dependent only on the null coordinate, it is shown that the Poisson brackets algebra of the conserved charges conjugate to asymptotic Killing vectors does not acquire nontrivial central charges. Finally, by considering extended symmetries, we discuss the fact that unnatural reduction of the symmetry group is necessary in order to obtain the Virasoro algebra with nontrivial central charges, which is not justified when we respect the spherical symmetry of Killing horizons.
NASA Astrophysics Data System (ADS)
Suhas, B. G.; Sathyabhama, A.
2017-08-01
The experimental study is carried out to determine forced convective and subcooled flow boiling heat transfer coefficient in conventional rectangular channels. The fluid is passed through rectangular channels of 0.01 m depth, 0.01 m width, and 0.15 m length. The parameters varied are heat flux, mass flux, inlet temperature and volume fraction of ethanol. Forced convective heat transfer coefficient increases with increase in heat flux and mass flux, but effect of mass flux is less significant. Subcooled flow boiling heat transfer increases with increase in heat flux and mass flux, but the effect of heat flux is dominant. During the subcooled flow boiling region, the effect of mass flux will not influence the heat transfer. The strong Marangoni effect will increase the heat transfer coeffient for mixture with 25% ethanol volume fraction. The results obtained for subcooled flow boiling heat transfer coefficient of water are compared with available literature correlations. It is found that Liu-Winterton equation predicts the experimental results better when compared with that of other literature correlations. An empirical correlation for subcooled flow boiling heat transfer coefficient as a function of mixture wall super heat, mass flux, volume fractions and inlet temperature is developed from the experimental results.
Asymptotically safe cosmology - A status report
NASA Astrophysics Data System (ADS)
Bonanno, Alfio; Saueressig, Frank
2017-03-01
Asymptotic safety, based on a non-Gaussian fixed point of the gravitational renormalization group flow, provides an elegant mechanism for completing the gravitational force at sub-Planckian scales. At high energies, the fixed point controls the scaling of couplings such that unphysical divergences are absent, while the emergence of classical low-energy physics is linked to a crossover between two renormalization group fixed points. These features make asymptotic safety an attractive framework for the building of a cosmological model. The resulting scenarios may naturally give rise to a quantum-gravity-driven inflationary phase in the very early universe and an almost scale-free fluctuation spectrum. Moreover, effective descriptions arising from an improvement of the renormalization group permit a direct comparison to cosmological observations as, e.g., Planck data.
Asymptotically safe grand unification
NASA Astrophysics Data System (ADS)
Bajc, Borut; Sannino, Francesco
2016-12-01
Phenomenologically appealing supersymmetric grand unified theories have large gauge representations and thus are not asymptotically free. Their ultraviolet validity is limited by the appearance of a Landau pole well before the Planck scale. One could hope that these theories save themselves, before the inclusion of gravity, by generating an interacting ultraviolet fixed point, similar to the one recently discovered in non-supersymmetric gauge-Yukawa theories. Employing a-maximization, a-theorem, unitarity bounds, as well as positivity of other central charges we nonperturbatively rule out this possibility for a broad class of prime candidates of phenomenologically relevant supersymmetric grand unified theories. We also uncover candidates passing these tests, which have either exotic matter or contain one field decoupled from the superpotential. The latter class of theories contains a model with the minimal matter content required by phenomenology.
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.
Dissipative photonic lattice solitons.
Ultanir, Erdem A; Stegeman, George I; Christodoulides, Demetrios N
2004-04-15
We show that discrete dissipative optical lattice solitons are possible in waveguide array configurations that involve periodically patterned semiconductor optical amplifiers and saturable absorbers. The characteristics of these low-power soliton states are investigated, and their propagation constant eigenvalues are mapped on Floquet-Bloch band diagrams. The prospect of observing such low-power dissipative lattice solitons is discussed in detail.
NASA Astrophysics Data System (ADS)
Pfahl, V.; Phani, M. K.; Büchsenschütz-Göbeler, M.; Kumar, A.; Moshnyaga, V.; Arnold, W.; Samwer, K.
2017-01-01
We report on friction measurements on a La0.6Sr0.4MnO3 (LSMO) thin film using atomic force microscopy cantilever contact-resonances. There is a contribution to the damping of the cantilever oscillations, which is caused by micro-sliding of the cantilever tip on the surface of the thin film. This frictional part decreases with temperature parallel to the increase in the resistivity of the thin film. The LSMO is well-known for a ferromagnetic to paramagnetic phase transition that occurs without changes in the rhombohedral (R-3c) crystalline structure. The magnetic transition at the Curie temperature TC ˜ 360 K is accompanied by a metal-to-metal transition with a large increase in electrical resistivity. The behavior of the cantilever damping constant demonstrates that there is a direct coupling between mechanical friction and the mobility of the electrons in the LSMO film.
Kalashnikov, Vladimir L; Sorokin, Evgeni
2014-12-01
A new type of dissipative solitons--dissipative Raman solitons--are revealed on the basis of numerical study of the generalized complex nonlinear Ginzburg-Landau equation. The stimulated Raman scattering significantly affects the energy scalability of the dissipative solitons, causing splitting to multiple pulses. We show, that an appropriate increase of the group-delay dispersion can suppress the multipulsing instability due to formation of the dissipative Raman soliton, which is chirped, has a Stokes-shifted spectrum, and chaotic modulation on its trailing edge. The strong perturbation of a soliton envelope caused by the stimulated Raman scattering confines the energy scalability preventing the so-called dissipative soliton resonance. We show, that in practical implementations, a spectral filter can extend the stability regions of high-energy pulses.
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.
Asymptotic behavior of the warm inflation scenario with viscous pressure
Mimoso, Jose P.; Nunes, Ana; Pavon, Diego
2006-01-15
We analyze the dynamics of models of warm inflation with general dissipative effects. We consider phenomenological terms both for the inflaton decay rate and for viscous effects within matter. We provide a classification of the asymptotic behavior of these models and show that the existence of a late-time scaling regime depends not only on an asymptotic behavior of the scalar field potential, but also on an appropriate asymptotic behavior of the inflaton decay rate. There are scaling solutions whenever the latter evolves to become proportional to the Hubble rate of expansion regardless of the steepness of the scalar field exponential potential. We show from thermodynamic arguments that the scaling regime is associated with a power-law dependence of the matter-radiation temperature on the scale factor, which allows a mild variation of the temperature of the matter/radiation fluid. We also show that the late-time contribution of the dissipative terms alleviates the depletion of matter, and increases the duration of inflation.
Asymptotic modal analysis and statistical energy analysis
NASA Astrophysics Data System (ADS)
Dowell, Earl H.
1988-07-01
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.
Asymptotic modal analysis and statistical energy analysis
NASA Technical Reports Server (NTRS)
Dowell, Earl H.
1988-01-01
Statistical Energy Analysis (SEA) is defined by considering the asymptotic limit of Classical Modal Analysis, an approach called Asymptotic Modal Analysis (AMA). The general approach is described for both structural and acoustical systems. The theoretical foundation is presented for structural systems, and experimental verification is presented for a structural plate responding to a random force. Work accomplished subsequent to the grant initiation focusses on the acoustic response of an interior cavity (i.e., an aircraft or spacecraft fuselage) with a portion of the wall vibrating in a large number of structural modes. First results were presented at the ASME Winter Annual Meeting in December, 1987, and accepted for publication in the Journal of Vibration, Acoustics, Stress and Reliability in Design. It is shown that asymptotically as the number of acoustic modes excited becomes large, the pressure level in the cavity becomes uniform except at the cavity boundaries. However, the mean square pressure at the cavity corner, edge and wall is, respectively, 8, 4, and 2 times the value in the cavity interior. Also it is shown that when the portion of the wall which is vibrating is near a cavity corner or edge, the response is significantly higher.
Singular asymptotic expansions in nonlinear rotordynamics
NASA Technical Reports Server (NTRS)
Day, W. B.
1984-01-01
During hot firing ground testing of the Space Shuttle's Main Engine, vibrations of the liquid oxygen pump occur at frequencies which cannot be explained by the linear Jeffcott model of the rotor. The model becomes nonlinear after accounting for deadband, side forces, and rubbing. Two phenomena present in the numerical solutions of the differential equations are unexpected periodic orbits of the rotor and tracking of the nonlinear frequency. A multiple scale asymptotic expansion of the differential equations is used to give an analytic explanation of these characteristics.
Singular asymptotic expansions in nonlinear rotordynamics
NASA Technical Reports Server (NTRS)
Day, W. B.
1985-01-01
During hot firing ground testing of the Space shuttle's Main Engine, vibrations of the liquid oxygen pump occur at frequencies which cannot be explained by the linear Jeffcott model of the rotor. The model becomes nonlinear after accounting for deadband, side forces, and rubbing. Two phenomena present in the numerical solutions of the differential equations are unexpected periodic orbits of the rotor and tracking of the nonlinear frequency. A multiple scale asymptotic expansion of the differential equations is used to give an analytic explanation of these characteristics.
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.
Rayleigh-Lagrange formalism for classical dissipative systems.
Virga, Epifanio G
2015-01-01
It is often believed that the Rayleigh-Lagrange formalism for classical dissipative systems is unable to encompass forces described by nonlinear functions of the velocities. Here we show that this is indeed a misconception.
Velmurugan, G; Rakkiyappan, R; Vembarasan, V; Cao, Jinde; Alsaedi, Ahmed
2017-02-01
As we know, the notion of dissipativity is an important dynamical property of neural networks. Thus, the analysis of dissipativity of neural networks with time delay is becoming more and more important in the research field. In this paper, the authors establish a class of fractional-order complex-valued neural networks (FCVNNs) with time delay, and intensively study the problem of dissipativity, as well as global asymptotic stability of the considered FCVNNs with time delay. Based on the fractional Halanay inequality and suitable Lyapunov functions, some new sufficient conditions are obtained that guarantee the dissipativity of FCVNNs with time delay. Moreover, some sufficient conditions are derived in order to ensure the global asymptotic stability of the addressed FCVNNs with time delay. Finally, two numerical simulations are posed to ensure that the attention of our main results are valuable. Copyright © 2016 Elsevier Ltd. All rights reserved.
Fluctuations, Dissipation and the Dynamical Casimir Effect
NASA Astrophysics Data System (ADS)
Dalvit, Diego A. R.; Neto, Paulo A. Maia; Mazzitelli, Francisco Diego
Vacuum fluctuations provide a fundamental source of dissipation for systems coupled to quantum fields by radiation pressure. In the dynamical Casimir effect, accelerating neutral bodies in free space give rise to the emission of real photons while experiencing a damping force which plays the role of a radiation reaction force. Analog models where non-stationary conditions for the electromagnetic field simulate the presence of moving plates are currently under experimental investigation. A dissipative force might also appear in the case of uniform relative motion between two bodies, thus leading to a new kind of friction mechanism without mechanical contact. In this paper, we review recent advances on the dynamical Casimir and non-contact friction effects, highlighting their common physical origin.
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…
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…
Energy dissipation in substorms
NASA Technical Reports Server (NTRS)
Weiss, Loretta A.; Reiff, P. H.; Moses, J. J.; Heelis, R. A.; Moore, B. D.
1992-01-01
The energy dissipated by substorms manifested in several ways is discussed: the Joule dissipation in the ionosphere; the energization of the ring current by the injection of plasma sheet particles; auroral election and ion acceleration; plasmoid ejection; and plasma sheet ion heating during the recovery phase. For each of these energy dissipation mechanisms, a 'rule of thumb' formula is given, and a typical dissipation rate and total energy expenditure is estimated. The total energy dissipated as Joule heat (approximately) 2 x 10(exp 15) is found about twice the ring current injection term, and may be even larger if small scale effects are included. The energy expended in auroral electron precipitation, on the other hand, is smaller than the Joule heating by a factor of five. The energy expended in refilling and heating the plasma sheets is estimated to be approximately 5 x 10(exp 14)J, while the energy lost due to plasmoid ejection is between (approximately) (10 exp 13)(exp 14)J.
Energy dissipation in substorms
NASA Technical Reports Server (NTRS)
Weiss, Loretta A.; Reiff, P. H.; Moses, J. J.; Heelis, R. A.; Moore, B. D.
1992-01-01
The energy dissipated by substorms manifested in several ways is discussed: the Joule dissipation in the ionosphere; the energization of the ring current by the injection of plasma sheet particles; auroral election and ion acceleration; plasmoid ejection; and plasma sheet ion heating during the recovery phase. For each of these energy dissipation mechanisms, a 'rule of thumb' formula is given, and a typical dissipation rate and total energy expenditure is estimated. The total energy dissipated as Joule heat (approximately) 2 x 10(exp 15) is found about twice the ring current injection term, and may be even larger if small scale effects are included. The energy expended in auroral electron precipitation, on the other hand, is smaller than the Joule heating by a factor of five. The energy expended in refilling and heating the plasma sheets is estimated to be approximately 5 x 10(exp 14)J, while the energy lost due to plasmoid ejection is between (approximately) (10 exp 13)(exp 14)J.
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.
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.
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.
Fractional dissipative standard map.
Tarasov, Vasily E; Edelman, M
2010-06-01
Using kicked differential equations of motion with derivatives of noninteger orders, we obtain generalizations of the dissipative standard map. The main property of these generalized maps, which are called fractional maps, is long-term memory. The memory effect in the fractional maps means that their present state of evolution depends on all past states with special forms of weights. Already a small deviation of the order of derivative from the integer value corresponding to the regular dissipative standard map (small memory effects) leads to the qualitatively new behavior of the corresponding attractors. The fractional dissipative standard maps are used to demonstrate a new type of fractional attractors in the wide range of the fractional orders of derivatives.
Graphene heat dissipating structure
Washburn, Cody M.; Lambert, Timothy N.; Wheeler, David R.; Rodenbeck, Christopher T.; Railkar, Tarak A.
2017-08-01
Various technologies presented herein relate to forming one or more heat dissipating structures (e.g., heat spreaders and/or heat sinks) on a substrate, wherein the substrate forms part of an electronic component. The heat dissipating structures are formed from graphene, with advantage being taken of the high thermal conductivity of graphene. The graphene (e.g., in flake form) is attached to a diazonium molecule, and further, the diazonium molecule is utilized to attach the graphene to material forming the substrate. A surface of the substrate is treated to comprise oxide-containing regions and also oxide-free regions having underlying silicon exposed. The diazonium molecule attaches to the oxide-free regions, wherein the diazonium molecule bonds (e.g., covalently) to the exposed silicon. Attachment of the diazonium plus graphene molecule is optionally repeated to enable formation of a heat dissipating structure of a required height.
Asymptotic conditions and conserved quantities
Koul, R.K.
1990-01-01
Two problems have been investigated in this dissertation. The first one deals with the relationship between stationary space-times which are flat at null infinity and stationary space-times which are asymptotic flat at space-like infinity. It is shown that the stationary space-times which are asymptotically flat, in the Penrose sense, at null infinity, are asymptotically flat at space-like infinity in the Geroch sense and metric at space like infinity is at least C{sup 1}. In the converse it is shown that the stationary space-times which are asymptotically flat at space like infinity, in the Beig sense, are asymptotically flat at null infinity in the Penrose sense. The second problem addressed deals with the theories of arbitrary dimensions. The theories treated are the ones which have fiber bundle structure, outside some compact region. For these theories the criterion for the choice of the background metric is specified, and the boundary condition for the initial data set (q{sub ab}, P{sup ab}) is given in terms of the background metric. Having these boundary conditions it is shown that the symplectic structure and the constraint functionals are well defined. The conserved quantities associated with internal Killing vector fields are specified. Lastly the energy relative to a fixed background and the total energy of the theory have been given. It is also shown that the total energy of the theory is independent of the choice of the background.
Circulation and Dissipation on Hot Jupiters
NASA Astrophysics Data System (ADS)
Li, J.; Goodman, J.
2010-12-01
Many global circulation models predict supersonic zonal winds and large vertical shears in the atmospheres of short-period Jovian exoplanets. Using linear analysis and nonlinear local simulations, we investigate hydrodynamic dissipation mechanisms to balance the thermal acceleration of these winds. The adiabatic Richardson criterion remains a good guide to linear stability, although thermal diffusion allows some modes to violate it at very long wavelengths and very low growth rates. Nonlinearly, wind speeds saturate at Mach numbers ≈2 and Richardson numbers lsim1/4 for a broad range of plausible diffusivities and forcing strengths. Turbulence and vertical mixing, though accompanied by weak shocks, dominate the dissipation, which appears to be the outcome of a recurrent Kelvin-Helmholtz instability. An explicit shear viscosity, as well as thermal diffusivity, is added to ZEUS to capture dissipation outside of shocks. The wind speed is neither monotonic nor single valued for a range of shear viscosities larger than about 10-3 of the sound speed times the pressure scale height. Coarsening the numerical resolution can also increase the speed. Hence global simulations that are incapable of representing vertical turbulence and shocks, either because of reduced physics or because of limited resolution, may overestimate wind speeds. We recommend that such simulations include artificial dissipation terms to control the Mach and Richardson numbers and to capture mechanical dissipation as heat.
CIRCULATION AND DISSIPATION ON HOT JUPITERS
Li, J.; Goodman, J.
2010-12-10
Many global circulation models predict supersonic zonal winds and large vertical shears in the atmospheres of short-period Jovian exoplanets. Using linear analysis and nonlinear local simulations, we investigate hydrodynamic dissipation mechanisms to balance the thermal acceleration of these winds. The adiabatic Richardson criterion remains a good guide to linear stability, although thermal diffusion allows some modes to violate it at very long wavelengths and very low growth rates. Nonlinearly, wind speeds saturate at Mach numbers {approx}2 and Richardson numbers {approx}<1/4 for a broad range of plausible diffusivities and forcing strengths. Turbulence and vertical mixing, though accompanied by weak shocks, dominate the dissipation, which appears to be the outcome of a recurrent Kelvin-Helmholtz instability. An explicit shear viscosity, as well as thermal diffusivity, is added to ZEUS to capture dissipation outside of shocks. The wind speed is neither monotonic nor single valued for a range of shear viscosities larger than about 10{sup -3} of the sound speed times the pressure scale height. Coarsening the numerical resolution can also increase the speed. Hence global simulations that are incapable of representing vertical turbulence and shocks, either because of reduced physics or because of limited resolution, may overestimate wind speeds. We recommend that such simulations include artificial dissipation terms to control the Mach and Richardson numbers and to capture mechanical dissipation as heat.
Ergodicity and asymptotic stability of Feller semigroups on Polish metric spaces
NASA Astrophysics Data System (ADS)
Gong, FuZhou; Liu, Yuan
2015-06-01
We provide some sharp criteria for studying the ergodicity and asymptotic stability of general Feller semigroups on Polish metric spaces. As application, the 2D Navier-Stokes equations with degenerate stochastic forcing will be simply revisited.
Dissipative 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…
Dissipative Work in Thermodynamics
ERIC Educational Resources Information Center
Anacleto, Joaquim; Pereira, Mario G.; Ferreira, J. M.
2011-01-01
This work explores the concept of dissipative work and shows that such a kind of work is an invariant non-negative quantity. This feature is then used to get a new insight into adiabatic irreversible processes; for instance, why the final temperature in any adiabatic irreversible process is always higher than that attained in a reversible process…
Asymptotic Normality of Quadratic Estimators.
Robins, James; Li, Lingling; Tchetgen, Eric; van der Vaart, Aad
2016-12-01
We prove conditional asymptotic normality of a class of quadratic U-statistics that are dominated by their degenerate second order part and have kernels that change with the number of observations. These statistics arise in the construction of estimators in high-dimensional semi- and non-parametric models, and in the construction of nonparametric confidence sets. This is illustrated by estimation of the integral of a square of a density or regression function, and estimation of the mean response with missing data. We show that estimators are asymptotically normal even in the case that the rate is slower than the square root of the observations.
Asymptotic Rayleigh instantaneous unit hydrograph
Troutman, B.M.; Karlinger, M.R.
1988-01-01
The instantaneous unit hydrograph for a channel network under general linear routing and conditioned on the network magnitude, N, tends asymptotically, as N grows large, to a Rayleigh probability density function. This behavior is identical to that of the width function of the network, and is proven under the assumption that the network link configuration is topologically random and the link hydraulic and geometric properties are independent and identically distributed random variables. The asymptotic distribution depends only on a scale factor, {Mathematical expression}, where ?? is a mean link wave travel time. ?? 1988 Springer-Verlag.
Wedge locality and asymptotic commutativity
NASA Astrophysics Data System (ADS)
Soloviev, M. A.
2014-05-01
In this paper, we study twist deformed quantum field theories obtained by combining the Wightman axiomatic approach with the idea of spacetime noncommutativity. We prove that the deformed fields with deformation parameters of opposite sign satisfy the condition of mutual asymptotic commutativity, which was used earlier in nonlocal quantum field theory as a substitute for relative locality. We also present an improved proof of the wedge localization property discovered for the deformed fields by Grosse and Lechner, and we show that the deformation leaves the asymptotic behavior of the vacuum expectation values in spacelike directions substantially unchanged.
Lorentzian proper vertex amplitude: Asymptotics
NASA Astrophysics Data System (ADS)
Engle, Jonathan; Vilensky, Ilya; Zipfel, Antonia
2016-09-01
In previous work, the Lorentzian proper vertex amplitude for a spin-foam model of quantum gravity was derived. In the present work, the asymptotics of this amplitude are studied in the semiclassical limit. The starting point of the analysis is an expression for the amplitude as an action integral with action differing from that in the Engle-Pereira-Rovelli-Livine (EPRL) case by an extra "projector" term. This extra term scales linearly with spins only in the asymptotic limit, and is discontinuous on a (lower dimensional) submanifold of the integration domain in the sense that its value at each such point depends on the direction of approach. New tools are introduced to generalize stationary phase methods to this case. For the case of boundary data which can be glued to a nondegenerate Lorentzian 4-simplex, the asymptotic limit of the amplitude is shown to equal the single Feynman term, showing that the extra term in the asymptotics of the EPRL amplitude has been eliminated.
Asymptotic screened hydrogenic radial integrals
NASA Technical Reports Server (NTRS)
Olsgaard, D. A.; Khan, F.; Khandelwal, G. S.
1988-01-01
The usefulness of the screened hydrogenic model for the transitions of the helium sequence is studied. The screened hydrogenic radial dipole integral for discrete-discrete transitions from the initial state to the final state is asymptotically expanded to the lowest order such that the final quantum number n approaches infinity. The analytical expression obtained is in terms of confluent hypergeometric functions.
Dissipative solitons in fiber lasers
NASA Astrophysics Data System (ADS)
Turitsyn, S. K.; Rosanov, N. N.; Yarutkina, I. A.; Bednyakova, A. E.; Fedorov, S. V.; Shtyrina, O. V.; Fedoruk, M. P.
2016-07-01
Dissipative solitons (also known as auto-solitons) are stable, nonlinear, time- or space-localized solitary waves that occur due to the balance between energy excitation and dissipation. We review the theory of dissipative solitons applied to fiber laser systems. The discussion context includes the classical Ginzburg-Landau and Maxwell-Bloch equations and their modifications that allow describing laser-cavity-produced waves. Practical examples of laser systems generating dissipative solitons are discussed.
Asymptotically dichotomic almost periodic differential equations
NASA Astrophysics Data System (ADS)
Campos, Juan; Tarallo, Massimo
2017-07-01
Consider a non-linear differential equation in RN which asymptotically behaves as a linear equation admitting an exponential dichotomy. We wonder if almost periodic solutions exist when we add to the equation an almost periodic forcing term, large enough and not vanishing too much. A positive answer has been given in [3] for the scalar case N = 1 and our aim is to extend that result to higher dimensions. We discover that the extension seems to be driven by a new ingredient, namely the type of the exponential dichotomy: besides the pure stable types, the mixed hyperbolic type is now possible and leads to a weaker than expected extension. An example shows that a stronger extension cannot be obtained by the same method. The approach is blended and mixes methods of differential equations and functional analysis, especially when estimating norm and spectral radius of some crucial positive but non-compact linear integral operators.
Current-induced dissipation in spectral wave models
NASA Astrophysics Data System (ADS)
Rapizo, H.; Babanin, A. V.; Provis, D.; Rogers, W. E.
2017-03-01
Despite many recent developments of the parameterization for wave dissipation in spectral models, it is evident that when waves propagate onto strong adverse currents the rate of energy dissipation is not properly estimated. The issue of current-induced dissipation is studied through a comprehensive data set in the tidal inlet of Port Phillip Heads, Australia. The wave parameters analyzed are significantly modulated by the tidal currents. Wave height in conditions of opposing currents (ebb tide) can reach twice the offshore value, whereas during coflowing currents (flood), it can be reduced to half. The wind-wave model SWAN is able to reproduce the tide-induced modulation of waves and the results show that the variation of currents is the dominant factor in modifying the wave field. In stationary simulations, the model provides an accurate representation of wave height for slack and flood tides. During ebb tides, wave energy is highly overestimated over the opposing current jet. None of the four parameterizations for wave dissipation tested performs satisfactorily. A modification to enhance dissipation as a function of the local currents is proposed. It consists of the addition of a factor that represents current-induced wave steepening and it is scaled by the ratio of spectral energy to the threshold breaking level. The new term asymptotes to the original form as the current in the wave direction tends to zero. The proposed modification considerably improves wave height and mean period in conditions of adverse currents, whereas the good model performance in coflowing currents is unaltered.
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 .
Classical to quantum correspondence in dissipative directed transport.
Carlo, Gabriel G; Rivas, Alejandro M F; Spina, María E
2015-11-01
We compare the quantum and classical properties of the (quantum) isoperiodic stable structures [(Q)ISSs], which organize the parameter space of a paradigmatic dissipative ratchet model, i.e., the dissipative modified kicked rotator. We study the spectral behavior of the corresponding classical Perron-Frobenius operators with thermal noise and the quantum superoperators without it for small ℏ(eff) values. We find a remarkable similarity between the classical and quantum spectra. This finding significantly extends previous results-obtained for the mean currents and asymptotic distributions only-and, on the other hand, unveils a classical to quantum correspondence mechanism where the classical noise is qualitatively different from the quantum one. This is crucial not only for simple attractors but also for chaotic ones, where just analyzing the asymptotic distribution is revealed as insufficient. Moreover, we provide with a detailed characterization of relevant eigenvectors by means of the corresponding Weyl-Wigner distributions, in order to better identify similarities and differences. Finally, this model being generic, it allows us to conjecture that this classical to quantum correspondence mechanism is a universal feature of dissipative systems.
Classical to quantum correspondence in dissipative directed transport
NASA Astrophysics Data System (ADS)
Carlo, Gabriel G.; Rivas, Alejandro M. F.; Spina, María E.
2015-11-01
We compare the quantum and classical properties of the (quantum) isoperiodic stable structures [(Q)ISSs], which organize the parameter space of a paradigmatic dissipative ratchet model, i.e., the dissipative modified kicked rotator. We study the spectral behavior of the corresponding classical Perron-Frobenius operators with thermal noise and the quantum superoperators without it for small ℏeff values. We find a remarkable similarity between the classical and quantum spectra. This finding significantly extends previous results—obtained for the mean currents and asymptotic distributions only—and, on the other hand, unveils a classical to quantum correspondence mechanism where the classical noise is qualitatively different from the quantum one. This is crucial not only for simple attractors but also for chaotic ones, where just analyzing the asymptotic distribution is revealed as insufficient. Moreover, we provide with a detailed characterization of relevant eigenvectors by means of the corresponding Weyl-Wigner distributions, in order to better identify similarities and differences. Finally, this model being generic, it allows us to conjecture that this classical to quantum correspondence mechanism is a universal feature of dissipative systems.
Dissipation in deforming chaotic billiards
NASA Astrophysics Data System (ADS)
Barnett, Alexander Harvey
Chaotic billiards (hard-walled cavities) in two or more dimensions are paradigm systems in the fields of classical and quantum chaos. We study the dissipation (irreversible heating) rate in such billiard systems due to general shape deformations which are periodic in time. We are motivated by older studies of one-body nuclear dissipation and by anticipated mesoscopic applications. We review the classical and quantum linear response theories of dissipation rate and demonstrate their correspondence in the semiclassical limit. In both pictures, heating is a result of stochastic energy spreading. The heating rate can be expressed as a frequency-dependent friction coefficient μ(ω), which depends on billiard shape and deformation choice. We show that there is a special class of deformations for which μ vanishes as like a power law in the small- ω limit. Namely, for deformations which cause translations and dilations μ ~ ω4 whereas for those which cause rotations μ ~ ω2. This contrasts the generic case for which μ ~ ω4 We show how a systematic treatment of this special class leads to an improved version of the `wall formula' estimate for μ(0). We show that the special nature of dilation (a new result) is semiclassically equivalent to a quasi- orthogonality relation between the (undeformed) billiard quantum eigenstates on the boundary. This quasi- orthogonality forms the heart of a `scaling method' for the numerical calculation of quantum eigenstates, invented recently by Vergini and Saraceno. The scaling method is orders of magnitude more efficient than any other known billiard quantization method, however an adequate explanation for its success has been lacking until now. We explain the scaling method, its errors, and applications. We also present improvements to Heller's plane wave method. Two smaller projects conclude the thesis. Firstly, we give a new formalism for quantum point contact (QPC) conductance in terms of scattering cross-section in the half
Skyrmionic spin Seebeck effect via dissipative thermomagnonic torques
NASA Astrophysics Data System (ADS)
Kovalev, Alexey A.
2014-06-01
We derive thermomagnonic torque and its "β-type" dissipative correction from the stochastic Landau-Lifshitz-Gilbert equation. The β-type dissipative correction describes viscous coupling between magnetic dynamics and magnonic current and it stems from spin mistracking of the magnetic order. We show that thermomagnonic torque is important for describing temperature gradient induced motion of skyrmions in helical magnets while dissipative correction plays an essential role in generating transverse Magnus force. We propose to detect such skyrmionic motion by employing the transverse spin Seebeck effect geometry.
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.
Dissipative quantum trajectories in complex space: Damped harmonic oscillator
Chou, Chia-Chun
2016-10-15
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.
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.
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.
Remarks on asymptotically safe inflation
NASA Astrophysics Data System (ADS)
Tye, S.-H. Henry; Xu, Jiajun
2010-12-01
We comment on Weinberg’s interesting analysis of asymptotically safe inflation [S. Weinberg, Phys. Rev. DPRVDAQ1550-7998 81, 083535 (2010).10.1103/PhysRevD.81.083535]. We find that even if the gravity theory exhibits an ultraviolet fixed point, the energy scale during inflation is way too low to drive the theory close to the fixed point value. We choose the specific renormalization group flow away from the fixed point towards the infrared region that reproduces the Newton’s constant and today’s cosmological constant. We follow this renormalization group flow path to scales below the Planck scale to study the stability of the inflationary scenario. Again, we find that some fine-tuning is necessary to get enough e folds of inflation in the asymptotically safe inflationary scenario.
Asymptotic safety goes on shell
NASA Astrophysics Data System (ADS)
Benedetti, Dario
2012-01-01
It is well known in quantum field theory that the off-shell effective action depends on the gauge choice and field parametrization used in calculating it. Nevertheless, the typical scheme in which the scenario of asymptotically safe gravity is investigated is an off-shell version of the functional renormalization group equation. Working with the Einstein-Hilbert truncation as a test bed, we develop a new scheme for the analysis of asymptotically safe gravity in which the on-shell part of the effective action is singled out and we show that the beta function for the essential coupling has no explicit gauge dependence. In order to reach our goal, we introduce several technical novelties, including a different decomposition of the metric fluctuations, a new implementation of the ghost sector and a new cut-off scheme. We find a nontrivial fixed point, with a value of the cosmological constant that is independent of the gauge-fixing parameters.
Asymptotic controllability and optimal control
NASA Astrophysics Data System (ADS)
Motta, M.; Rampazzo, F.
We consider a control problem where the state must approach asymptotically a target C while paying an integral cost with a non-negative Lagrangian l. The dynamics f is just continuous, and no assumptions are made on the zero level set of the Lagrangian l. Through an inequality involving a positive number p and a Minimum Restraint FunctionU=U(x) - a special type of Control Lyapunov Function - we provide a condition implying that (i) the system is asymptotically controllable, and (ii) the value function is bounded by U/p. The result has significant consequences for the uniqueness issue of the corresponding Hamilton-Jacobi equation. Furthermore it may be regarded as a first step in the direction of a feedback construction.
Composite operators in asymptotic safety
NASA Astrophysics Data System (ADS)
Pagani, Carlo; Reuter, Martin
2017-03-01
We study the role of composite operators in the asymptotic safety program for quantum gravity. By including in the effective average action an explicit dependence on new sources, we are able to keep track of operators which do not belong to the exact theory space and/or are normally discarded in a truncation. Typical examples are geometric operators such as volumes, lengths, or geodesic distances. We show that this setup allows us to investigate the scaling properties of various interesting operators via a suitable exact renormalization group equation. We test our framework in several settings including quantum Einstein gravity, the conformally reduced Einstein-Hilbert truncation, and two-dimensional quantum gravity. Finally, we briefly argue that our construction paves the way to approach observables in the asymptotic safety program.
Asymptotic Techniques in Ignition Theory.
1980-12-01
conduction, until the exothermic reaction leads to a thermal runaway at a finite ignition time. Since the heat conductivity of the wire is often very large...Large activation energy asymptotics have been very useful in describing thermal ignition with different tyres of heating mechanisms. These methods...good agreement with the results of numerical integra- tions. -2- Thermal runaway leading to ignition is a strongly dependent function of temperature
Asymptotic prime partitions of integers
NASA Astrophysics Data System (ADS)
Bartel, Johann; Bhaduri, R. K.; Brack, Matthias; Murthy, M. V. N.
2017-05-01
In this paper, we discuss P (n ) , the number of ways a given integer n may be written as a sum of primes. In particular, an asymptotic form Pas(n ) valid for n →∞ is obtained analytically using standard techniques of quantum statistical mechanics. First, the bosonic partition function of primes, or the generating function of unrestricted prime partitions in number theory, is constructed. Next, the density of states is obtained using the saddle-point method for Laplace inversion of the partition function in the limit of large n . This gives directly the asymptotic number of prime partitions Pas(n ) . The leading term in the asymptotic expression grows exponentially as √{n /ln(n ) } and agrees with previous estimates. We calculate the next-to-leading-order term in the exponent, proportional to ln[ln(n )]/ln(n ) , and we show that an earlier result in the literature for its coefficient is incorrect. Furthermore, we also calculate the next higher-order correction, proportional to 1 /ln(n ) and given in Eq. (43), which so far has not been available in the literature. Finally, we compare our analytical results with the exact numerical values of P (n ) up to n ˜8 ×106 . For the highest values, the remaining error between the exact P (n ) and our Pas(n ) is only about half of that obtained with the leading-order approximation. But we also show that, unlike for other types of partitions, the asymptotic limit for the prime partitions is still quite far from being reached even for n ˜107 .
Perspective: Dissipative particle dynamics
NASA Astrophysics Data System (ADS)
Español, Pep; Warren, Patrick B.
2017-04-01
Dissipative particle dynamics (DPD) belongs to a class of models and computational algorithms developed to address mesoscale problems in complex fluids and soft matter in general. It is based on the notion of particles that represent coarse-grained portions of the system under study and allow, therefore, reaching time and length scales that would be otherwise unreachable from microscopic simulations. The method has been conceptually refined since its introduction almost twenty five years ago. This perspective surveys the major conceptual improvements in the original DPD model, along with its microscopic foundation, and discusses outstanding challenges in the field. We summarize some recent advances and suggest avenues for future developments.
Perspective: Dissipative particle dynamics.
Español, Pep; Warren, Patrick B
2017-04-21
Dissipative particle dynamics (DPD) belongs to a class of models and computational algorithms developed to address mesoscale problems in complex fluids and soft matter in general. It is based on the notion of particles that represent coarse-grained portions of the system under study and allow, therefore, reaching time and length scales that would be otherwise unreachable from microscopic simulations. The method has been conceptually refined since its introduction almost twenty five years ago. This perspective surveys the major conceptual improvements in the original DPD model, along with its microscopic foundation, and discusses outstanding challenges in the field. We summarize some recent advances and suggest avenues for future developments.
On asymptotically lacunary invariant statistical equivalent set sequences
NASA Astrophysics Data System (ADS)
Pancaroglu, Nimet; Nuray, Fatih; Savas, Ekrem
2013-10-01
In this paper, we define asymptotically invariant equivalence, strongly asymptotically invariant equivalence, asymptotically invariant statistical equivalence, asymptotically lacunary invariant statistical equivalence, strongly asymptotically lacunary invariant equivalence, asymptotically lacunary invariant equivalence (Wijsman sense) for sequences of sets. Also we investigate some relations between asymptotically lacunary invariant statistical equivalence and asymptotically invariant statistical equivalence for sequences of sets. We introduce some notions and theorems as follows, asymptotically lacunary invariant statistical equivalence, strongly asymptotically lacunary invariant equivalence, asymptotically lacunary invariant equivalence (Wijsman sense) for sequences of sets.
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
NASA Astrophysics Data System (ADS)
Couderc, F.; Duran, A.; Vila, J.-P.
2017-08-01
We present an explicit scheme for a two-dimensional multilayer shallow water model with density stratification, for general meshes and collocated variables. The proposed strategy is based on a regularized model where the transport velocity in the advective fluxes is shifted proportionally to the pressure potential gradient. Using a similar strategy for the potential forces, we show the stability of the method in the sense of a discrete dissipation of the mechanical energy, in general multilayer and non-linear frames. These results are obtained at first-order in space and time and extended using a second-order MUSCL extension in space and a Heun's method in time. With the objective of minimizing the diffusive losses in realistic contexts, sufficient conditions are exhibited on the regularizing terms to ensure the scheme's linear stability at first and second-order in time and space. The other main result stands in the consistency with respect to the asymptotics reached at small and large time scales in low Froude regimes, which governs large-scale oceanic circulation. Additionally, robustness and well-balanced results for motionless steady states are also ensured. These stability properties tend to provide a very robust and efficient approach, easy to implement and particularly well suited for large-scale simulations. Some numerical experiments are proposed to highlight the scheme efficiency: an experiment of fast gravitational modes, a smooth surface wave propagation, an initial propagating surface water elevation jump considering a non-trivial topography, and a last experiment of slow Rossby modes simulating the displacement of a baroclinic vortex subject to the Coriolis force.
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
A Lagrangian fluctuation-dissipation relation for scalar turbulence
NASA Astrophysics Data System (ADS)
Drivas, Theodore; Eyink, Gregory
2016-11-01
An exact relation is derived between the dissipation of scalar fluctuations and the variance of the scalar inputs (due to initial scalar values, scalar sources, and boundary fluxes) as those are sampled by stochastic Lagrangian trajectories. Previous work on the Kraichnan (1968) model of turbulent scalar advection has shown that anomalous scalar dissipation, non-vanishing in the limit of vanishing viscosity and diffusivity, is in that model due to Lagrangian spontaneous stochasticity, or non-determinism of the Lagrangian particle trajectories in the limit. We here extend this result to scalars advected by any incompressible velocity field. For fluid flows in domains without walls (e.g. periodic boxes) and for insulating/impermeable walls with zero scalar fluxes, we prove that anomalous scalar dissipation and spontaneous stochasticity are completely equivalent. For flows with imposed scalar values or non-vanishing scalar fluxes at the walls, spontaneous stochasticity still implies anomalous scalar dissipation but simple examples show that a distinct mechanism of non-vanishing dissipation can be thin scalar boundary layers near the walls. As an example, we consider turbulent Rayleigh-Benard convection. We here obtain an exact relation between steady-state thermal dissipation and the time for diffusive tracer particles released at the top or bottom wall to mix to their final uniform value near those walls. We show that an "ultimate regime" of turbulent convection as predicted by Kraichnan (1962) will occur at high Rayleigh numbers, unless this near-wall mixing time is asymptotically much longer than the large-scale circulation time.
The asymptotic limit of an integro-differential equation modelling complex systems
NASA Astrophysics Data System (ADS)
Bianca, C.; Ferrara, M.; Guerrini, L.
2014-12-01
This paper is devoted to the asymptotic analysis of a mathematical framework that has recently been proposed for modelling complex systems in the applied sciences under the action of an external force field. This framework consists in an integro-differential kinetic equation coupled with a Gaussian isokinetic thermostat. The asymptotic limit obtained here using low-field scaling shows the emergence of diffusive behaviour on a macroscopic scale.
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.
Energy dissipation in flows through curved spaces
Debus, J.-D.; Mendoza, M.; Succi, S.; Herrmann, H. J.
2017-01-01
Fluid dynamics in intrinsically curved geometries is encountered in many physical systems in nature, ranging from microscopic bio-membranes all the way up to general relativity at cosmological scales. Despite the diversity of applications, all of these systems share a common feature: the free motion of particles is affected by inertial forces originating from the curvature of the embedding space. Here we reveal a fundamental process underlying fluid dynamics in curved spaces: the free motion of fluids, in the complete absence of solid walls or obstacles, exhibits loss of energy due exclusively to the intrinsic curvature of space. We find that local sources of curvature generate viscous stresses as a result of the inertial forces. The curvature- induced viscous forces are shown to cause hitherto unnoticed and yet appreciable energy dissipation, which might play a significant role for a variety of physical systems involving fluid dynamics in curved spaces. PMID:28195148
Energy dissipation in flows through curved spaces
NASA Astrophysics Data System (ADS)
Debus, J.-D.; Mendoza, M.; Succi, S.; Herrmann, H. J.
2017-02-01
Fluid dynamics in intrinsically curved geometries is encountered in many physical systems in nature, ranging from microscopic bio-membranes all the way up to general relativity at cosmological scales. Despite the diversity of applications, all of these systems share a common feature: the free motion of particles is affected by inertial forces originating from the curvature of the embedding space. Here we reveal a fundamental process underlying fluid dynamics in curved spaces: the free motion of fluids, in the complete absence of solid walls or obstacles, exhibits loss of energy due exclusively to the intrinsic curvature of space. We find that local sources of curvature generate viscous stresses as a result of the inertial forces. The curvature- induced viscous forces are shown to cause hitherto unnoticed and yet appreciable energy dissipation, which might play a significant role for a variety of physical systems involving fluid dynamics in curved spaces.
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.
Vibrational resonance in an inhomogeneous medium with periodic dissipation
NASA Astrophysics Data System (ADS)
Roy-Layinde, T. O.; Laoye, J. A.; Popoola, O. O.; Vincent, U. E.; McClintock, P. V. E.
2017-09-01
The role of nonlinear dissipation in vibrational resonance (VR) is investigated in an inhomogeneous system characterized by a symmetric and spatially periodic potential and subjected to nonuniform state-dependent damping and a biharmonic driving force. The contributions of the parameters of the high-frequency signal to the system's effective dissipation are examined theoretically in comparison to linearly damped systems, for which the parameter of interest is the effective stiffness in the equation of slow vibration. We show that the VR effect can be enhanced by varying the nonlinear dissipation parameters and that it can be induced by a parameter that is shared by the damping inhomogeneity and the system potential. Furthermore, we have apparently identified the origin of the nonlinear-dissipation-enhanced response: We provide evidence of its connection to a Hopf bifurcation, accompanied by monotonic attractor enlargement in the VR regime.
The effects of dissipation on topological mechanical systems.
Xiong, Ye; Wang, Tianxiang; Tong, Peiqing
2016-09-08
We theoretically study the effects of isotropic dissipation in a topological mechanical system which is an analogue of Chern insulator in mechanical vibrational lattice. The global gauge invariance is still conserved in this system albeit it is destroyed by the dissipation in the quantum counterpart. The chiral edge states in this system are therefore robust against strong dissipation. The dissipation also causes a dispersion of damping for the eigenstates. It will modify the equation of motion of a wave packet by an extra effective force. After taking into account the Berry curvature in the wave vector space, the trace of a free wave packet in the real space should be curved, feinting to break the Newton's first law.
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.
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].
Asymptotic density and effective negligibility
NASA Astrophysics Data System (ADS)
Astor, Eric P.
In this thesis, we join the study of asymptotic computability, a project attempting to capture the idea that an algorithm might work correctly in all but a vanishing fraction of cases. In collaboration with Hirschfeldt and Jockusch, broadening the original investigation of Jockusch and Schupp, we introduce dense computation, the weakest notion of asymptotic computability (requiring only that the correct answer is produced on a set of density 1), and effective dense computation, where every computation halts with either the correct answer or (on a set of density 0) a symbol denoting uncertainty. A few results make more precise the relationship between these notions and work already done with Jockusch and Schupp's original definitions of coarse and generic computability. For all four types of asymptotic computation, including generic computation, we demonstrate that non-trivial upper cones have measure 0, building on recent work of Hirschfeldt, Jockusch, Kuyper, and Schupp in which they establish this for coarse computation. Their result transfers to yield a minimal pair for relative coarse computation; we generalize their method and extract a similar result for relative dense computation (and thus for its corresponding reducibility). However, all of these notions of near-computation treat a set as negligible iff it has asymptotic density 0. Noting that this definition is not computably invariant, this produces some failures of intuition and a break with standard expectations in computability theory. For instance, as shown by Hamkins and Miasnikov, the halting problem is (in some formulations) effectively densely computable, even in polynomial time---yet this result appears fragile, as indicated by Rybalov. In independent work, we respond to this by strengthening the approach of Jockusch and Schupp to avoid such phenomena; specifically, we introduce a new notion of intrinsic asymptotic density, invariant under computable permutation, with rich relations to both
Asymptotic safety, emergence and minimal length
NASA Astrophysics Data System (ADS)
Percacci, Roberto; Vacca, Gian Paolo
2010-12-01
There seems to be a common prejudice that asymptotic safety is either incompatible with, or at best unrelated to, the other topics in the title. This is not the case. In fact, we show that (1) the existence of a fixed point with suitable properties is a promising way of deriving emergent properties of gravity, and (2) there is a sense in which asymptotic safety implies a minimal length. In doing so we also discuss possible signatures of asymptotic safety in scattering experiments.
Every composition operator is (mean) asymptotically Toeplitz
NASA Astrophysics Data System (ADS)
Shapiro, Joel H.
2007-09-01
Nazarov and Shapiro recently showed that, while composition operators on the Hardy space H2 can only trivially be Toeplitz, or even "Toeplitz plus compact," it is an interesting problem to determine which of them can be "asymptotically Toeplitz." I show here that if "asymptotically" is interpreted in, for example, the Cesaro (C,[alpha]) sense ([alpha]>0), then every composition operator on H2 becomes asymptotically Toeplitz.
Energy dissipation of moved magnetic vortices
NASA Astrophysics Data System (ADS)
Magiera, Martin P.
2013-09-01
A two-dimensional easy-plane ferromagnetic substrate, interacting with a dipolar tip which is magnetised perpendicularly with respect to the easy plane is studied numerically by solving the Landau-Lifshitz Gilbert equation. The dipolar tip stabilises a vortex structure which is dragged through the system and dissipates energy. An analytical expression for the friction force in the v {\\rightarrow} 0 limit based on the Thiele equation is presented. The limitations of this result which predicts a diverging friction force in the thermodynamic limit, are demonstrated by a study of the size dependence of the friction force. While for small system sizes the dissipation depends logarithmically on the system size, it saturates at a specific velocity-dependent value. This size can be regarded as an effective vortex size and it is shown how this effective vortex size agrees with the infinite extension of a vortex in the thermodynamic limit. A magnetic friction number is defined which represents a general criterion for the validity of the Thiele equation and quantifies the degree of nonlinearity in the response of a driven spin configuration.
Asymptotic and Fredholm representations of discrete groups
NASA Astrophysics Data System (ADS)
Manuilov, V. M.; Mishchenko, A. S.
1998-10-01
A C^*-algebra servicing the theory of asymptotic representations and its embedding into the Calkin algebra that induces an isomorphism of K_1-groups is constructed. As a consequence, it is shown that all vector bundles over the classifying space B\\pi that can be obtained by means of asymptotic representations of a discrete group \\pi can also be obtained by means of representations of the group \\pi \\times {\\mathbb Z} into the Calkin algebra. A generalization of the concept of Fredholm representation is also suggested, and it is shown that an asymptotic representation can be regarded as an asymptotic Fredholm representation.
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.
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.
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.
Transient Dissipation and Structural Costs of Physical Information Transduction
NASA Astrophysics Data System (ADS)
Boyd, Alexander B.; Mandal, Dibyendu; Riechers, Paul M.; Crutchfield, James P.
2017-06-01
A central result that arose in applying information theory to the stochastic thermodynamics of nonlinear dynamical systems is the information-processing second law (IPSL): the physical entropy of the Universe can decrease if compensated by the Shannon-Kolmogorov-Sinai entropy change of appropriate information-carrying degrees of freedom. In particular, the asymptotic-rate IPSL precisely delineates the thermodynamic functioning of autonomous Maxwellian demons and information engines. How do these systems begin to function as engines, Landauer erasers, and error correctors? We identify a minimal, and thus inescapable, transient dissipation of physical information processing, which is not captured by asymptotic rates, but is critical to adaptive thermodynamic processes such as those found in biological systems. A component of transient dissipation, we also identify an implementation-dependent cost that varies from one physical substrate to another for the same information processing task. Applying these results to producing structured patterns from a structureless information reservoir, we show that "retrodictive" generators achieve the minimal costs. The results establish the thermodynamic toll imposed by a physical system's structure as it comes to optimally transduce information.
The asymptotic degrees of freedom of fluid flows
Foias, C.
1990-09-01
We have obtained rigorous estimates for the attractors of some basic dissipative differential equations which are within the physical or numerical ranges (e.g. 2D Navier-Stokes equations). We have shown that the ring laser cavity equations have a finite dimensional attractor. We have constructed inertial manifolds for a large class of dissipative differential equations (e.g. Kuramoto-Sivashinsky and Ginzberg-Landau equations). For a large class of equations including the 2D Navier-Stokes equations we have introduced several approximate intertial manifolds which yield new approximative ordinary differential equations with better error estimates then those of the usual Galerkin approximations. We have evidence that the new approximating schemes lead to computational improvements upon the Galerkin schemes. We have given a normal form for the Navier-Stokes which allows the explicit asymptotic integration of the equations. We have also proposed a new theoretical approach to decaying homogeneous turbulence. We also made some contribution to robust control theory which may be relevant to fluid dynamics.
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.
Planar radial weakly dissipative diffeomorphisms.
Simó, C; Vieiro, A
2010-12-01
We study the effect of a small dissipative radial perturbation acting on a one parameter family of area preserving diffeomorphisms. This is a specific type of dissipative perturbation. The interest is on the global effect of the dissipation on a fixed domain around an elliptic fixed/periodic point of the family, rather than on the effects around a single resonance. We describe the local/global bifurcations observed in the transition from the conservative to a weakly dissipative case: the location of the resonant islands, the changes in the domains of attraction of the foci inside these islands, how the resonances disappear, etc. The possible ω-limits are determined in each case. This topological description gives rise to three different dynamical regimes according to the size of dissipative perturbation. Moreover, we determine the conservative limit of the probability of capture in a generic resonance from the interpolating flow approximation, hence assuming no homoclinics in the resonance. As a paradigm of weakly dissipative radial maps, we use a dissipative version of the Hénon map. © 2010 American Institute of Physics.
Asymptotic Behavior in Liquid Drop Coalescence
NASA Astrophysics Data System (ADS)
Paulsen, Joseph; Burton, Justin; Nagel, Sidney; Appathurai, Santosh; Harris, Michael; Basaran, Osman
2012-02-01
During coalescence, two drops first touch and then merge, as a liquid bridge grows from initially microscopic scales to a macroscopic size comparable to the drop diameter. The initial dynamics of coalescence are expected to be universal, owing to a singularity in the Laplace pressure, which diverges when the curvature of the liquid interface is infinite at the point where the drops first touch. Conventionally, this process has been thought to have just two regimes: a highly viscous one dominated by macroscopic flows pulling the two drops together and an inertial one described by local deformations near the growing neck. We use high-speed imaging, electrical measurements and full Navier-Stokes simulations to reveal a new regime that dominates the asymptotic dynamics of coalescence for any finite viscosity. The character of this new regime improves our understanding of the unexpectedly late viscous-to-inertial crossover [1]. An argument based on force balance and an appropriate choice of length-scales allow the construction of a new phase diagram of coalescence.[4pt] [1] J. D. Paulsen, J. C. Burton, S. R. Nagel, PRL 106, 114501 (2011).
Thermal dissipation in quantum turbulence.
Kobayashi, Michikazu; Tsubota, Makoto
2006-10-06
The microscopic mechanism of thermal dissipation in quantum turbulence is numerically studied by solving the coupled system involving the Gross-Pitaevskii equation and the Bogoliubov-de Gennes equation. At low temperatures, the obtained dissipation does not work at scales greater than the vortex core size. However, as the temperature increases, dissipation works at large scales and it affects the vortex dynamics. We successfully obtain the mutual friction coefficients of the vortex in dilute Bose-Einstein condensates dynamics as functions of temperature.
Thermal Dissipation in Quantum Turbulence
Kobayashi, Michikazu; Tsubota, Makoto
2006-10-06
The microscopic mechanism of thermal dissipation in quantum turbulence is numerically studied by solving the coupled system involving the Gross-Pitaevskii equation and the Bogoliubov-de Gennes equation. At low temperatures, the obtained dissipation does not work at scales greater than the vortex core size. However, as the temperature increases, dissipation works at large scales and it affects the vortex dynamics. We successfully obtain the mutual friction coefficients of the vortex in dilute Bose-Einstein condensates dynamics as functions of temperature.
Einstein-Yang-Mills theory: Asymptotic symmetries
NASA Astrophysics Data System (ADS)
Barnich, Glenn; Lambert, Pierre-Henry
2013-11-01
Asymptotic symmetries of the Einstein-Yang-Mills system with or without cosmological constant are explicitly worked out in a unified manner. In agreement with a recent conjecture, one finds a Virasoro-Kac-Moody type algebra not only in three dimensions but also in the four-dimensional asymptotically flat case.
On SLλ(I)-asymptotically statistical equivalent sequences
NASA Astrophysics Data System (ADS)
Gumus, Hafize; Savas, Ekrem
2012-09-01
This paper presents the notion of SLλ(I)-asymptotically statistical equivalence which is a natural combination of asymptotic I-equivalence and λ-statistical equivalence. We find its relation to I-asymptotically statistical convergence, strong λI-asymptotically equivalence and strong Cesàro I-asymptotically equivalence.
Nonlocal dynamics of dissipative phononic fluids
NASA Astrophysics Data System (ADS)
Nemati, Navid; Lee, Yoonkyung E.; Lafarge, Denis; Duclos, Aroune; Fang, Nicholas
2017-06-01
We describe the nonlocal effective properties of a two-dimensional dissipative phononic crystal made by periodic arrays of rigid and motionless cylinders embedded in a viscothermal fluid such as air. The description is based on a nonlocal theory of sound propagation in stationary random fluid/rigid media that was proposed by Lafarge and Nemati [Wave Motion 50, 1016 (2013), 10.1016/j.wavemoti.2013.04.007]. This scheme arises from a deep analogy with electromagnetism and a set of physics-based postulates including, particularly, the action-response procedures, whereby the effective density and bulk modulus are determined. Here, we revisit this approach, and clarify further its founding physical principles through presenting it in a unified formulation together with the two-scale asymptotic homogenization theory that is interpreted as the local limit. Strong evidence is provided to show that the validity of the principles and postulates within the nonlocal theory extends to high-frequency bands, well beyond the long-wavelength regime. In particular, we demonstrate that up to the third Brillouin zone including the Bragg scattering, the complex and dispersive phase velocity of the least-attenuated wave in the phononic crystal which is generated by our nonlocal scheme agrees exactly with that reproduced by a direct approach based on the Bloch theorem and multiple scattering method. In high frequencies, the effective wave and its associated parameters are analyzed by treating the phononic crystal as a random medium.
Tidal Energy Dissipation over long Geological Time Scales
NASA Astrophysics Data System (ADS)
Daher, H.; Adcroft, A.; Ansong, J. K.; Arbic, B. K.; Austermann, J.; Mitrovica, J. X.; Maloof, A. C.
2016-02-01
Over most of the history of the Earth-Moon system, tidal dissipation has been substantially lower than it is today. This is somewhat perplexing because in the past the moon was closer to the Earth and therefore tidal forces were larger. Previous work on this problem, done with highly idealized models, has shown that tidal dissipation is sensitive to Earth's rotation rate and the configuration of continents, which together set the time scale of the ocean's normal modes and hence their degree of resonance with the tidal forcing. Here, we employ a state-of-the-art global high-resolution ocean model, forced by the M2 tidal constituent, to explore the history of tidal resonance in a model with realistic bathymetries and continental geometries. Increasing Earth's rotation rate, while keeping geometries and bathymetries fixed to present-day values, yields substantially lower dissipation rates, consistent with the results of idealized models. We also show results from simulations with different continental configurations, increased tidal forcings, and smoother coastlines that mimic hundreds of millions of years without glacioeustasy in the Archaean and Proterozoic, to help unravel the puzzle of tidal dissipation over long geological time scales.
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.
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. ...
Non-Dissipative Structural Evolutions in Granular Materials
NASA Astrophysics Data System (ADS)
Pouragha, Mehdi; Wan, Richard
2017-06-01
The structure of the contact network in granular assemblies can evolve due to either dissipative mechanisms such as sliding at contact points, or non-dissipative mechanisms through the phenomenon of contact gain and loss. Being associated with negligible deformations, non-dissipative mechanisms is actually active even in the small strain range of 10-3, especially in the case of densely packed assemblies. Hence, from a constitutive modelling point of view, it is crucial to be able to estimate such non-dissipative evolutions since both elastic and plastic properties of granular assemblies highly depend on contact network characteristics. The current study proposes an analytical scheme that allows us to estimate the non-dissipative contact gain/loss regime in terms of directional changes in the average contact force. The probability distribution of contact forces is used to compute the number of lost contact for each direction. Similarly, the number of newly formed contacts is estimated by considering the probability distribution of the gap between neighbouring particles. Based on the directional contact gain/loss computed, the changes in coordination number and fabric anisotropy can be found which, together with statistical treatments of Love-Weber stress expression, form a complete system of equations describing the evolution of other controlling microvariables. Finally, the results of the calculations have been compared with DEM simulations which verify the accuracy of the proposed scheme.
Dissipation, interaction, and relative entropy.
Gaveau, B; Granger, L; Moreau, M; Schulman, L S
2014-03-01
Many thermodynamic relations involve inequalities, with equality if a process does not involve dissipation. In this article we provide equalities in which the dissipative contribution is shown to involve the relative entropy (also called the Kullback-Leibler divergence). The processes considered are general time evolutions in both classical and quantum mechanics, and the initial state is sometimes thermal, sometimes partially so. As an application, the relative entropy is related to transport coefficients.
Power dissipation in automotive suspensions
NASA Astrophysics Data System (ADS)
Smith, Malcolm C.; Swift, Stuart J.
2011-02-01
For a standard quarter-car vehicle model and a road disturbance whose velocity profile is white noise, it is shown that the power dissipated in the suspension is proportional to the tyre vertical stiffness and the noise intensity, but is independent of all masses and suspension parameters. The dependence of this result on the modelling assumptions is explored. It is shown that the road disturbance model is ill-posed for the computation of power dissipation in the tyre and a modification is suggested. Computational results then indicate that the total power dissipation is still very insensitive to variations in vehicle and suspension parameters, but not tyre parameters, even though the suspension power dissipation and the tyre power dissipation vary individually. The extension of the result to half-car vehicle models is also considered. For both the pitch-plane and roll-plane models, it is found from numerical examples that the broad conclusion of large dependence of the total power dissipation on tyre parameters and small dependence on all other parameters remains. A brief discussion is included on the contribution to power loss due to rolling resistance.
Nonlinear Localized Dissipative Structures for Long-Time Solution of Wave Equation
2009-07-01
Fatemi, E., Engquist, B., and Osher, S., " Numerical Solution of the High Frequency Asymptotic Expansion for the Scalar Wave Equation ", Journal of...FINAL REPORT Grant Title: Nonlinear Localized Dissipative Structures for Long-Time Solution of Wave Equation By Dr. John Steinhoff Grant number... numerical method, "Wave Confinement" (WC), is developed to efficiently solve the linear wave equation . This is similar to the originally developed
NASA Astrophysics Data System (ADS)
Notari, Alessio; Tywoniuk, Konrad
2016-12-01
We analyze in detail the background cosmological evolution of a scalar field coupled to a massless abelian gauge field through an axial term phi/fγ F ~F, such as in the case of an axion. Gauge fields in this case are known to experience tachyonic growth and therefore can backreact on the background as an effective dissipation into radiation energy density ρR, which can lead to inflation without the need of a flat potential. We analyze the system, for momenta k smaller than the cutoff fγ, including the backreaction numerically. We consider the evolution from a given static initial condition and explicitly show that, if fγ is smaller than the field excursion phi0 by about a factor of at least Script O (20), there is a friction effect which turns on before the field can fall down and which can then lead to a very long stage of inflation with a generic potential. In addition we find superimposed oscillations, which would get imprinted on any kind of perturbations, scalars and tensors. Such oscillations have a period of 4-5 efolds and an amplitude which is typically less than a few percent and decreases linearly with fγ. We also stress that the curvature perturbation on uniform density slices should be sensitive to slow-roll parameters related to ρR rather than dot phi2/2 and we discuss the existence of friction terms acting on the perturbations, although we postpone a calculation of the power spectrum and of non-gaussianity to future work and we simply define and compute suitable slow roll parameters. Finally we stress that this scenario may be realized in the axion case, if the coupling 1/fγ to U(1) (photons) is much larger than the coupling 1/fG to non-abelian gauge fields (gluons), since the latter sets the range of the potential and therefore the maximal allowed phi0~ fG.
Asymptotics of Simple Branching Populations
NASA Astrophysics Data System (ADS)
Huillet, Thierry; Kłopotowski, Andrzej; Porzio, Anna
1995-09-01
In this paper we study a simple deterministic tree structure: an initial individual generates a finite number of offspring, each of which has given integer valued lifetime, iterating the same procedure when dying. Three asymptotic distributions of this asynchronous deterministic branching procedure are considered: the generation distribution, the ability of individuals to generate offspring and the age distribution. Thermodynamic formalism is then developped to reveal the multifractal nature of the mass splitting associated to our process. On considère l'itération d'une structure déterministe arborescente selon laquelle un ancêtre engendre un nombre fini de descendants dont la durée de vie (à valeurs entières) est donnée. Dans un premier temps on s'intéresse aux trois distributions asymptotiques suivantes : répartition des générations, aptitude à engendrer des descendants et répartition selon l'âge. Ensuite nous développons le formalisme thermodynamique pour mettre en évidence le caractère multifractal de la scission d'une masse unitaire associée à cette arborescence.
Asymptotic Potential for Simulated Annealing.
NASA Astrophysics Data System (ADS)
Jones, Philip Andrew
1995-01-01
Potential theory is an important area of mathematical physics which has been intensively studied in the areas of partial differential equations and probability. The purpose of this thesis is to develop a potential theory for the time-inhomogeneous Markov chains defined by simulated annealing. First the notion of global recurrence orders is extended to that of global recurrence functions. Then this idea is condensed to local attractors (cups), resulting in improved and sharper estimates for the exit probabilities. For each cup, the weighted activity of a point in the cup is considered, that is the value of sum_sp {n=m}{sigma}lambda_sp {n}{c}P(X_ n=x) for a suitable value of c. Here sigma is the exit time from the cup, representing our localized viewpoint. The convergence as m goes to infinity is considered, the result having many properties of classical potentials, and hence is called the asymptotic potential. A consequence is to simplify previous results and produce calculable constants for estimates. This is important for practical applications where such knowledge is often required and used.
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.
Dynamics of nonlinear dissipative systems in the vicinity of resonance
NASA Astrophysics Data System (ADS)
Plaksiy, K. Y.; Mikhlin, Y. V.
2015-01-01
The behavior of nonlinear dissipative 2-DOF mechanical systems in the vicinity of resonance is studied in this paper. Namely, the free resonance vibrations of a spring-mass-pendulum system and the forced resonance vibrations of a 2-DOF dissipative system containing a nonlinear absorber are considered. A reduced system stated with respect to the system energy, the arctangent of the vibration amplitudes ratio, and the phase difference, is obtained and analyzed. The nonlinear normal mode approach is used in this analysis. Conditions for vibration energy localization are discussed.
Dissipation in small systems: Landau-Zener approach
NASA Astrophysics Data System (ADS)
Barra, Felipe; Esposito, Massimiliano
2016-06-01
We establish a stochastic thermodynamics for a Fermionic level driven by a time-dependent force and interacting with initially thermalized levels playing the role of a reservoir. The driving induces consecutive avoided crossings between system and reservoir levels described within Landau-Zener theory. We derive the resulting system dynamics and thermodynamics and identify energy, work, heat, entropy, and dissipation. Our theory perfectly reproduces the numerically exact quantum work statistics obtained using a two point measurements approach of the total energy and provides an explicit expression for the dissipation in terms of diabatic transitions.
Dissipation in small systems: Landau-Zener approach.
Barra, Felipe; Esposito, Massimiliano
2016-06-01
We establish a stochastic thermodynamics for a Fermionic level driven by a time-dependent force and interacting with initially thermalized levels playing the role of a reservoir. The driving induces consecutive avoided crossings between system and reservoir levels described within Landau-Zener theory. We derive the resulting system dynamics and thermodynamics and identify energy, work, heat, entropy, and dissipation. Our theory perfectly reproduces the numerically exact quantum work statistics obtained using a two point measurements approach of the total energy and provides an explicit expression for the dissipation in terms of diabatic transitions.
Particle creation in asymptotically Minkowskian spacetimes
NASA Astrophysics Data System (ADS)
Moradi, Shahpoor
2009-02-01
Exact solutions of Klein-Gordon and Dirac equations are obtained for two classes of Robertson-Walker (RW) spacetimes with asymptotically Minkowskian regions. One class is Minkowskian in the remote past and future. In this class in and out vacua are well defined, because the scale factor reduces to a constant at the asymptotic regions. Another class is asymptotically flat only in the far past. Using the obtained exact solutions we calculate the density of scalar and Dirac particles created through the Bogolubov transformations technique. For Dirac field it is shown that the rates of creation of particles and antiparticles are equal.
Renormalized asymptotic enumeration of Feynman diagrams
NASA Astrophysics Data System (ADS)
Borinsky, Michael
2017-10-01
A method to obtain all-order asymptotic results for the coefficients of perturbative expansions in zero-dimensional quantum field is described. The focus is on the enumeration of the number of skeleton or primitive diagrams of a certain QFT and its asymptotics. The procedure heavily applies techniques from singularity analysis. To utilize singularity analysis, a representation of the zero-dimensional path integral as a generalized hyperelliptic curve is deduced. As applications the full asymptotic expansions of the number of disconnected, connected, 1PI and skeleton Feynman diagrams in various theories are given.
Mixing and dissipation in a geostrophic buoyancy-driven circulation
NASA Astrophysics Data System (ADS)
Vreugdenhil, Catherine A.; Gayen, Bishakhdatta; Griffiths, Ross W.
2016-08-01
Turbulent mixing and energy dissipation have important roles in the global circulation but are not resolved by ocean models. We use direct numerical simulations of a geostrophic circulation, resolving turbulence and convection, to examine the rates of dissipation and mixing. As a starting point, we focus on circulation in a rotating rectangular basin forced by a surface temperature difference but no wind stress. Emphasis is on the geostrophic regime for the horizontal circulation, but also on the case of strong buoyancy forcing (large Rayleigh number), which implies a turbulent convective boundary layer. The computed results are consistent with existing scaling theory that predicts dynamics and heat transport dependent on the relative thicknesses of thermal and Ekman boundary layers, hence on the relative roles of buoyancy and rotation. Scaling theory is extended to describe the volume-integrated rate of mixing, which is proportional to heat transport and decreases with increasing rotation rate or decreasing temperature difference. In contrast, viscous dissipation depends crucially on whether the thermal boundary layer is laminar or turbulent, with no direct Coriolis effect on the turbulence unless rotation is extremely strong. For strong forcing, in the geostrophic regime, the mechanical energy input from buoyancy goes primarily into mixing rather than dissipation. For a buoyancy-driven circulation in a basin comparable to the North Atlantic we estimate that the total rate of mixing accounts for over 95% of the mechanical energy supply, implying that buoyancy is an efficient driver of mixing in the oceans.
NASA Astrophysics Data System (ADS)
Zhang, Junshi; Chen, Hualing; Li, Dichen
2017-09-01
Subject to a high voltage, leakage current and induced electrical energy dissipation inevitably occur during the actuation of dielectric elastomers (DEs). In this article, a theoretical model is developed to investigate the dissipative performance of DEs in dynamic actuation. Effects of three different actuation conditions, including DE materials’ viscoelasticity intensity, amplitude of applied voltage, and mechanical tensile force, are considered. Numerical calculations are employed to detect the dynamic dissipative performance of DEs including leakage current, electrical power density, and electrical energy density in certain vibrational periods. Leakage current and induced electrical energy dissipation are enhanced with the enlargement of amplitude of applied voltage and mechanical force, and are suppressed as the intensity of DEs’ viscoelastic creep increases. The electrical energy for dissipation and actuation is also analyzed and compared.
Modelling thrombosis using dissipative particle dynamics method
Filipovic, N; Kojic, M; Tsuda, A
2008-01-01
Aim. Arterial occlusion is a leading cause of cardiovascular disease. The main mechanism causing vessel occlusion is thrombus formation, which may be initiated by the activation of platelets. The focus of this study is on the mechanical aspects of platelet-mediated thrombosis which includes the motion, collision, adhesion and aggregation of activated platelets in the blood. A review of the existing continuum-based models is given. A mechanical model of platelet accumulation onto the vessel wall is developed using the dissipative particle dynamics (DPD) method in which the blood (i.e. colloidal-composed medium) is treated as a group of mesoscale particles interacting through conservative, dissipative, attractive and random forces. Methods. Colloidal fluid components (plasma and platelets) are discretized by mesoscopic (micrometre-size) particles that move according to Newton's law. The size of each mesoscopic particle is small enough to allow tracking of each constituent of the colloidal fluid, but significantly larger than the size of atoms such that, in contrast to the molecular dynamics approach, detailed atomic level analysis is not required. Results. To test this model, we simulated the deposition of platelets onto the wall of an expanded tube and compared our computed results with the experimental data of Karino et al. (Miscrovasc. Res. 17, 238–269, 1977). By matching our simulations to the experimental results, the platelet aggregation/adhesion binding force (characterized by an effective spring constant) was determined and found to be within a physiologically reasonable range. Conclusion. Our results suggest that the DPD method offers a promising new approach to the modelling of platelet-mediated thrombosis. The DPD model includes interaction forces between platelets both when they are in the resting state (non-activated) and when they are activated, and therefore it can be extended to the analysis of kinetics of binding and other phenomena relevant to
Wave dissipation by muddy seafloors
NASA Astrophysics Data System (ADS)
Elgar, Steve; Raubenheimer, Britt
2008-04-01
Muddy seafloors cause tremendous dissipation of ocean waves. Here, observations and numerical simulations of waves propagating between 5- and 2-m water depths across the muddy Louisiana continental shelf are used to estimate a frequency- and depth-dependent dissipation rate function. Short-period sea (4 s) and swell (7 s) waves are shown to transfer energy to long-period (14 s) infragravity waves, where, in contrast with theories for fluid mud, the observed dissipation rates are highest. The nonlinear energy transfers are most rapid in shallow water, consistent with the unexpected strong increase of the dissipation rate with decreasing depth. These new results may explain why the southwest coast of India offers protection for fishing (and for the 15th century Portuguese fleet) only after large waves and strong currents at the start of the monsoon move nearshore mud banks from about 5- to 2-m water depth. When used with a numerical nonlinear wave model, the new dissipation rate function accurately simulates the large reduction in wave energy observed in the Gulf of Mexico.
Asymptotic unbounded root loci - Formulas and computation
NASA Technical Reports Server (NTRS)
Sastry, S. S.; Desoer, C. A.
1983-01-01
A new geometric way of computing the asymptotic behavior of unbounded root loci of a strictly proper linear time-invariant control system as loop gain goes to infinity is presented. Properties of certain restricted linear maps and nested restrictions of linear maps are developed, and formulas are obtained for the leading coefficient of the asymptotic values of the unbounded multivariable root loci are obtained in terms of eigenvalues of those maps. Published results and a certain simple null structure assumption are used to relate these asymptotic values to the structure at infinity of the Smith-McMillan form of the open loop transfer function. Explicit matrix formulas for the more abstract derived formulas are given and additional geometric insights are developed with orthogonal projections and singular value decomposition. Formulas for the pivots of the unbounded root loci are calculated and shown to have the same form as the coefficients of the unbounded asymptotic root loci.
On asymptotically generalized statistical equivalent set sequences
NASA Astrophysics Data System (ADS)
Savas, Ekrem
2013-10-01
In this paper we shall study the asymptotically λ-statistical equivalent (Wijsman sense) of multiple L. In addition to these definition, natural inclusion theorems shall also be presented. This approach has not been considered in any context before.
Asymptotic unbounded root loci - Formulas and computation
NASA Technical Reports Server (NTRS)
Sastry, S. S.; Desoer, C. A.
1983-01-01
A new geometric way of computing the asymptotic behavior of unbounded root loci of a strictly proper linear time-invariant control system as loop gain goes to infinity is presented. Properties of certain restricted linear maps and nested restrictions of linear maps are developed, and formulas are obtained for the leading coefficient of the asymptotic values of the unbounded multivariable root loci are obtained in terms of eigenvalues of those maps. Published results and a certain simple null structure assumption are used to relate these asymptotic values to the structure at infinity of the Smith-McMillan form of the open loop transfer function. Explicit matrix formulas for the more abstract derived formulas are given and additional geometric insights are developed with orthogonal projections and singular value decomposition. Formulas for the pivots of the unbounded root loci are calculated and shown to have the same form as the coefficients of the unbounded asymptotic root loci.
Asymptotic Poincare lemma and its applications
Ziolkowski, R.W.; Deschamps, G.A.
1984-05-01
An asymptotic version of Poincare's lemma is defined and solutions are obtained with the calculus of exterior differential forms. They are used to construct the asymptotic approximations of multidimensional oscillatory integrals whose forms are commonly encountered, for example, in electromagnetic problems. In particular, the boundary and stationary point evaluations of these integrals are considered. The former is applied to the Kirchhoff representation of a scalar field diffracted through an aperture and simply recovers the Maggi-Rubinowicz-Miyamoto-Wolf results. Asymptotic approximations in the presence of other (standard) critical points are also discussed. Techniques developed for the asymptotic Poincare lemma are used to generate a general representation of the Leray form. All of the (differential form) expressions presented are generalizations of known (vector calculus) results. 14 references, 4 figures.
Prodanovic, Srdjan; Gracewski, Sheryl; Nam, Jong-Hoon
2015-01-01
The stereocilia bundle is the mechano-transduction apparatus of the inner ear. In the mammalian cochlea, the stereocilia bundles are situated in the subtectorial space (STS)—a micrometer-thick space between two flat surfaces vibrating relative to each other. Because microstructures vibrating in fluid are subject to high-viscous friction, previous studies considered the STS as the primary place of energy dissipation in the cochlea. Although there have been extensive studies on how metabolic energy is used to compensate the dissipation, much less attention has been paid to the mechanism of energy dissipation. Using a computational model, we investigated the power dissipation in the STS. The model simulates fluid flow around the inner hair cell (IHC) stereocilia bundle. The power dissipation in the STS because of the presence IHC stereocilia increased as the stimulating frequency decreased. Along the axis of the stimulating frequency, there were two asymptotic values of power dissipation. At high frequencies, the power dissipation was determined by the shear friction between the two flat surfaces of the STS. At low frequencies, the power dissipation was dominated by the viscous friction around the IHC stereocilia bundle—the IHC stereocilia increased the STS power dissipation by 50- to 100-fold. There exists a characteristic frequency for STS power dissipation, CFSTS, defined as the frequency where power dissipation drops to one-half of the low frequency value. The IHC stereocilia stiffness and the gap size between the IHC stereocilia and the tectorial membrane determine the characteristic frequency. In addition to the generally assumed shear flow, nonshear STS flow patterns were simulated. Different flow patterns have little effect on the CFSTS. When the mechano-transduction of the IHC was tuned near the vibrating frequency, the active motility of the IHC stereocilia bundle reduced the power dissipation in the STS. PMID:25650916
Asymptotic Symmetries of Spacelike Stretched ADS Gravity
NASA Astrophysics Data System (ADS)
Blagojević, Milutin; Cvetković, Branislav
We study asymptotic symmetries in the spacelike stretched AdS sector of topologically massive gravity. The Poisson bracket algebra of the canonical generators is shown to be centrally extended semi-direct sum of the Virasoro and u(1) Kac-Moody algebra. By using the Sugawara construction, we prove that the asymptotic symmetry coincides with the conformal symmetry, described by two independent Virasoro algebras with central charges.
Preconditioning via asymptotically-defined domain decomposition
Ashby, S.F.; Kelley, C.T.; Scroggs, J.S.; Saylor, P.E.
1994-06-01
Asymptotic analysis is used to derive preconditioners based on operator splitting and domain decomposition for the numerical solution of the advection-diffusion equation. Specifically, asymptotics is used to identify subdomains in which the solution is dominated by a certain operator, and this information is used to construct an effective preconditioner. The authors analyze the one-dimensional case in a function space setting and present numerical results for both one and two dimensions.
Nanomechanical dissipation at a tip-induced Kondo onset
NASA Astrophysics Data System (ADS)
Baruselli, Pier Paolo; Fabrizio, Michele; Tosatti, Erio
2017-08-01
The onset or demise of Kondo effect in a magnetic impurity on a metal surface can be triggered, as sometimes observed, by the simple mechanical nudging of a tip. Such a mechanically driven quantum phase transition must reflect in a corresponding mechanical dissipation peak; yet, this kind of signature has not been focused upon so far. Aiming at the simplest theoretical modeling, we treat the impurity as an Anderson impurity model, the tip action as a hybridization switching, and solve the problem by numerical renormalization group. Studying this model as function of temperature and magnetic field we are able to isolate the Kondo contribution to dissipation. While that is, reasonably, of the order of the Kondo energy, its temperature evolution shows a surprisingly large tail even above the Kondo temperature. The detectability of Kondo mechanical dissipation in atomic force microscopy is also discussed.
Classical counterparts of quantum attractors in generic dissipative systems.
Carlo, Gabriel G; Ermann, Leonardo; Rivas, Alejandro M F; Spina, María E; Poletti, Dario
2017-06-01
In the context of dissipative systems, we show that for any quantum chaotic attractor a corresponding classical chaotic attractor can always be found. We provide a general way to locate them, rooted in the structure of the parameter space (which is typically bidimensional, accounting for the forcing strength and dissipation parameters). In cases where an approximate pointlike quantum distribution is found, it can be associated with exceptionally large regular structures. Moreover, supposedly anomalous quantum chaotic behavior can be very well reproduced by the classical dynamics plus Gaussian noise of the size of an effective Planck constant ℏ_{eff}. We give support to our conjectures by means of two paradigmatic examples of quantum chaos and transport theory. In particular, a dissipative driven system becomes fundamental in order to extend their validity to generic cases.
Response of driven sessile drops with contact-line dissipation.
Bostwick, Joshua B; Steen, Paul H
2016-11-04
A partially-wetting sessile drop is driven by a sinusoidal pressure field that produces capillary waves on the liquid/gas interface. Response diagrams and phase shifts for the droplet, whose contact-line moves with contact-angle that is a smooth function of the contact line speed, are reported. Contact-line dissipation originating from the contact-line speed condition leads to damping for drops with finite contact-line mobility, even for inviscid fluids. The critical mobility and associated driving frequency to generate the largest contact-line dissipation is computed. Viscous dissipation is approximated using the irrotational flow and the critical Ohnesorge number bounding regions beyond which a given mode becomes over-damped is computed. Regions of modal coexistence where two modes can be simultaneously excited by a single forcing frequency are identified. Predictions compare favorably to related experiments on vibrated drops.
DISSIPATIVE DIVERGENCE OF RESONANT ORBITS
Batygin, Konstantin; Morbidelli, Alessandro
2013-01-01
A considerable fraction of multi-planet systems discovered by the observational surveys of extrasolar planets reside in mild proximity to first-order mean-motion resonances. However, the relative remoteness of such systems from nominal resonant period ratios (e.g., 2:1, 3:2, and 4:3) has been interpreted as evidence for lack of resonant interactions. Here, we show that a slow divergence away from exact commensurability is a natural outcome of dissipative evolution and demonstrate that libration of critical angles can be maintained tens of percent away from nominal resonance. We construct an analytical theory for the long-term dynamical evolution of dissipated resonant planetary pairs and confirm our calculations numerically. Collectively, our results suggest that a significant fraction of the near-commensurate extrasolar planets are in fact resonant and have undergone significant dissipative evolution.
Model of dissipative dielectric elastomers
NASA Astrophysics Data System (ADS)
Chiang Foo, Choon; Cai, Shengqiang; Jin Adrian Koh, Soo; Bauer, Siegfried; Suo, Zhigang
2012-02-01
The dynamic performance of dielectric elastomer transducers and their capability of electromechanical energy conversion are affected by dissipative processes, such as viscoelasticity, dielectric relaxation, and current leakage. This paper describes a method to construct a model of dissipative dielectric elastomers on the basis of nonequilibrium thermodynamics. We characterize the state of the dielectric elastomer with kinematic variables through which external loads do work, and internal variables that measure the progress of the dissipative processes. The method is illustrated with examples motivated by existing experiments of polyacrylate very-high-bond dielectric elastomers. This model predicts the dynamic response of the dielectric elastomer and the leakage current behavior. We show that current leakage can be significant under large deformation and for long durations. Furthermore, current leakage can result in significant hysteresis for dielectric elastomers under cyclic voltage.
Iacocca, Ezio; Dumas, Randy K; Bookman, Lake; Mohseni, Majid; Chung, Sunjae; Hoefer, Mark A; Akerman, Johan
2014-01-31
Magnetic dissipative droplets are localized, strongly nonlinear dynamical modes excited in nanocontact spin valves with perpendicular magnetic anisotropy. These modes find potential application in nanoscale structures for magnetic storage and computation, but dissipative droplet studies have so far been limited to extended thin films. Here, numerical and asymptotic analyses are used to demonstrate the existence and properties of novel solitons in confined structures. As a nanowire's width is decreased with a nanocontact of fixed size at its center, the observed modes undergo transitions from a fully localized two-dimensional droplet into a two-dimensional droplet edge mode and then a pulsating one-dimensional droplet. These solitons are interpreted as dissipative versions of classical, conservative solitons, allowing for an analytical description of the modes and the mechanisms of bifurcation. The presented results open up new possibilities for the study of low-dimensional solitons and droplet applications in nanostructures.
Tumbling asteroid rotation with the YORP torque and inelastic energy dissipation
NASA Astrophysics Data System (ADS)
Breiter, S.; Murawiecka, M.
2015-05-01
The Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect and rotational energy dissipation due to inelastic deformations are two key mechanisms affecting rotation of tumbling asteroids in long term. Each of the effects used to be discussed separately. We present the first results concerning a simulation of their joint action. Asteroids (3103) Eger and (99942) Apophis, as well as their scaled variants, are used as test bodies. Plugging in the dissipation destroys limit cycles of the pure YORP, but creates a new asymptotic state of stationary tumbling with a fixed rotation period. The present model does not contradict finding Eger in the principal axis rotation. For Apophis, the model suggests that its current rotation state should be relatively young. In general, the fraction of initial conditions leading to the principal axis rotation is too small, compared to the actual data. The model requires a stronger energy dissipation and weaker YORP components in the nutation angle and obliquity.
Parameter estimation in the presence of the most general Gaussian dissipative reservoir
NASA Astrophysics Data System (ADS)
Jarzyna, Marcin; Zwierz, Marcin
2017-01-01
We analyze the performance of quantum parameter estimation in the presence of the most general Gaussian dissipative reservoir. We derive lower bounds on the precision of phase estimation and a closely related problem of frequency estimation. For both problems we show that it is impossible to achieve the Heisenberg limit asymptotically in the presence of such a reservoir. However, we also find that for any fixed number of probes used in the setup there exists a Gaussian dissipative reservoir, which, in principle, allows for the Heisenberg-limited performance for that number of probes. We discuss a realistic implementation of a frequency estimation scheme in the presence of a Gaussian dissipative reservoir in a cavity system.
Quantum dissipative Rashba spin ratchets.
Smirnov, Sergey; Bercioux, Dario; Grifoni, Milena; Richter, Klaus
2008-06-13
We predict the possibility to generate a finite stationary spin current by applying an unbiased ac driving to a quasi-one-dimensional asymmetric periodic structure with Rashba spin-orbit interaction and strong dissipation. We show that under a finite coupling strength between the orbital degrees of freedom the electron dynamics at low temperatures exhibits a pure spin ratchet behavior, i.e., a finite spin current and the absence of charge transport in spatially asymmetric structures. It is also found that the equilibrium spin currents are not destroyed by the presence of strong dissipation.
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)
Self-organization in a driven dissipative plasma system
NASA Astrophysics Data System (ADS)
Shaikh, Dastgeer; Dasgupta, B.; Hu, Q.; Zank, G. P.
2010-02-01
We perform a fully self-consistent three-dimensional numerical simulation for a compressible, dissipative magnetoplasma driven by large-scale perturbations, that contain a fairly broad spectrum of characteristic modes, ranging from largest scales to intermediate scales and down to the smallest scales, where the energy of the system is dissipated by collisional (ohmic) and viscous dissipations. Additionally, our simulation includes nonlinear interactions amongst a wide range of fluctuations that are initialized with random spectral amplitudes, leading to the cascade of spectral energy in the inertial range spectrum, and takes into account large-scale as well as small-scale perturbations that may have been induced by the background plasma fluctuations, as well as the non-adiabatic exchange of energy leading to the migration of energy from the energy-containing modes or randomly injected energy driven by perturbations and further dissipated by the smaller scales. Besides demonstrating the comparative decays of the total energy and the dissipation rate of the energy, our results show the existence of a perpendicular component of the current, thus clearly confirming that the self-organized state is non-force free.
ENERGY DISSIPATION PROCESSES IN SOLAR WIND TURBULENCE
Wang, Y.; Wei, F. S.; Feng, X. S.; Sun, T. R.; Zuo, P. B.; Xu, X. J.; Zhang, J.
2015-12-15
Turbulence is a chaotic flow regime filled by irregular flows. The dissipation of turbulence is a fundamental problem in the realm of physics. Theoretically, dissipation ultimately cannot be achieved without collisions, and so how turbulent kinetic energy is dissipated in the nearly collisionless solar wind is a challenging problem. Wave particle interactions and magnetic reconnection (MR) are two possible dissipation mechanisms, but which mechanism dominates is still a controversial topic. Here we analyze the dissipation region scaling around a solar wind MR region. We find that the MR region shows unique multifractal scaling in the dissipation range, while the ambient solar wind turbulence reveals a monofractal dissipation process for most of the time. These results provide the first observational evidences for intermittent multifractal dissipation region scaling around a MR site, and they also have significant implications for the fundamental energy dissipation process.
How nanomechanical systems can minimize dissipation
NASA Astrophysics Data System (ADS)
Muratore-Ginanneschi, Paolo; Schwieger, Kay
2014-12-01
Information processing machines at the nanoscales are unavoidably affected by thermal fluctuations. Efficient design requires understanding how nanomachines can operate at minimal energy dissipation. Here we focus on mechanical systems controlled by smoothly varying potential forces. We show that optimal control equations come about in a natural way if the energy cost to manipulate the potential is taken into account. When such a cost becomes negligible, an optimal control strategy can be constructed by transparent geometrical methods which recover the solution of optimal mass transport equations in the overdamped limit. Our equations are equivalent to hierarchies of kinetic equations of a form well known in the theory of dilute gases. From our results, optimal strategies for energy efficient nanosystems may be devised by established techniques from kinetic theory.
Dissipative tides - Application to Venus' lower atmosphere
NASA Technical Reports Server (NTRS)
Covey, Curt; Walterscheid, Richard L.; Schubert, Gerald
1986-01-01
A linearized planetary scale wave model is used to investigate the effects of thermal and mechanical damping on atmospheric tides. When the damping rate is comparable to the frequency of solar diurnal forcing the circulation consists of three parts: a classical vertically propagating 'atmospheric tide' in the upper atmosphere, a simple thermally direct subsolar-to-antisolar circulation or 'Halley cell' in most of the lower atmosphere, and finally, a reversed 'anti-Halley cell' near the surface. The near-surface circulation produces horizontal divergence near the subsolar point. While tides are a frequently encountered phenomenon (Venus, earth, and Mars), there is so far no observational evidence of a Halley circulation in any planetary atmosphere. A subsolar-antisolar circulation might be possible in Venus' slowly rotating lower atmosphere if the mechanical dissipation time scale is of the order of or less than a Venusian day. Such a circulation could be a factor in maintaining the superrotation of Venus' upper atmosphere.
How nanomechanical systems can minimize dissipation.
Muratore-Ginanneschi, Paolo; Schwieger, Kay
2014-12-01
Information processing machines at the nanoscales are unavoidably affected by thermal fluctuations. Efficient design requires understanding how nanomachines can operate at minimal energy dissipation. Here we focus on mechanical systems controlled by smoothly varying potential forces. We show that optimal control equations come about in a natural way if the energy cost to manipulate the potential is taken into account. When such a cost becomes negligible, an optimal control strategy can be constructed by transparent geometrical methods which recover the solution of optimal mass transport equations in the overdamped limit. Our equations are equivalent to hierarchies of kinetic equations of a form well known in the theory of dilute gases. From our results, optimal strategies for energy efficient nanosystems may be devised by established techniques from kinetic theory.
Spacecraft detumbling through energy dissipation
NASA Technical Reports Server (NTRS)
Fitz-Coy, Norman; Chatterjee, Anindya
1993-01-01
The attitude motion of a tumbling, rigid, axisymmetric spacecraft is considered. A methodology for detumbling the spacecraft through energy dissipation is presented. The differential equations governing this motion are stiff, and therefore an approximate solution, based on the variation of constants method, is developed and utilized in the analysis of the detumbling strategy. Stability of the detumbling process is also addressed.
Variational Derivation of Dissipative Equations
NASA Astrophysics Data System (ADS)
Sogo, Kiyoshi
2017-03-01
A new variational principle is formulated to derive various dissipative equations. Model equations considered are the damping equation, Bloch equation, diffusion equation, Fokker-Planck equation, Kramers equation and Smoluchowski equation. Each equation and its time reversal equation are simultaneously obtained in our variational principle.
On Some Numerical Dissipation Schemes
NASA Technical Reports Server (NTRS)
Swanson, R. C.; Radespiel, R.; Turkel, E.
1998-01-01
Several schemes for introducing an artificial dissipation into a central difference approximation to the Euler and Navier Stokes equations are considered. The focus of the paper is on the convective upwind and split pressure (CUSP) scheme, which is designed to support single interior point discrete shock waves. This scheme is analyzed and compared in detail with scalar dissipation and matrix dissipation (MATD) schemes. Resolution capability is determined by solving subsonic, transonic, and hypersonic flow problems. A finite-volume discretization and a multistage time-stepping scheme with multigrid are used to compute solutions to the flow equations. Numerical solutions are also compared with either theoretical solutions or experimental data. For transonic airfoil flows the best accuracy on coarse meshes for aerodynamic coefficients is obtained with a simple MATD scheme. The coarse-grid accuracy for the original CUSP scheme is improved by modifying the limiter function used with the scheme, giving comparable accuracy to that obtained with the MATD scheme. The modifications reduce the background dissipation and provide control over the regions where the scheme can become first order.
On the asymptotic behaviour of 2D stationary Navier–Stokes solutions with symmetry conditions
NASA Astrophysics Data System (ADS)
Decaster, Agathe; Iftimie, Dragoş
2017-10-01
We consider the 2D stationary incompressible Navier-Stokes equations in ℝ2. Under suitable symmetry, smallness and decay at infinity conditions on the forcing we determine the behaviour at infinity of the solutions. Moreover, when the forcing is small, satisfies suitable symmetry conditions and decays at infinity like a vector field homogeneous of degree -3, we show that there exists a unique small solution whose asymptotic behaviour at infinity is homogeneous of degree -1.
Estimates of M2 Tidal Energy Dissipation from TOPEX/Poseidon Altimeter Data
NASA Technical Reports Server (NTRS)
Egbert, Gary D.; Ray, Richard D.
2001-01-01
Most of the tidal energy dissipation in the ocean occurs in shallow seas, as has long been recognized. However, recent work has suggested that a significant fraction of the dissipation, perhaps 1 TW or more, occurs in the deep ocean. This paper builds further evidence for that conclusion. More than 6 years of data from the TOPEX/Poseidon satellite altimeter are used to map the tidal dissipation rate throughout the world ocean. The dissipation rate is estimated as a balance between the rate of working by tidal forces and the energy flux divergence, computed using currents derived by least squares fitting of the altimeter data and the shallow water equations. Such calculations require dynamical assumptions, in particular about the nature of dissipation. To assess sensitivity of dissipation estimates to input assumptions, a large suite of tidal inversions based on a wide range of drag parameterizations and employing both real and synthetic altimeter data are compared. These experiments and Monte Carlo error fields from a generalized inverse model are used to establish error uncertainties for the dissipation estimates. Owing to the tight constraints on tidal elevation fields provided by the altimeter, area integrals of the energy balance are remarkably insensitive to required dynamical assumptions. Tidal energy dissipation is estimated for all major shallow seas (excluding individual polar seas) and compared with previous model and data-based estimates. Dissipation in the open ocean is significantly tnhanced around major bathymetric features, in a manner consistent with simple theories the generation of baroclinic tides.
Avoiding dissipation in a system of three quantum harmonic oscillators
NASA Astrophysics Data System (ADS)
Manzano, Gonzalo; Galve, Fernando; Zambrini, Roberta
2013-03-01
We analyze the symmetries in an open quantum system composed by three coupled and detuned harmonic oscillators in the presence of a common heat bath. It is shown analytically how to engineer the couplings and frequencies of the system so as to have several degrees of freedom unaffected by decoherence, irrespective of the specific spectral density or initial state of the bath. This partial thermalization allows observing asymptotic entanglement at moderate temperatures, even in the nonresonant case. This latter feature cannot be seen in the simpler situation of only two oscillators, highlighting the richer structural variety of the three-body case. When departing from the strict conditions for partial thermalization, a hierarchical structure of dissipation rates for the normal modes is observed, leading to a long transient where quantum correlations such as the quantum discord are largely preserved, as well as to synchronous dynamics of the oscillators quadratures.
Fedosov, Dmitry A; Em Karniadakis, George; Caswell, Bruce
2008-04-14
The flows of dilute polymer solutions in micro- and nanoscale channels are of both fundamental and practical importance in variety of applications in which the channel gap is of the same order as the size of the suspended particles or macromolecules. In such systems depletion layers are observed near solid-fluid interfaces, even in equilibrium, and the imposition of flow results in further cross-stream migration of the particles. In this work we employ dissipative particle dynamics to study depletion and migration in dilute polymer solutions in channels several times larger than the radius of gyration (Rg) of bead-spring chains. We compare depletion layers for different chain models and levels of chain representation, solvent quality, and relative wall-solvent-polymer interactions. By suitable scaling the simulated depletion layers compare well with the asymptotic lattice theory solution of depletion near a repulsive wall. In Poiseuille flow, polymer migration across the streamlines increases with the Peclet and the Reynolds number until the center-of-mass distribution develops two symmetric off-center peaks which identify the preferred chain positions across the channel. These appear to be governed by the balance of wall-chain repulsive interactions and an off-center driving force of the type known as the Segre-Silberberg effect.
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.
Time course of sleep inertia dissipation in human performance and alertness
NASA Technical Reports Server (NTRS)
Jewett, M. E.; Wyatt, J. K.; Ritz-De Cecco, A.; Khalsa, S. B.; Dijk, D. J.; Czeisler, C. A.
1999-01-01
Alertness and performance on a wide variety of tasks are impaired immediately upon waking from sleep due to sleep inertia, which has been found to dissipate in an asymptotic manner following waketime. It has been suggested that behavioural or environmental factors, as well as sleep stage at awakening, may affect the severity of sleep inertia. In order to determine the time course of sleep inertia dissipation under normal entrained conditions, subjective alertness and cognitive throughput were measured during the first 4 h after habitual waketime from a full 8-h sleep episode on 3 consecutive days. We investigated whether this time course was affected by either sleep stage at awakening or behavioural/environmental factors. Sleep inertia dissipated in an asymptotic manner and took 2-4 h to near the asymptote. Saturating exponential functions fitted the sleep inertia data well, with time constants of 0.67 h for subjective alertness and 1.17 h for cognitive performance. Most awakenings occurred out of stage rapid eye movement (REM), 2 or 1 sleep, and no effect of sleep stage at awakening on either the severity of sleep inertia or the time course of its dissipation could be detected. Subjective alertness and cognitive throughput were significantly impaired upon awakening regardless of whether subjects got out of bed, ate breakfast, showered and were exposed to ordinary indoor room light (approximately 150 lux) or whether subjects participated in a constant routine (CR) protocol in which they remained in bed, ate small hourly snacks and were exposed to very dim light (10-15 lux). These findings allow for the refinement of models of alertness and performance, and have important implications for the scheduling of work immediately upon awakening in many occupational settings.
Asymptotic permanent profile of the ion acoustic wave driven by the Langmuir wave
NASA Astrophysics Data System (ADS)
Kaup, D. J.; Latifi, A.; Leon, J.
1992-08-01
We study the evolution of Langmuir waves coupled to the ion acoustic wave by means of the ponderomotive force in the Karpman limit (caviton equation). Using the spectral transform with singular dispersion relation, it is shown that the background noise (fluctuations in the ion density) is amplified and its time asymptotic behavior will be a static solution which is totally reflective for the Langmuir wave. Moreover, if the initial ion density contains a local depression, the asymptotic profile will contain a number of permanent localized density depressions (cavitons), static in the rest frame of the acoustic wave and entrained in its wake.
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.
A model for nonexponential relaxation and aging in dissipative systems
NASA Astrophysics Data System (ADS)
Pérez-Madrid, A.
2005-06-01
The nonexponential relaxation and aging inherent to complex dynamics manifested in a wide variety of dissipative systems are analyzed through a model of diffusion in phase space in the presence of a nonconservative force. The action of this force establishes a heat flow which maintains the system away from equilibrium. The inability of the system to find its equilibrium state becomes apparent through the presence of an effective temperature field. This is the temperature of the stationary nonequilibrium state reached by the system satisfying a generalized version of the fluctuation-dissipation theorem. The presence of a nonequilibrium temperature leads to a hierarchy of relaxation times responsible for the aging phenomena and to a relation similar to the Vogel-Fulcher-Tammann law [H. Vogel, Phys. Z. 22, 645 (1921); G. S. Fulcher, J. Am. Ceram. Soc. 8, 339 (1925); 8, 789 (1925); G. Tammann and W. Hesse, Z. Anorg. Allg. Chem. 156, 245 (1926)].
Asymptotic cost in document conversion
NASA Astrophysics Data System (ADS)
Blostein, Dorothea; Nagy, George
2012-01-01
In spite of a hundredfold decrease in the cost of relevant technologies, the role of document image processing systems is gradually declining due to the transition to an on-line world. Nevertheless, in some high-volume applications, document image processing software still saves millions of dollars by accelerating workflow, and similarly large savings could be realized by more effective automation of the multitude of low-volume personal document conversions. While potential cost savings, based on estimates of costs and values, are a driving force for new developments, quantifying such savings is difficult. The most important trend is that the cost of computing resources for DIA is becoming insignificant compared to the associated labor costs. An econometric treatment of document processing complements traditional performance evaluation, which focuses on assessing the correctness of the results produced by document conversion software. Researchers should look beyond the error rate for advancing both production and personal document conversion.
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.
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.
Asymptotic stability of singularly perturbed differential equations
NASA Astrophysics Data System (ADS)
Artstein, Zvi
2017-02-01
Asymptotic stability is examined for singularly perturbed ordinary differential equations that may not possess a natural split into fast and slow motions. Rather, the right hand side of the equation is comprised of a singularly perturbed component and a regular one. The limit dynamics consists then of Young measures, with values being invariant measures of the fast contribution, drifted by the slow one. Relations between the asymptotic stability of the perturbed system and the limit dynamics are examined, and a Lyapunov functions criterion, based on averaging, is established.
Directions for model building from asymptotic safety
NASA Astrophysics Data System (ADS)
Bond, Andrew D.; Hiller, Gudrun; Kowalska, Kamila; Litim, Daniel F.
2017-08-01
Building on recent advances in the understanding of gauge-Yukawa theories we explore possibilities to UV-complete the Standard Model in an asymptotically safe manner. Minimal extensions are based on a large flavor sector of additional fermions coupled to a scalar singlet matrix field. We find that asymptotic safety requires fermions in higher representations of SU(3) C × SU(2) L . Possible signatures at colliders are worked out and include R-hadron searches, diboson signatures and the evolution of the strong and weak coupling constants.
Initial Dynamics of Cell Spreading Are Governed by Dissipation in the Actin Cortex
Étienne, Jocelyn; Duperray, Alain
2011-01-01
The initial stages of spreading of a suspended cell onto a substrate under the effect of (specific or nonspecific) adhesion exhibit a universal behavior, which is cell-type independent. We show that this behavior is governed only by cell-scale phenomena. This can be understood if the main retarding force that opposes cell adhesion is of mechanical origin, that is, dissipation occurring during the spreading. By comparing several naive models that generate different patterns of dissipation, we show by numerical simulation that only dissipation due to the deformation of the actin cortex is compatible with the experimental observations. This viscous-like dissipation corresponds to the energetic cost of rearranging the cytoskeleton, and is the trace of all dissipative events occurring in the cell cortex during the early spreading, such as the binding and unbinding of cross-linkers and molecular friction. PMID:21806929
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.
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.
Dynamics of strongly dissipative systems
NASA Astrophysics Data System (ADS)
Fang, H. P.
1994-06-01
The attractors in two-dimensional (2D) phase space of the strongly dissipative Hénon map are reduced to those of an effectively 1D map. From the grammar for this effectively 1D map we can generate all of the unstable periodic orbits, which are exactly consistent with those from the 2D map obtained directly both with a Newton procedure and the techniques of Biham and Wenzel [Phys. Rev. Lett. 63, 819 (1989)]. This idea provides a method to give a very precise and not too cumbersome estimate of the characteristic quantities of strange attractors of strongly dissipative systems. It is also helpful to understand many observations on high-dimensional systems both experimentally and numerically.
Dissipative ring solitons with vorticity.
Soto-Crespo, J M; Akhmediev, N; Mejia-Cortés, C; Devine, N
2009-03-16
We study dissipative ring solitons with vorticity in the frame of the (2+1)-dimensional cubic-quintic complex Ginzburg-Landau equation. In dissipative media, radially symmetric ring structures with any vorticity m can be stable in a finite range of parameters. Beyond the region of stability, the solitons lose the radial symmetry but may remain stable, keeping the same value of the topological charge. We have found bifurcations into solitons with n-fold bending symmetry, with n independent on m. Solitons without circular symmetry can also display (m + 1)-fold modulation behaviour. A sequence of bifurcations can transform the ring soliton into a pulsating or chaotic state which keeps the same value of the topological charge as the original ring.
Kinetic approach to relativistic dissipation
NASA Astrophysics Data System (ADS)
Gabbana, A.; Mendoza, M.; Succi, S.; Tripiccione, R.
2017-08-01
Despite a long record of intense effort, the basic mechanisms by which dissipation emerges from the microscopic dynamics of a relativistic fluid still elude complete understanding. In particular, several details must still be finalized in the pathway from kinetic theory to hydrodynamics mainly in the derivation of the values of the transport coefficients. In this paper, we approach the problem by matching data from lattice-kinetic simulations with analytical predictions. Our numerical results provide neat evidence in favor of the Chapman-Enskog [The Mathematical Theory of Non-Uniform Gases, 3rd ed. (Cambridge University Press, Cambridge, U.K., 1970)] procedure as suggested by recent theoretical analyses along with qualitative hints at the basic reasons why the Chapman-Enskog expansion might be better suited than Grad's method [Commun. Pure Appl. Math. 2, 331 (1949), 10.1002/cpa.3160020403] to capture the emergence of dissipative effects in relativistic fluids.
Doublon lifetimes in dissipative environments
NASA Astrophysics Data System (ADS)
Bello, Miguel; Platero, Gloria; Kohler, Sigmund
2017-07-01
We study the dissipative decay of states with a doubly occupied site in a two-electron Hubbard model, known as doublons. For the environment, we consider charge and current noise, which are modeled as a bosonic heat bath that couples to the on-site energies and the tunnel couplings, respectively. It turns out that the dissipative decay depends qualitatively on the type of environment, as for charge noise, the lifetime grows with the electron-electron interaction. For current noise, by contrast, doublons become increasingly unstable with larger interaction. Numerical studies within a Bloch-Redfield approach are complemented by analytical estimates for the decay rates. For typical quantum dot parameters, we predict doublon lifetimes up to 50 ns.
A dissipative model of solar system
NASA Astrophysics Data System (ADS)
Vladimir, V. G.
2009-04-01
rotation of planets, and the small tidal deformations arising under influence of gradients of gravitational forces. The method of division of movements receives the equations describing movements of the centers of weights of planets and their own rotations. In the offered model takes place a dissipation of the energy which source are internally viscous forces of each planet. The system supposes the first integral - the law of preservation of the kinetic moment concerning the centre of weights of system. As a result of deformations of planets in the law of the universal gravitation which has been written down for material points, there are small conservative amendments. The equations of movement describe movement of the centers of weights of planets and their rotation around of the centers of weights in view of the tidal phenomena and the dissipative forces. The connected system of the equations consists of 3N the vector equations of the second order representing the theorems of movement of the centers of weights of planets, and N the vector equations of the first order determining changes of the own kinetic moments of each planet. Stationary values of full mechanical energy on the variety set in integral of the kinetic moment, correspond to stationary movements - to rotations of system as firm body with constant angular speed around of the centre of weights of all system. Angular speed of stationary rotation is directed along a constant vector of the kinetic moment, and the axis of rotation is the main central axis of inertia of system. We shall notice, that deformations of planets in stationary movement are constant, as in system of coordinates rotating with constant angular speed centrifugal forces and forces of gravitational interaction of planets are constant. Stationary configurations of system are determined according to Routh`s technique as stationary points of the changed potential energy submitted by the sum potential energies of centrifugal and gravitational
Dissipative extension of the Ghirardi-Rimini-Weber model
NASA Astrophysics Data System (ADS)
Smirne, Andrea; Vacchini, Bassano; Bassi, Angelo
2014-12-01
In this paper, we present an extension of the Ghirardi-Rimini-Weber model for the spontaneous collapse of the wave function. Through the inclusion of dissipation, we avoid the divergence of the energy on the long-time scale, which affects the original model. In particular, we define jump operators, which depend on the momentum of the system and lead to an exponential relaxation of the energy to a finite value. The finite asymptotic energy is naturally associated to a collapse noise with a finite temperature, which is a basic realistic feature of our extended model. Remarkably, even in the presence of a low-temperature noise, the collapse model is effective. The action of the jump operators still localizes the wave function and the relevance of the localization increases with the size of the system, according to the so-called amplification mechanism, which guarantees a unified description of the evolution of microscopic and macroscopic systems. We study in detail the features of our model, at the level of both the trajectories in the Hilbert space and the master equation for the average state of the system. In addition, we show that the dissipative Ghirardi-Rimini-Weber model, as well as the original one, can be fully characterized in a compact way by means of a proper stochastic differential equation.
Asymptotic Floquet states of open quantum systems: the role of interaction
NASA Astrophysics Data System (ADS)
Hartmann, M.; Poletti, D.; Ivanchenko, M.; Denisov, S.; Hänggi, P.
2017-08-01
When a periodically modulated many-body quantum system is weakly coupled to an environment, the combined action of these temporal modulations and dissipation steers the system towards a state characterized by a time-periodic density operator. To resolve this asymptotic non-equilibrium state at stroboscopic instants of time, we use the dissipative propagator over one period of modulations, ‘Floquet map’, and evaluate the stroboscopic density operator as its invariant. Particle interactions control properties of the map and thus the features of its invariant. In addition, the spectrum of the map provides insight into the system relaxation towards the asymptotic state and may help to understand whether it is possible (or not) to construct a stroboscopic time-independent Lindblad generator which mimics the action of the original time-dependent one. We illustrate the idea with a scalable many-body model, a periodically modulated Bose-Hubbard dimer. We contrast the relations between the interaction-induced bifurcations in a mean-field description with the numerically exact stroboscopic evolution and discuss the characteristics of the genuine quantum many-body state vs the characteristics of its mean-field counterpart.
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.
Quantum dissipation and CP violation in MINOS
NASA Astrophysics Data System (ADS)
Oliveira, R. L. N.; Guzzo, M. M.; de Holanda, P. C.
2014-03-01
We use the open quantum systems framework to analyze the MINOS data and perform this analysis considering two different dissipative models. In the first model, the dissipative parameter describes the decoherence effect and in the second, the dissipative parameter describes other dissipative effects including decoherence. With the second model it is possible to study CP violation since we consider Majorana neutrinos. The analysis from the muon neutrino and antineutrino beam assigns different values to all the parameters of the models, but is consistent between them. Assuming that neutrinos are equivalent to antineutrinos, the global analysis presents a nonvanishing Majorana CP phase depending on the energetic parametrization of the dissipative parameter.
Temperature dependent dissipation in magnetic nanoparticles
NASA Astrophysics Data System (ADS)
Regmi, R.; Naik, A.; Thakur, J. S.; Vaishnava, P. P.; Lawes, G.
2014-05-01
We parameterized the temperature dependent magnetic dissipation of iron oxide nanoparticles fixed in a frozen aqueous solution in an ac magnetic field. The magnetic power dissipated can be modeled by considering only Neel relaxation. This dissipation increased monotonically with temperature, increasing by approximately 50% between -40 °C and -10 °C. These experimental results provide quantitative confirmation for the Neel model of magnetic dissipative heating for nanoparticles rigidly confined in a solid matrix. We also find substantial temperature dependence in the magnetic dissipation of nanoparticles suspended in a liquid, which has important consequences for potential applications of magnetic nanoparticles for hyperthermia.
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.
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.
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.
Stationary solutions and asymptotic flatness I
NASA Astrophysics Data System (ADS)
Reiris, Martin
2014-08-01
In general relativity, a stationary isolated system is defined as an asymptotically flat (AF) stationary spacetime with compact material sources. Other definitions that are less restrictive on the type of asymptotic could in principle be possible. Between this article and its sequel, we show that under basic assumptions, asymptotic flatness indeed follows as a consequence of Einstein's theory. In particular, it is proved that any vacuum stationary spacetime-end whose (quotient) manifold is diffeomorphic to {{{R}}^{3}} minus a ball and whose Killing field has its norm bounded away from zero, is necessarily AF with Schwarzschildian fall off. The ‘excised’ ball would contain (if any) the actual material body, but this information is unnecessary to reach the conclusion. In this first article, we work with weakly asymptotically flat (WAF) stationary ends, a notion that generalizes as much as possible that of the AF end, and prove that WAF ends are AF with Schwarzschildian fall off. Physical and mathematical implications are also discussed.
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.
Layer tracking, asymptotics, and domain decomposition
NASA Technical Reports Server (NTRS)
Brown, D. L.; Chin, R. C. Y.; Hedstrom, G. W.; Manteuffel, T. A.
1991-01-01
A preliminary report is presented on the work on the tracking of internal layers in a singularly-perturbed convection-diffusion equation. It is shown why such tracking may be desirable, and it is also shown how to do it using domain decomposition based on asymptotic analysis.
On asymptotic properties of biharmonic Steklov eigenvalues
NASA Astrophysics Data System (ADS)
Liu, Genqian
2016-11-01
In this paper, by explicitly calculating the principal symbols of pseudodifferential operators, we establish two Weyl-type asymptotic formulas with sharp remainder estimates for the counting functions of the two classes of biharmonic Steklov eigenvalue problems of smooth bounded domains in a Riemannian manifold.
Behavior of asymptotically electro-Λ spacetimes
NASA Astrophysics Data System (ADS)
Saw, Vee-Liem
2017-04-01
We present the asymptotic solutions for spacetimes with nonzero cosmological constant Λ coupled to Maxwell fields, using the Newman-Penrose formalism. This extends a recent work that dealt with the vacuum Einstein (Newman-Penrose) equations with Λ ≠0 . The results are given in two different null tetrads: the Newman-Unti and Szabados-Tod null tetrads, where the peeling property is exhibited in the former but not the latter. Using these asymptotic solutions, we discuss the mass loss of an isolated electrogravitating system with cosmological constant. In a universe with Λ >0 , the physics of electromagnetic (EM) radiation is relatively straightforward compared to those of gravitational radiation: (1) It is clear that outgoing EM radiation results in a decrease to the Bondi mass of the isolated system. (2) It is also perspicuous that if any incoming EM radiation from elsewhere is present, those beyond the isolated system's cosmological horizon would eventually arrive at the spacelike I and increase the Bondi mass of the isolated system. Hence, the (outgoing and incoming) EM radiation fields do not couple with Λ in the Bondi mass-loss formula in an unusual manner, unlike the gravitational counterpart where outgoing gravitational radiation induces nonconformal flatness of I . These asymptotic solutions to the Einstein-Maxwell-de Sitter equations presented here may be used to extend a raft of existing results based on Newman-Unti's asymptotic solutions to the Einstein-Maxwell equations where Λ =0 , to now incorporate the cosmological constant Λ .
Asymptotic Distributions for Tests of Combined Significance.
ERIC Educational Resources Information Center
Becker, Betsy Jane
This paper discusses distribution theory and power computations for four common "tests of combined significance." These tests are calculated using one-sided sample probabilities or p values from independent studies (or hypothesis tests), and provide an overall significance level for the series of results. Noncentral asymptotic sampling…
Magnetorheological rotational flow with viscous dissipation
NASA Astrophysics Data System (ADS)
Ashrafi, Nariman
2017-05-01
Effects of a magnetic field and fluid nonlinearity are investigated for the rotational flow of the Carreau-type fluid while viscous dissipation is taken into account. The governing motion and energy balance equations are coupled, adding complexity to the already highly correlated set of differential equations. The numerical solution is obtained for the narrow-gap limit and steady-state base flow. Magnetic field effect on local entropy generation due to steady two-dimensional laminar forced convection flow was investigated. This study was focused on the entropy generation characteristics and its dependency on various dimensionless parameters. The effects of the Hartmann number, the Brinkman number, and the Deborah number on the stability of the flow were investigated. The introduction of the magnetic field induces a resistive force acting in the opposite direction of the flow, thus causing its deceleration. Moreover, the study shows that the presence of magnetic field tends to slow down the fluid motion. It, however, increases the fluid temperature. Moreover, the total entropy generation number decreases as the Hartmann number and fluid elasticity increase and increases with increasing Brinkman number.
Dissipative Particle Dynamics simulation of colloidal suspensions
NASA Astrophysics Data System (ADS)
Jamali, Safa; Boromand, Arman; Maia, Joao
2014-03-01
DPD as a mesoscale method was firstly proposed to study dynamics of suspensions under flow condition. However the proposed method failed to capture shear properties of suspensions because it lacked: first a potential to reproduce lubrication forces and second a clear definition for the colloid surface. Recently we reported a modified DPD method which defines colloidal particles as particles with hard core and a dissipative coat. An additional lubrication force was introduced to include the short-range hydrodynamics that are not captured in original DPD. The model was found to be able to reproduce shear properties of suspensions for a wide range of different systems, from monodisperse to bimodal with different volume fractions, compositions and size ratios. In present work our modified DPD method is employed to study both equilibrium and flow properties of colloidal suspension. Zero shear viscosity of suspension is measured using Green-Kubo expressions and the results are compared to theoretical predictions. Furthermore, structure formation in suspensions is studied in respect to energy landscape of the fluid both at rest and under flow.
Magnetohydrodynamic shocks in a dissipative quantum plasma with exchange-correlation effects
NASA Astrophysics Data System (ADS)
Sahu, Biswajit; Misra, A. P.
2017-07-01
We investigate the nonlinear propagation of multidimensional magnetosonic shock waves (MSWs) in a dissipative quantum magnetoplasma. A macroscopic quantum magnetohydrodynamic (QMHD) model is used to include the quantum force associated with the Bohm potential, the pressure-like spin force, the exchange and correlation force of electrons, as well as the dissipative force due to the kinematic viscosity of ions and the magnetic diffusivity. The effects of these forces on the properties of arbitrary amplitude MSWs are examined numerically. It is found that the contribution from the exchange-correlation force appears to be dominant over those from the pressure gradient and the other similar quantum forces, and it results in a transition from monotonic to oscillatory shocks in the presence of either the ion kinematic viscosity or the magnetic diffusivity.
Turbulent collision statistics of cloud droplets at low dissipation rates
NASA Astrophysics Data System (ADS)
Banerjee, Sandipan
Collisions of sedimenting droplets in a turbulent flow is of great importance in cloud physics. Collision efficiency and collision enhancement over gravitational collision by air turbulence govern the growth of the cloud droplets leading to warm rain initiation and precipitation dynamics. In this thesis we present direct numerical simulation (DNS) results for collision statistics of droplets in turbulent flows of low dissipation rates (in the range of 3 cm2/s3-100 cm2/s3) relevant to strato-cumulus clouds. First, we revisit the case of gravitational collision in still fluid to validate the details of the collision detection algorithm used in our code. We compare the collision statistics with either new analytical predictions regarding the percentages of different collision types, or results from published papers. The effect of initial conditions on the collision statistics and statistical uncertainties are analyzed both analytically and through the simulation data. Second, we consider the case of weak turbulence (as in strato-cumulus clouds). In this case the particle motion is mainly driven by gravity. The standard deviation (or the uncertainty) of the average collision statistics is examined analytically in terms of time correlation function of the data. We then report new DNS results of collision statistics in a turbulent flow, showing how air turbulence increases the geometric colli- sion statistics and the collision efficiency. We find that the collision-rate enhancement due to turbulence depends nonlinearly on the flow dissipation rate. This result calls for a more careful parameterization of the collision statistics in strato-cumulus clouds. Due to the low flow dissipation rate in stratocumulus clouds, a related challenge is low droplet Stokes number. Here the Stokes number is the ratio of droplet inertial response time to the flow Kolmogorov time. A very low Stokes number implies that the numerical integration time step is now governed by the droplet
Dimant
2000-01-24
Linearly unstable dissipative systems with quadratic nonlinearity occurring in plasma physics, optics, fluid mechanics, etc. are often modeled by a general set of three-wave mode-coupled ordinary differential equations for complex variables. Bounded attractors of the set approximate nonlinearly saturated turbulent states of real physical systems. Exact criteria for boundedness of the attractors are found. Fundamentally different kinds of asymptotic behavior of the wave triad are classified in the parameter space and quantitatively assessed.
Exchange-correlation asymptotics and high harmonic spectra
NASA Astrophysics Data System (ADS)
Mack, Michael R.; Whitenack, Daniel; Wasserman, Adam
2013-02-01
High harmonic spectra of N2 are calculated using time-dependent density functional theory. The adiabatic local density approximation (A-LDA) and the adiabatic van Leeuwen-Baerends (A-LB94) approximations are used to study effects of differing spatial asymptotics. The LB94 potential corrects the LDA potential to the exact -1/r decay, but does not satisfy the zero-force condition. The A-LB94 makes a significant change in ionization probabilities but not in the relevant orbital contributions to ionization. This leads to qualitatively similar spectra, the exception being harmonic intensities. We also discuss why spurious dipoles induced by the A-LB94 do not affect significantly the structure of the N2 harmonic spectrum.
Asymptotic self-restabilization of a continuous elastic structure
NASA Astrophysics Data System (ADS)
Bosi, F.; Misseroni, D.; Dal Corso, F.; Neukirch, S.; Bigoni, D.
2016-12-01
A challenge in soft robotics and soft actuation is the determination of an elastic system that spontaneously recovers its trivial path during postcritical deformation after a bifurcation. The interest in this behavior is that a displacement component spontaneously cycles around a null value, thus producing a cyclic soft mechanism. An example of such a system is theoretically proven through the solution of the elastica and a stability analysis based on dynamic perturbations. It is shown that the asymptotic self-restabilization is driven by the development of a configurational force, of similar nature to the Peach-Koehler interaction between dislocations in crystals, which is derived from the principle of least action. A proof-of-concept prototype of the discovered elastic system is designed, realized, and tested, showing that this innovative behavior can be obtained in a real mechanical apparatus.
Designing Biomimetic, Dissipative Material Systems
Balazs, Anna C.; Whitesides, George M.; Brinker, C. Jeffrey; Aranson, Igor S.; Chaikin, Paul; Dogic, Zvonimir; Glotzer, Sharon; Hammer, Daniel; Irvine, Darrell; Little, Steven R.; Olvera de la Cruz, Monica; Parikh, Atul N.; Stupp, Samuel; Szostak, Jack
2016-01-21
Throughout human history, new materials have been the foundation of transformative technologies: from bronze, paper, and ceramics to steel, silicon, and polymers, each material has enabled far-reaching advances. Today, another new class of materials is emerging—one with both the potential to provide radically new functions and to challenge our notion of what constitutes a “material”. These materials would harvest, transduce, or dissipate energy to perform autonomous, dynamic functions that mimic the behaviors of living organisms. Herein, we discuss the challenges and benefits of creating “dissipative” materials that can potentially blur the boundaries between living and non-living matter.
Tidal disruption of dissipative planetesimals
NASA Technical Reports Server (NTRS)
Mizuno, H.; Boss, A. P.
1985-01-01
A self-consistent numerical model is developed for the tidal disruption of a solid planetesimal. The planetesimal is treated as a highly viscous, slightly compressible fluid whose disturbed parts are an inviscid, pressureless fluid undergoing distortion and disruption. The distortions were constrained to being symmetrical above and below the equatorial plane. The tidal potential is expanded in terms of Legendre polynomials, which eliminates the center of mass acceleration effects, permitting definition of equations of motion in a noninertial frame. Consideration is given to viscous dissipation and to characteristics of the solid-atmosphere boundary. The model is applied to sample cases in one, two and three dimensions.
Galerkin approximations for dissipative magnetohydrodynamics
NASA Technical Reports Server (NTRS)
Chen, Hudong; Shan, Xiaowen; Montgomery, David
1990-01-01
A Galerkin approximation scheme is proposed for voltage-driven, dissipative magnetohydrodynamics. The trial functions are exact eigenfunctions of the linearized continuum equations and represent helical deformations of the axisymmetric, zero-flow, driven steady state. The lowest nontrivial truncation is explored: one axisymmetric trial function and one helical trial function each for the magnetic and velocity fields. The system resembles the Lorenz approximation to Benard convection, but in the region of believed applicability, its dynamical behavior is rather different, including relaxation to a helically deformed state similar to those that have emerged in the much higher resolution computations of Dahlburg et al.
Tidal disruption of dissipative planetesimals
NASA Technical Reports Server (NTRS)
Mizuno, H.; Boss, A. P.
1985-01-01
A self-consistent numerical model is developed for the tidal disruption of a solid planetesimal. The planetesimal is treated as a highly viscous, slightly compressible fluid whose disturbed parts are an inviscid, pressureless fluid undergoing distortion and disruption. The distortions were constrained to being symmetrical above and below the equatorial plane. The tidal potential is expanded in terms of Legendre polynomials, which eliminates the center of mass acceleration effects, permitting definition of equations of motion in a noninertial frame. Consideration is given to viscous dissipation and to characteristics of the solid-atmosphere boundary. The model is applied to sample cases in one, two and three dimensions.
Entropy Splitting and Numerical Dissipation
NASA Technical Reports Server (NTRS)
Yee, H. C.; Vinokur, M.; Djomehri, M. J.
1999-01-01
A rigorous stability estimate for arbitrary order of accuracy of spatial central difference schemes for initial-boundary value problems of nonlinear symmetrizable systems of hyperbolic conservation laws was established recently by Olsson and Oliger (1994) and Olsson (1995) and was applied to the two-dimensional compressible Euler equations for a perfect gas by Gerritsen and Olsson (1996) and Gerritsen (1996). The basic building block in developing the stability estimate is a generalized energy approach based on a special splitting of the flux derivative via a convex entropy function and certain homogeneous properties. Due to some of the unique properties of the compressible Euler equations for a perfect gas, the splitting resulted in the sum of a conservative portion and a non-conservative portion of the flux derivative. hereafter referred to as the "Entropy Splitting." There are several potential desirable attributes and side benefits of the entropy splitting for the compressible Euler equations that were not fully explored in Gerritsen and Olsson. The paper has several objectives. The first is to investigate the choice of the arbitrary parameter that determines the amount of splitting and its dependence on the type of physics of current interest to computational fluid dynamics. The second is to investigate in what manner the splitting affects the nonlinear stability of the central schemes for long time integrations of unsteady flows such as in nonlinear aeroacoustics and turbulence dynamics. If numerical dissipation indeed is needed to stabilize the central scheme, can the splitting help minimize the numerical dissipation compared to its un-split cousin? Extensive numerical study on the vortex preservation capability of the splitting in conjunction with central schemes for long time integrations will be presented. The third is to study the effect of the non-conservative proportion of splitting in obtaining the correct shock location for high speed complex shock
Harnessing spin precession with dissipation.
Crisan, A D; Datta, S; Viennot, J J; Delbecq, M R; Cottet, A; Kontos, T
2016-01-27
Non-collinear spin transport is at the heart of spin or magnetization control in spintronics devices. The use of nanoscale conductors exhibiting quantum effects in transport could provide new paths for that purpose. Here we study non-collinear spin transport in a quantum dot. We use a device made out of a single-wall carbon nanotube connected to orthogonal ferromagnetic electrodes. In the spin transport signals, we observe signatures of out of equilibrium spin precession that are electrically tunable through dissipation. This could provide a new path to harness spin precession in nanoscale conductors.
Harnessing spin precession with dissipation
NASA Astrophysics Data System (ADS)
Crisan, A. D.; Datta, S.; Viennot, J. J.; Delbecq, M. R.; Cottet, A.; Kontos, T.
2016-01-01
Non-collinear spin transport is at the heart of spin or magnetization control in spintronics devices. The use of nanoscale conductors exhibiting quantum effects in transport could provide new paths for that purpose. Here we study non-collinear spin transport in a quantum dot. We use a device made out of a single-wall carbon nanotube connected to orthogonal ferromagnetic electrodes. In the spin transport signals, we observe signatures of out of equilibrium spin precession that are electrically tunable through dissipation. This could provide a new path to harness spin precession in nanoscale conductors.
Ray Tracing Modeling of Gravity Wave Propagation and Dissipation
NASA Astrophysics Data System (ADS)
Vadas, Sharon; Crowley, Geoff
In this paper, we describe a ray trace model which calculates the wavevector, location and phase of a gravity wave (GW) as it propagates in the lower atmosphere and thermosphere. If used for a discreet transient source (such as a deep convective plume), we describe how this model can calculate the body forcing and the heat/cooling that are created when the GWs within a wave packet dissipate in the thermosphere from kinematic viscosity and thermal diffusivity. Although the body force calculation requires only the divergence of the momentum flux, the heat/cooling calculation requires the reconstructed GW field (e.g., density, velocity perturbations), which in turn requires the GW dissipative polarization relations. We describe these relations. We then describe the results of a recent study involving GWs identified from TIDDBIT HF Doppler sounder data taken at Wallops Island, VI, USA. Using this ray trace model, we determine if the unusual neutral wind profile measured by a rocket experiment at high altitudes (~290-370 km) could have been caused by the propagation and dissipation of several waves observed by TIDDBIT at lower altitudes.
Traits of estuarine marsh plants affect wave dissipation
NASA Astrophysics Data System (ADS)
Schulte Ostermann, Tilla; Heuner, Maike; Bouma, Tjeerd
2017-04-01
Estuarine vegetation can attenuate hydrodynamic forces such as waves or flow velocities and therefore has an important role in natural tidal bank protection. This function depends on the degree of hydrodynamic forces, bank morphology and on plant traits of the dominant species. The traits vary between the species but also between different marsh sites. Biomass, stem density and biomechanical properties are crucial factors that influence the rate of wave dissipation. These properties illustrate the trade-offs a species is facing in such a dynamic habitat and highlight the ability of dominant species such as Bolboschoenus maritimus and Schoenoplectus tabernaemontani to protect the tidal bank. Along the Elbe estuary, traits of dominant marsh plant species were measured on different sites. The sites vary e.g. in their elevation, salt levels and inundation periods. To analyse the role that plant traits can play in wave dissipation, the structure of the vegetation as well as the composition was recorded. Biomechanical tests helped to understand the species traits regarding stem flexibility and to determine the effects of plant traits on wave dynamics and vice versa. On the conference, we will present how plant traits affect the wave dissipation on tidal marshes and why they vary.
Fractional Stochastic Differential Equations Satisfying Fluctuation-Dissipation Theorem
NASA Astrophysics Data System (ADS)
Li, Lei; Liu, Jian-Guo; Lu, Jianfeng
2017-09-01
We propose in this work a fractional stochastic differential equation (FSDE) model consistent with the over-damped limit of the generalized Langevin equation model. As a result of the `fluctuation-dissipation theorem', the differential equations driven by fractional Brownian noise to model memory effects should be paired with Caputo derivatives, and this FSDE model should be understood in an integral form. We establish the existence of strong solutions for such equations and discuss the ergodicity and convergence to Gibbs measure. In the linear forcing regime, we show rigorously the algebraic convergence to Gibbs measure when the `fluctuation-dissipation theorem' is satisfied, and this verifies that satisfying `fluctuation-dissipation theorem' indeed leads to the correct physical behavior. We further discuss possible approaches to analyze the ergodicity and convergence to Gibbs measure in the nonlinear forcing regime, while leave the rigorous analysis for future works. The FSDE model proposed is suitable for systems in contact with heat bath with power-law kernel and subdiffusion behaviors.
Damping and energy dissipation in soft tissue vibrations during running.
Khassetarash, Arash; Hassannejad, Reza; Enders, Hendrik; Ettefagh, Mir Mohammad
2015-01-21
It has been well accepted that the vibrations of soft tissue cannot be simulated by a single sinusoidal function. In fact, these vibrations are a combination of several vibration modes. In this study, these modes are extracted applying a recently developed method namely, partly ensemble empirical mode decomposition (PEEMD). Then, a methodology for estimating the damping properties and energy dissipation caused by damping for each mode is used. Applying this methodology on simulated signals demonstrates high accuracy. This methodology is applied to the acceleration signals of the gastrocnemius muscle during sprinting and the differences between the damping properties of different vibration modes were identified. The results were 1) the damping property of high-frequency mode was higher than that for low-frequency modes. 2) All identified modes were in under damped condition, therefore, the vibrations had an oscillatory nature. 3) The damping ratios of lower modes are about 100% increased compared to higher modes. 4) The energy dissipation occurred in lower modes were much more than that for higher mode; According to the power spectrum of the ground reaction force (GRF), which is the input force into the body, the recent finding supports the muscle tuning paradigm. It is suggested that the damping properties and energy dissipation can be used to distinguish between different running conditions (surface, fatigue, etc.).
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.
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.
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.
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.
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.
Asymptotic Dynamics of Attractive-Repulsive Swarms
NASA Astrophysics Data System (ADS)
Leverentz, Andrew J.; Topaz, Chad M.; Bernoff, Andrew J.
2009-01-01
We classify and predict the asymptotic dynamics of a class of swarming models. The model consists of a conservation equation in one dimension describing the movement of a population density field. The velocity is found by convolving the density with a kernel describing attractive-repulsive social interactions. The kernel's first moment and its limiting behavior at the origin determine whether the population asymptotically spreads, contracts, or reaches steady state. For the spreading case, the dynamics approach those of the porous medium equation. The widening, compactly supported population has edges that behave like traveling waves whose speed, density, and slope we calculate. For the contracting case, the dynamics of the cumulative density approach those of Burgers' equation. We derive an analytical upper bound for the finite blow-up time after which the solution forms one or more delta-functions.
Brane model with two asymptotic regions
NASA Astrophysics Data System (ADS)
Lubo, Musongela
2005-02-01
Some brane models rely on a generalization of the Melvin magnetic universe including a complex scalar field among the sources. We argue that the geometric interpretation of Kip. S. Thorne of this geometry restricts the kind of potential a complex scalar field can display to keep the same asymptotic behavior. While a finite energy is not obtained for a Mexican hat potential in this interpretation, this is the case for a potential displaying a broken phase and an unbroken one. We use for technical simplicity and illustrative purposes an ad hoc potential which however shares some features with those obtained in some supergravity models. We construct a sixth dimensional cylindrically symmetric solution which has two asymptotic regions: the Melvin-like metric on one side and a flat space displaying a conical singularity on the other. The causal structure of the configuration is discussed. Unfortunately, gravity is not localized on the brane.
The Asymptotic Safety Scenario in Quantum Gravity.
Niedermaier, Max; Reuter, Martin
2006-01-01
The asymptotic safety scenario in quantum gravity is reviewed, according to which a renormalizable quantum theory of the gravitational field is feasible which reconciles asymptotically safe couplings with unitarity. The evidence from symmetry truncations and from the truncated flow of the effective average action is presented in detail. A dimensional reduction phenomenon for the residual interactions in the extreme ultraviolet links both results. For practical reasons the background effective action is used as the central object in the quantum theory. In terms of it criteria for a continuum limit are formulated and the notion of a background geometry self-consistently determined by the quantum dynamics is presented. Self-contained appendices provide prerequisites on the background effective action, the effective average action, and their respective renormalization flows.
Asymptotic scaling in turbulent pipe flow.
McKeon, B J; Morrison, J F
2007-03-15
The streamwise velocity component in turbulent pipe flow is assessed to determine whether it exhibits asymptotic behaviour that is indicative of high Reynolds numbers. The asymptotic behaviour of both the mean velocity (in the form of the log law) and that of the second moment of the streamwise component of velocity in the outer and overlap regions is consistent with the development of spectral regions which indicate inertial scaling. It is shown that an 'inertial sublayer' in physical space may be considered as a spatial analogue of the inertial subrange in the velocity spectrum and such behaviour only appears for Reynolds numbers R+>5 x 10(3), approximately, much higher than was generally thought.
Asymptotic Markov inequality on Jordan arcs
NASA Astrophysics Data System (ADS)
Totik, V.
2017-03-01
Markov's inequality for the derivative of algebraic polynomials is considered on C^2-smooth Jordan arcs. The asymptotically best estimate is given for the kth derivative for all k=1,2,\\dots . The best constant is related to the behaviour around the endpoints of the arc of the normal derivative of the Green's function of the complementary domain. The result is deduced from the asymptotically sharp Bernstein inequality for the kth derivative at inner points of a Jordan arc, which is derived from a recent result of Kalmykov and Nagy on the Bernstein inequality on analytic arcs. In the course of the proof we shall also need to reduce the analyticity condition in this last result to C^2-smoothness. Bibliography: 21 titles.
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.
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
Asymptotic safety and the cosmological constant
NASA Astrophysics Data System (ADS)
Falls, Kevin
2016-01-01
We study the non-perturbative renormalisation of quantum gravity in four dimensions. Taking care to disentangle physical degrees of freedom, we observe the topological nature of conformal fluctuations arising from the functional measure. The resulting beta functions possess an asymptotically safe fixed point with a global phase structure leading to classical general relativity for positive, negative or vanishing cosmological constant. If only the conformal fluctuations are quantised we find an asymptotically safe fixed point predicting a vanishing cosmological constant on all scales. At this fixed point we reproduce the critical exponent, ν = 1/3, found in numerical lattice studies by Hamber. Returning to the full theory we find that by setting the cosmological constant to zero the critical exponent agrees with the conformally reduced theory. This suggests the fixed point may be physical while hinting at solution to the cosmological constant problem.
Dissipative solitons for mode-locked lasers
NASA Astrophysics Data System (ADS)
Grelu, Philippe; Akhmediev, Nail
2012-02-01
Dissipative solitons are localized formations of an electromagnetic field that are balanced through an energy exchange with the environment in presence of nonlinearity, dispersion and/or diffraction. Their growing use in the area of passively mode-locked lasers is remarkable: the concept of a dissipative soliton provides an excellent framework for understanding complex pulse dynamics and stimulates innovative cavity designs. Reciprocally, the field of mode-locked lasers serves as an ideal playground for testing the concept of dissipative solitons and revealing their unusual dynamics. This Review provides basic definitions of dissipative solitons, summarizes their implications for the design of high-energy mode-locked fibre laser cavities, highlights striking emerging dynamics such as dissipative soliton molecules, pulsations, explosions and rain, and finally provides an outlook for dissipative light bullets.
Multicolour nonlinearly bound chirped dissipative solitons.
Babin, Sergey A; Podivilov, Evgeniy V; Kharenko, Denis S; Bednyakova, Anastasia E; Fedoruk, Mikhail P; Kalashnikov, Vladimir L; Apolonski, Alexander
2014-08-13
The dissipative soliton regime is one of the most advanced ways to generate high-energy femtosecond pulses in mode-locked lasers. On the other hand, the stimulated Raman scattering in a fibre laser may convert the excess energy out of the coherent dissipative soliton to a noisy Raman pulse, thus limiting its energy. Here we demonstrate that intracavity feedback provided by re-injection of a Raman pulse into the laser cavity leads to formation of a coherent Raman dissipative soliton. Together, a dissipative soliton and a Raman dissipative soliton (of the first and second orders) form a two (three)-colour stable complex with higher total energy and broader spectrum than those of the dissipative soliton alone. Numerous applications can benefit from this approach, including frequency comb spectroscopy, transmission lines, seeding femtosecond parametric amplifiers, enhancement cavities and multiphoton fluorescence microscopy.
Modular quantum-information processing by dissipation
NASA Astrophysics Data System (ADS)
Marshall, Jeffrey; Campos Venuti, Lorenzo; Zanardi, Paolo
2016-11-01
Dissipation can be used as a resource to control and simulate quantum systems. We discuss a modular model based on fast dissipation capable of performing universal quantum computation, and simulating arbitrary Lindbladian dynamics. The model consists of a network of elementary dissipation-generated modules and it is in principle scalable. In particular, we demonstrate the ability to dissipatively prepare all single-qubit gates, and the controlled-not gate; prerequisites for universal quantum computing. We also show a way to implement a type of quantum memory in a dissipative environment, whereby we can arbitrarily control the loss in both coherence, and concurrence, over the evolution. Moreover, our dissipation-assisted modular construction exhibits a degree of inbuilt robustness to Hamiltonian and, indeed, Lindbladian errors, and as such is of potential practical relevance.
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.
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.
Thermodynamic geometry of minimum-dissipation driven barrier crossing.
Sivak, David A; Crooks, Gavin E
2016-11-01
We explore the thermodynamic geometry of a simple system that models the bistable dynamics of nucleic acid hairpins in single molecule force-extension experiments. Near equilibrium, optimal (minimum-dissipation) driving protocols are governed by a generalized linear response friction coefficient. Our analysis demonstrates that the friction coefficient of the driving protocols is sharply peaked at the interface between metastable regions, which leads to minimum-dissipation protocols that drive rapidly within a metastable basin, but then linger longest at the interface, giving thermal fluctuations maximal time to kick the system over the barrier. Intuitively, the same principle applies generically in free energy estimation (both in steered molecular dynamics simulations and in single-molecule experiments), provides a design principle for the construction of thermodynamically efficient coupling between stochastic objects, and makes a prediction regarding the construction of evolved biomolecular motors.
Thermodynamic geometry of minimum-dissipation driven barrier crossing
NASA Astrophysics Data System (ADS)
Sivak, David A.; Crooks, Gavin E.
2016-11-01
We explore the thermodynamic geometry of a simple system that models the bistable dynamics of nucleic acid hairpins in single molecule force-extension experiments. Near equilibrium, optimal (minimum-dissipation) driving protocols are governed by a generalized linear response friction coefficient. Our analysis demonstrates that the friction coefficient of the driving protocols is sharply peaked at the interface between metastable regions, which leads to minimum-dissipation protocols that drive rapidly within a metastable basin, but then linger longest at the interface, giving thermal fluctuations maximal time to kick the system over the barrier. Intuitively, the same principle applies generically in free energy estimation (both in steered molecular dynamics simulations and in single-molecule experiments), provides a design principle for the construction of thermodynamically efficient coupling between stochastic objects, and makes a prediction regarding the construction of evolved biomolecular motors.
Efficient Schmidt number scaling in dissipative particle dynamics
Krafnick, Ryan C.; García, Angel E.
2015-01-01
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. PMID:26723591
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.
Influence of dissipation on two-atom dispersion interactions
NASA Astrophysics Data System (ADS)
Barcellona, Pablo; Buhmann, Stefan Yoshi
2015-03-01
We consider the dispersion interaction between two neutral, ground-state atoms at zero and finite temperature by means of a dynamical approach. Our result differs from the previous ones obtained with time-independent perturbation theory because it correctly accounts for the influence of dissipation via the atomic decay rates. Modern measurements of Casimir force seem to suggest a suppressed influence of dissipation. Our new result shows similar features and can hence help resolve the Drude-plasma debate. We also consider the interaction between a ground-state atom and an excited atom. There are discordant results in the literature for the retarded potential: one oscillating and one monotonous. Our dynamical result uniquely leads to the oscillating result when taking into account the decay rates. This work was supported by the DFG (Grant BU 1803/3-1).
Non-asymptotic Analysis of Bandlimited Functions
2012-01-12
Illustration of Theorem 10 with c = 1000 and n = 670. 44 References [1] Richard K. Miller, Anthony N. Michel, Ordinary Differential Equations, Dover ...Publications, Inc., 1982. [2] Yoel Shkolnisky, Mark Tygert, Vladimir Rokhlin, Approximation of Ban - dlimited Functions. [3] Andreas Glaser, Xiangtao Liu...A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, Dover Publications, 1964. [22] M.V. Fedoryuk, Asymptotic
Asymptotic properties of path integral ideals
Bogojevic, A.; Balaz, A.; Belic, A.
2005-09-01
We introduce and analyze an interesting quantity, the path integral ideal, governing the flow of generic discrete theories to the continuum limit and greatly increasing their convergence. The said flow is classified according to the degree of divergence of the potential at spatial infinity. Studying the asymptotic behavior of path integral ideals we isolate the dominant terms in the effective potential that determine the behavior of a generic theory for large discrete time steps.
Quantum speed meter based on dissipative coupling
NASA Astrophysics Data System (ADS)
Vyatchanin, Sergey P.; Matsko, Andrey B.
2017-01-01
We consider dissipative coupling Fabry-Perot cavity, i.e. its input mirror transmittance depends on position of probe mass. We show that dissipative coupling provide possibility to realize quantum speed meter by natural way, without additional setup for subtraction of position x(t) and delayed position x(t-τ). Quantum speed meter is a quantum non demolition (QND) meter which allow to overcome Standatd Quantum Limit — we show it for speed meter based on dissipative coupling.
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.
Some asymptotic properties of duplication graphs
NASA Astrophysics Data System (ADS)
Raval, Alpan
2003-12-01
Duplication graphs are graphs that grow by duplication of existing vertices, and are important models of biological networks, including protein-protein interaction networks and gene regulatory networks. Three models of graph growth are studied: pure duplication growth, and two two-parameter models in which duplication forms one element of the growth dynamics. A power-law degree distribution is found to emerge in all three models. However, the parameter space of the latter two models is characterized by a range of parameter values for which duplication is the predominant mechanism of graph growth. For parameter values that lie in this “duplication-dominated” regime, it is shown that the degree distribution either approaches zero asymptotically, or approaches a nonzero power-law degree distribution very slowly. In either case, the approach to the true asymptotic degree distribution is characterized by a dependence of the scaling exponent on properties of the initial degree distribution. It is therefore conjectured that duplication-dominated, scale-free networks may contain identifiable remnants of their early structure. This feature is inherited from the idealized model of pure duplication growth, for which the exact finite-size degree distribution is found and its asymptotic properties studied.
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}.
Dissipation of sleep pressure is stable across adolescence.
Tarokh, L; Carskadon, M A; Achermann, P
2012-08-02
The sleep electroencephalogram (EEG) undergoes many changes during adolescence. We assessed whether sleep homeostasis is altered across adolescent development using two measures: the dissipation of slow-wave activity (SWA, 0.6-4.6Hz) across the night and the rate of build-up of SWA in the first non-rapid eye movement (NREM) sleep episode. Furthermore, we examined the association between homeostatic and circadian measures, by correlating the build-up of SWA in the first non-rapid eye movement (NREM) sleep episode with circadian phase. Finally, we compared the dissipation of SWA in individuals with (PH+) and without (PH-) a parental history of alcohol abuse/dependence. Twenty children (8 PH+) and 25 teens (10 PH+) underwent two consecutive polysomnographic recordings at ages 9/10 and 15/16 years and again 1.5-3 years later. Thirteen young adults (ages 20-23 years; no PH+) were assessed one time. The decay of Process S was modeled for each individual at each assessment using data from both recordings. Four parameters of Process S were derived for EEG derivation C3/A2: time constant of the decay, lower asymptote (LA), the level of S at sleep onset (S(SO)), and S(SO) minus LA. We found no change in these parameters between assessments for the children and teen cohorts. Between-subject analysis of the follow-up assessment for children (ages 11-13 years) and the initial assessment for teens (ages 15/16 years) showed no difference in these parameters, nor did follow-up assessment of teens (ages 17-19 years) compared to the single assessment of young adults (ages 20-23 years). Similarly, we observed no developmental changes in the rate of the build-up of SWA in the first NREM sleep episode for our within- and between-subject analyses, or a correlation between this measure and circadian phase for either cohort. With regard to parental alcohol history, we found no difference in the dissipation of sleep pressure between PH+ and PH- children and teens. These results indicate
Dissipation of Sleep Pressure is Stable Across Adolescence
Tarokh, Leila; Carskadon, Mary A.; Achermann, Peter
2014-01-01
The sleep EEG undergoes many changes during adolescence. We assessed whether sleep homeostasis is altered across adolescent development using two measures: the dissipation of slow-wave activity (SWA, 0.6 to 4.6 Hz) across the night and the rate of build-up of SWA in the first NREM sleep episode. Furthermore, we examined the association between homeostatic and circadian measures, by correlating the build-up of SWA in the first NREM sleep episode with circadian phase. Finally, we compared the dissipation of SWA in individuals with (PH+) and without (PH-) a parental history of alcohol abuse/dependence. Twenty children (8 PH+) and twenty-five teens (10 PH+) underwent two consecutive polysomnographic recordings at ages 9/10 and 15/16 years and again 1.5 to 3 years later. Thirteen young adults (ages 20 to 23; no PH+) were assessed one time. The decay of Process S was modeled for each individual at each assessment using data from both recordings. Four parameters of Process S were derived for EEG derivation C3/A2: time constant of the decay, lower asymptote (LA), the level of S at sleep onset (SSO), and SSO minus LA. We found no change in these parameters between assessments for the children and teen cohorts. Between-subjects analysis of the follow-up assessment for children (ages 11-13) and the initial assessment for teens (ages 15/16) showed no difference in these parameters, nor did follow-up assessment of teens (ages 17-19) compared to the single assessment of young adults (ages 20-23). Similarly, we observed no developmental changes in the rate of the build-up of SWA in the first NREM sleep episode for our within- and between-subjects analyses, or a correlation between this measure and circadian phase for either cohort. With regards to parental alcohol history, we found no difference in the dissipation of sleep pressure between PH+ and PH- children and teens. These results indicate that the dissipation of sleep pressure does not change across adolescent development
Non-unique results of collisions of quasi-one-dimensional dissipative solitons.
Descalzi, Orazio; Brand, Helmut R
2015-12-13
We investigate collisions of quasi-one-dimensional dissipative solitons (DSs) for a large class of initial conditions, which are not temporally asymptotic quasi-one-dimensional DSs. For the case of sufficiently small approach velocity and sufficiently large values of the dissipative cross-coupling between the counter-propagating DSs, we find non-unique results for the outcome of collisions. We demonstrate that these non-unique results are intrinsically related to a modulation instability along the crest of the quasi-one-dimensional objects. As a model, we use coupled cubic-quintic complex Ginzburg-Landau equations. Among the final results found are stationary and oscillatory compound states as well as more complex assemblies consisting of quasi-one-dimensional and localized states. We analyse to what extent the final results can be described by the solutions of one cubic-quintic complex Ginzburg-Landau equation with effective parameters. © 2015 The Author(s).
NASA Technical Reports Server (NTRS)
Busemann, A.; Vinh, N. X.; Culp, R. D.
1976-01-01
The problem of determining the trajectories, partially or wholly contained in the atmosphere of a spherical, nonrotating planet, is considered. The exact equations of motion for three-dimensional, aerodynamically affected flight are derived. Modified Chapman variables are introduced and the equations are transformed into a set suitable for analytic integration using asymptotic expansions. The trajectory is solved in two regions: the outer region, where the force may be considered a gravitational field with aerodynamic perturbations, and the inner region, where the force is predominantly aerodynamic, with gravity as a perturbation. The two solutions are matched directly. A composite solution, valid everywhere, is constructed by additive composition. This approach of directly matched asymptotic expansions applied to the exact equations of motion couched in terms of modified Chapman variables yields an analytical solution which should prove to be a powerful tool for aerodynamic orbit calculations.
Dissipative entanglement of quantum spin fluctuations
Benatti, F.; Carollo, F.; Floreanini, R.
2016-06-15
We consider two non-interacting infinite quantum spin chains immersed in a common thermal environment and undergoing a local dissipative dynamics of Lindblad type. We study the time evolution of collective mesoscopic quantum spin fluctuations that, unlike macroscopic mean-field observables, retain a quantum character in the thermodynamical limit. We show that the microscopic dissipative dynamics is able to entangle these mesoscopic degrees of freedom, through a purely mixing mechanism. Further, the behaviour of the dissipatively generated quantum correlations between the two chains is studied as a function of temperature and dissipation strength.
Dissipation-induced instabilities and symmetry
NASA Astrophysics Data System (ADS)
Kirillov, Oleg N.; Verhulst, Ferdinand
2011-02-01
The paradox of destabilization of a conservative or non-conservative system by small dissipation, or Ziegler's paradox (1952), has stimulated a growing interest in the sensitivity of reversible and Hamiltonian systems with respect to dissipative perturbations. Since the last decade it has been widely accepted that dissipation-induced instabilities are closely related to singularities arising on the stability boundary, associated with Whitney's umbrella. The first explanation of Ziegler's paradox was given (much earlier) by Oene Bottema in 1956. The aspects of the mechanics and geometry of dissipation-induced instabilities with an application to rotor dynamics are discussed.
Geometric Integration of Weakly Dissipative Systems
NASA Astrophysics Data System (ADS)
Modin, K.; Führer, C.; Soöderlind, G.
2009-09-01
Some problems in mechanics, e.g. in bearing simulation, contain subsystems that are conservative as well as weakly dissipative subsystems. Our experience is that geometric integration methods are often superior for such systems, as long as the dissipation is weak. Here we develop adaptive methods for dissipative perturbations of Hamiltonian systems. The methods are "geometric" in the sense that the form of the dissipative perturbation is preserved. The methods are linearly explicit, i.e., they require the solution of a linear subsystem. We sketch an analysis in terms of backward error analysis and numerical comparisons with a conventional RK method of the same order is given.
Dissipative entanglement of quantum spin fluctuations
NASA Astrophysics Data System (ADS)
Benatti, F.; Carollo, F.; Floreanini, R.
2016-06-01
We consider two non-interacting infinite quantum spin chains immersed in a common thermal environment and undergoing a local dissipative dynamics of Lindblad type. We study the time evolution of collective mesoscopic quantum spin fluctuations that, unlike macroscopic mean-field observables, retain a quantum character in the thermodynamical limit. We show that the microscopic dissipative dynamics is able to entangle these mesoscopic degrees of freedom, through a purely mixing mechanism. Further, the behaviour of the dissipatively generated quantum correlations between the two chains is studied as a function of temperature and dissipation strength.
Correlated electrons in a dissipative environment
NASA Astrophysics Data System (ADS)
Bulla, R.
2009-12-01
When a system of correlated electrons is embedded in a dissipative environment, new emergent phenomena might occur due to the interplay of correlation and dissipation. Here we focus on quantum impurity systems with coupling to a bosonic bath. For the theoretical investigation we introduce the bosonic numerical renormalization group method which has been initially set up for the spin-boson model. The role of both correlations and dissipation is described in the context of two-electron transfer systems. We also discuss prospects for the investigation of lattice models of correlated electrons with coupling to a dissipative bath.
An asymptotically safe solution to the U(1) triviality problem
NASA Astrophysics Data System (ADS)
Christiansen, Nicolai; Eichhorn, Astrid
2017-07-01
We explore whether quantum gravity effects within the asymptotic safety paradigm can provide a predictive ultraviolet completion for Abelian gauge theories. We evaluate the effect of quantum gravity fluctuations on the running couplings in the gauge sector and discover an asymptotically safe fixed point of the Renormalization Group. In particular, if the strength of gravitational interactions remains below a critical strength, the minimal gauge coupling becomes asymptotically free. Further, we point out that a completely asymptotically free dynamics for the gauge field is impossible to achieve, as asymptotically safe quantum gravity necessarily induces non-vanishing higher-order interactions for the gauge field in the ultraviolet.
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)].
Konow, Nicolai; Roberts, Thomas J
2015-04-07
During downhill running, manoeuvring, negotiation of obstacles and landings from a jump, mechanical energy is dissipated via active lengthening of limb muscles. Tendon compliance provides a 'shock-absorber' mechanism that rapidly absorbs mechanical energy and releases it more slowly as the recoil of the tendon does work to stretch muscle fascicles. By lowering the rate of muscular energy dissipation, tendon compliance likely reduces the risk of muscle injury that can result from rapid and forceful muscle lengthening. Here, we examine how muscle-tendon mechanics are modulated in response to changes in demand for energy dissipation. We measured lateral gastrocnemius (LG) muscle activity, force and fascicle length, as well as leg joint kinematics and ground-reaction force, as turkeys performed drop-landings from three heights (0.5-1.5 m centre-of-mass elevation). Negative work by the LG muscle-tendon unit during landing increased with drop height, mainly owing to greater muscle recruitment and force as drop height increased. Although muscle strain did not increase with landing height, ankle flexion increased owing to increased tendon strain at higher muscle forces. Measurements of the length-tension relationship of the muscle indicated that the muscle reached peak force at shorter and likely safer operating lengths as drop height increased. Our results indicate that tendon compliance is important to the modulation of energy dissipation by active muscle with changes in demand and may provide a mechanism for rapid adjustment of function during deceleration tasks of unpredictable intensity.
asymptoticMK: A Web-Based Tool for the Asymptotic McDonald-Kreitman Test.
Haller, Benjamin C; Messer, Philipp W
2017-05-05
The McDonald-Kreitman (MK) test is a widely used method for quantifying the role of positive selection in molecular evolution. One key shortcoming of this test lies in its sensitivity to the presence of slightly deleterious mutations, which can severely bias its estimates. An asymptotic version of the MK test was recently introduced that addresses this problem by evaluating polymorphism levels for different mutation frequencies separately, and then extrapolating a function fitted to that data. Here, we present asymptoticMK, a web-based implementation of this asymptotic MK test. Our web service provides a simple R-based interface into which the user can upload the required data (polymorphism and divergence data for the genomic test region and a neutrally evolving reference region). The web service then analyzes the data and provides plots of the test results. This service is free to use, open-source, and available at http://benhaller.com/messerlab/asymptoticMK.html We provide results from simulations to illustrate the performance and robustness of the asymptoticMK test under a wide range of model parameters. Copyright © 2017 Haller and Messer.
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.
Dissipative adaptation in driven self-assembly.
England, Jeremy L
2015-11-01
In a collection of assembling particles that is allowed to reach thermal equilibrium, the energy of a given microscopic arrangement and the probability of observing the system in that arrangement obey a simple exponential relationship known as the Boltzmann distribution. Once the same thermally fluctuating particles are driven away from equilibrium by forces that do work on the system over time, however, it becomes significantly more challenging to relate the likelihood of a given outcome to familiar thermodynamic quantities. Nonetheless, it has long been appreciated that developing a sound and general understanding of the thermodynamics of such non-equilibrium scenarios could ultimately enable us to control and imitate the marvellous successes that living things achieve in driven self-assembly. Here, I suggest that such a theoretical understanding may at last be emerging, and trace its development from historic first steps to more recent discoveries. Focusing on these newer results, I propose that they imply a general thermodynamic mechanism for self-organization via dissipation of absorbed work that may be applicable in a broad class of driven many-body systems.
Soap film vibration: origin of the dissipation.
Acharige, Sébastien Kosgodagan; Elias, Florence; Derec, Caroline
2014-11-07
We investigate the complex dispersion relationship of a transverse antisymmetric wave on a horizontal soap film. Experimentally, the complex wave number k at a fixed forcing frequency is determined by measuring the vibrating amplitude of the soap film: the wavelength (linked to the real part of k) is determined by the spatial variation of the amplitude; the decay length (linked to the imaginary part of k) is determined by analyzing the resonance curves of the vibrating wave as a function of frequency. Theoretically, we compute the complex dispersion relationship taking into account the physical properties of the bulk liquid and gas phase, and of the gas-liquid interfaces. The comparison between the computation (developed to the leading order under our experimental conditions) and the experimental results confirms that the phase velocity is fixed by the interplay between surface tension, and liquid and air inertia, as reported in previous studies. Moreover, we show that the attenuation of the transverse antisymmetric wave originates from the viscous dissipation in the gas phase surrounding the liquid film. This result is an important step in understanding the propagation of an acoustic wave in liquid foam, using a bottom-up approach.
Granular flows on a dissipative base.
Louge, Michel Y; Valance, Alexandre; Lancelot, Paul; Delannay, Renaud; Artières, Olivier
2015-08-01
We study inclined channel flows of sand over a sensor-enabled composite geotextile fabric base that dissipates granular fluctuation energy. We record strain of the fabric along the flow direction with imbedded fiber-optic Bragg gratings, flow velocity on the surface by correlating grain position in successive images, flow thickness with the streamwise shift of an oblique laser light sheet, velocity depth profile through a transparent side wall using a high-speed camera, and overall discharge rate. These independent measurements at inclinations between 33∘ and 37∘ above the angle of repose at 32.1±0.8∘ are consistent with a mass flow rate scaling as the 3/2 power of the flow depth, which is markedly different than flows on a rigid bumpy boundary. However, this power changes to 5/2 when flows are forced on the sand bed below its angle of repose. Strain measurements imply that the mean solid volume fraction in the flowing layer above the angle of repose is 0.268±0.033, independent of discharge rate or inclination.
Internal dissipation of a polymer
Deutsch, J. M.
2010-06-15
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.
Variational principles for dissipative waves
NASA Astrophysics Data System (ADS)
Dodin, I. Y.; Ruiz, D. E.
2016-10-01
Variational methods are a powerful tool in plasma theory. However, their applications are typically restricted to conservative systems or require doubling of variables, which often contradicts the purpose of the variational approach altogether. We show that these restrictions can be relaxed for some classes of dynamical systems that are of practical interest in plasma physics, particularly including dissipative plasma waves. Applications will be discussed to calculating dispersion relations and modulational dynamics of individual plasma waves and wave ensembles. The work was supported by the NNSA SSAA Program through DOE Research Grant No. DE-NA0002948, by the U.S. DOE through Contract No. DE-AC02-09CH11466, and by the U.S. DOD NDSEG Fellowship through Contract No. 32-CFR-168a.
Dissipative shocks behind bacteria gliding.
Virga, Epifanio G
2014-11-28
Gliding is a means of locomotion on rigid substrates used by a number of bacteria, including myxobacteria and cyanobacteria. One of the hypotheses advanced to explain this motility mechanism hinges on the role played by the slime filaments continuously extruded from gliding bacteria. This paper solves, in full, a non-linear mechanical theory that treats as dissipative shocks both the point where the extruded slime filament comes into contact with the substrate, called the filament's foot, and the pore on the bacterium outer surface from where the filament is ejected. I prove that kinematic compatibility for shock propagation requires that the bacterium uniform gliding velocity (relative to the substrate) and the slime ejecting velocity (relative to the bacterium) must be equal, a coincidence that seems to have already been observed. © 2014 The Author(s) Published by the Royal Society. All rights reserved.
Internal dissipation of a polymer
NASA Astrophysics Data System (ADS)
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.
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.
Dissipative Dynamics with Exotic Beams
NASA Astrophysics Data System (ADS)
di Toro, M.; Colonna, M.; Greco, V.; Ferini, G.; Rizzo, C.; Rizzo, J.; Baran, V.; Wolter, H. H.; Zielinska-Pfabe, M.
2008-04-01
Heavy Ion Collisions (HIC) represent a unique tool to probe the in-medium nuclear interaction in regions away from saturation and at high nucleon momenta. In this report we present a selection of reaction observables particularly sensitive to the isovector part of the interaction, i.e. to the symmetry term of the nuclear Equation of State (EoS) At low and Fermi energies the behavior of the symmetry energy around saturation influences dissipation and fragment production mechanisms. Predictions are shown for fusion, deep-inelastic and fragmentation collisions induced by neutron rich projectiles. At all energies the isospin transport data are supplying valuable information on value and slope of the symmetry term below saturation. The importance of studying violent collisions with radioactive beams in this energy range is finally stressed.
Unravelling tidal dissipation in gaseous giant planets
NASA Astrophysics Data System (ADS)
Guenel, M.; Mathis, S.; Remus, F.
2014-06-01
Context. Tidal dissipation in planetary interiors is one of the key physical mechanisms that drive the evolution of star-planet and planet-moon systems. New constraints on this dissipation are now obtained both in the solar and exo-planetary systems. Aims: Tidal dissipation in planets is intrinsically related to their internal structure. Indeed, the dissipation behaves very differently when we compare its properties in solid and fluid planetary layers. Since planetary interiors consist of both types of regions, it is necessary to be able to assess and compare the respective intensity of the reservoir of dissipation in each type of layers. Therefore, in the case of giant planets, the respective contribution of the potential central dense rocky/icy core and of the deep convective fluid envelope must be computed as a function of the mass and the radius of the core. This will allow us to obtain their respective strengths. Methods: Using a method that evaluates the reservoir of dissipation associated to each region, which is a frequency-average of complex tidal Love numbers, we compared the respective contributions of the central core and of the fluid envelope. Results: For Jupiter- and Saturn-like planets, we show that the viscoelastic dissipation in the core could dominate the turbulent friction acting on tidal inertial waves in the envelope. However, the fluid dissipation would not be negligible. This demonstrates that it is necessary to build complete models of tidal dissipation in planetary interiors from their deep interior to their surface without any arbitrary assumptions. Conclusions: We demonstrate how important it is to carefully evaluate the respective strength of each type of dissipation mechanism in planetary interiors and to go beyond the usually adopted ad-hoc models. We confirm the significance of tidal dissipation in the potential dense core of gaseous giant planets.
Forced synchronization of a self-sustained chaotic oscillator.
González Salas, J S; Campos Cantón, E; Ordaz Salazar, F C; Campos Cantón, I
2008-06-01
This work presents a forced synchronization phenomenon like the asymptotic correlated behavior between chaotic oscillators forced by an external signal. Different kinds of forced synchronization are presented and given a theoretical justification explaining why it is possible to find some of them. Numerical results are presented for different cases such as antisymmetric, lag, phase, and identical forced synchronization.
Asymptotic properties of mathematical models of excitability.
Biktasheva, I V; Simitev, R D; Suckley, R; Biktashev, V N
2006-05-15
We analyse small parameters in selected models of biological excitability, including Hodgkin-Huxley (Hodgkin & Huxley 1952 J. Physiol.117, 500-544) model of nerve axon, Noble (Noble 1962 J. Physiol.160, 317-352) model of heart Purkinje fibres and Courtemanche et al. (Courtemanche et al. 1998 Am. J. Physiol.275, H301-H321) model of human atrial cells. Some of the small parameters are responsible for differences in the characteristic time-scales of dynamic variables, as in the traditional singular perturbation approaches. Others appear in a way which makes the standard approaches inapplicable. We apply this analysis to study the behaviour of fronts of excitation waves in spatially extended cardiac models. Suppressing the excitability of the tissue leads to a decrease in the propagation speed, but only to a certain limit; further suppression blocks active propagation and leads to a passive diffusive spread of voltage. Such a dissipation may happen if a front propagates into a tissue recovering after a previous wave, e.g. re-entry. A dissipated front does not recover even when the excitability restores. This has no analogy in FitzHugh-Nagumo model and its variants, where fronts can stop and then start again. In two spatial dimensions, dissipation accounts for breakups and self-termination of re-entrant waves in excitable media with Courtemanche et al. kinetics.
Dissipation of anomalous pressures in the subsurface
NASA Astrophysics Data System (ADS)
Muggeridge, Ann; Abacioglu, Yafes; England, William; Smalley, Craig
2004-11-01
Zones of anomalous pressure, higher and lower than hydrostatic pressure, have been observed in many sedimentary basins around the world. These normally consist of groups of pressure compartments: volumes of higher-permeability rock surrounded on all sides by lower-permeability barriers. Knowledge of the timescales over which these abnormal pressures are maintained and the mechanisms by which they dissipate is critical for understanding how fluids, such as oil and gas, move in the subsurface. Existing analytic solutions investigate pressure dissipation through low-permeability barriers on top of or underneath an isolated pressure compartment. There are no analytic solutions describing pressure dissipation through lateral barriers, such as faults, or investigating the impact of groups of pressure compartments on the rate of pressure dissipation. This paper presents simple analytic models to investigate pressure dissipation through barriers, such as faults, forming the sides of pressure compartments. The timescales are compared with a solution for pressure dissipation through barriers on top of and underneath the compartment. It also investigates analytically the rate of pressure dissipation from groups of pressure compartments. Lateral seal permeabilities of 10-19 m2 may delay pressure equilibration for millions of years provided the compartment has a sufficiently high fluid storage capacity. Factors contributing toward a high fluid storage capacity include a high fluid compressibility (as is the case in hydrocarbon reservoirs) and a high porosity. The grouping of abnormally pressured compartments into "megacompartment complexes" may delay pressure dissipation for hundreds of millions of years.
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.
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 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.
Energy dissipation in fragmented geomaterials associated with impacting oscillators
NASA Astrophysics Data System (ADS)
Khudyakov, Maxim; Pasternak, Elena; Dyskin, Arcady
2016-04-01
In wave propagation through fragmented geomaterials forced by periodic loadings, the elements (fragments) strike against each other when passing through the neutral position (position with zero mutual rotation), quickly damping the oscillations. Essentially the impacts act as shock absorbers albeit localised at the neutral points. In order to analyse the vibrations of and wave propagation in such structures, a differential equation of a forced harmonic oscillator was investigated, where the each time the system passes through the neutral point the velocity gets reduced by multiplying it with the restitution coefficient which characterise the impact of the fragments. In forced vibrations the impact times depend on both the forced oscillations and the restitution coefficient and form an irregular sequence. Numerical solution of the differential equation was performed using Mathematica software. Along with vibration diagrams, the dependence of the energy dissipation on the ratio of the forcing frequency to the natural frequency was obtained. For small positive values of the restitution coefficient (less than 0.5), the asymmetric oscillations were found, and the phase of the forced vibrations determined the direction of the asymmetry. Also, at some values of the forcing frequencies and the restitution coefficient chaotic behaviour was found.
Theory of harmonic dissipation in disordered solids
NASA Astrophysics Data System (ADS)
Damart, T.; Tanguy, A.; Rodney, D.
2017-02-01
Mechanical spectroscopy, i.e., cyclic deformations at varying frequencies, is used theoretically and numerically to compute dissipation in model glasses. From a normal mode analysis, we show that in the high-frequency terahertz regime where dissipation is harmonic, the quality factor (or loss angle) can be expressed analytically. This expression is validated through nonequilibrium molecular dynamics simulations applied to a model of amorphous silica (SiO2). Dissipation is shown to arise from nonaffine relaxations triggered by the applied strain through the excitation of vibrational eigenmodes that act as damped harmonic oscillators. We discuss an asymmetry vector field, which encodes the information about the structural origin of dissipation computed by mechanical spectroscopy. In the particular case of silica, we find that the motion of oxygen atoms, which induce a deformation of the Si-O-Si bonds, is the main contributor to harmonic energy dissipation.
Exploring quantum phases by driven dissipation
NASA Astrophysics Data System (ADS)
Lang, Nicolai; Büchler, Hans Peter
2015-07-01
Dephasing and decay are the intrinsic dissipative processes prevalent in any open quantum system and the dominant mechanisms for the loss of coherence and entanglement. This inadvertent effect not only can be overcome but can even be capitalized on in a dissipative quantum simulation by means of tailored couplings between the quantum system and the environment. In this context it has been demonstrated that universal quantum computation can be performed using purely dissipative elements, and furthermore, the efficient preparation of highly entangled states is possible. In this article, we are interested in nonequilibrium phase transitions appearing in purely dissipative systems and the exploration of quantum phases in terms of a dissipative quantum simulation. To elucidate these concepts, we scrutinize exemplarily two paradigmatic models: the transverse-field Ising model and the considerably more complex Z2 lattice gauge theory. We show that the nonequilibrium phase diagrams parallel the quantum phase diagrams of the Hamiltonian "blueprint" theories.
Abnormal single or composite dissipative solitons generation
NASA Astrophysics Data System (ADS)
Zhong, Xianqiong; Liu, Dingyao; Cheng, Ke; Sheng, Jianan
2016-12-01
The evolution dynamics of the initial finite energy Airy pulses and Airy pulse pairs are numerically investigated in the cubic-quintic complex Ginzberg-Laudau equation governed dissipative system. Depending on different initial excitations and system parameters, abnormal double, triple, and quadruple composite dissipative solitons as well as single dissipative solitons can be observed. The composite dissipative solitons may consist of identical or different types of pulsating solitons. Moreover, the creeping solitons and the single ordinary pulsating solitons can even appear in the parameter regions where originally the other types of pulsating solitons exist. Besides, before evolving into each abnormal dissipative soliton, the initial finite energy Airy pulse or pulse pairs generally exhibit very interesting and unique early evolution behavior.
Precisely timing dissipative quantum information processing.
Kastoryano, M J; Wolf, M M; Eisert, J
2013-03-15
Dissipative engineering constitutes a framework within which quantum information processing protocols are powered by system-environment interaction rather than by unitary dynamics alone. This framework embraces noise as a resource and, consequently, offers a number of advantages compared to one based on unitary dynamics alone, e.g., that the protocols are typically independent of the initial state of the system. However, the time independent nature of this scheme makes it difficult to imagine precisely timed sequential operations, conditional measurements, or error correction. In this work, we provide a path around these challenges, by introducing basic dissipative gadgets which allow us to precisely initiate, trigger, and time dissipative operations while keeping the system Liouvillian time independent. These gadgets open up novel perspectives for thinking of timed dissipative quantum information processing. As an example, we sketch how measurement-based computation can be simulated in the dissipative setting.
Precisely Timing Dissipative Quantum Information Processing
NASA Astrophysics Data System (ADS)
Kastoryano, M. J.; Wolf, M. M.; Eisert, J.
2013-03-01
Dissipative engineering constitutes a framework within which quantum information processing protocols are powered by system-environment interaction rather than by unitary dynamics alone. This framework embraces noise as a resource and, consequently, offers a number of advantages compared to one based on unitary dynamics alone, e.g., that the protocols are typically independent of the initial state of the system. However, the time independent nature of this scheme makes it difficult to imagine precisely timed sequential operations, conditional measurements, or error correction. In this work, we provide a path around these challenges, by introducing basic dissipative gadgets which allow us to precisely initiate, trigger, and time dissipative operations while keeping the system Liouvillian time independent. These gadgets open up novel perspectives for thinking of timed dissipative quantum information processing. As an example, we sketch how measurement-based computation can be simulated in the dissipative setting.
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.
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
The Two Isotropic Asymptotes of Fiber Composites,
1988-03-01
Voigt and Reuss models of summed stiffness and compliance. The compliance quasi-isotropic asymptote, which >’-:’ has evidently not been discussed in the...i,j,e)de o0 The resulting pseudo -isotropic compliance (series-model) Hooke’s law matrix is similar but not identical to Eq. (3): W(1) W(4) 0 a aIE...given by 1 W( ) 14) E : - Vc Wc 4W(5) 2[W(1) - W()] (8) c W() W(14 12 Direct formulas for the pseudo -isctrcpic moduli, in terms of the ply 1s natural
Asymptotic 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.
Network asymptotics for high contrast impedance tomography
Borcea, L.; Papanicolaou, G.C.; Berryman, J.G.
1996-05-01
Fluid contaminant plumes underground are often electrically conducting and, therefore, can be imaged using electrical impedance tomography. The authors introduce an output least-squares method for impedance tomography problems that have regions of high conductivity surrounded by regions of lower conductivity. The high conductivity is modeled on network approximation results from an asymptotic analysis and its recovery is based on this model. The smoothly varying part of the conductivity is recovered by a linearization process as is usual. The authors present the results of several numerical experiments that illustrate the performance of the method.
Asymptotics of loop quantum gravity fusion coefficients
NASA Astrophysics Data System (ADS)
Alesci, Emanuele; Bianchi, Eugenio; Magliaro, Elena; Perini, Claudio
2010-05-01
The fusion coefficients from SO(3) to SO(4) play a key role in the definition of spin foam models for the dynamics in loop quantum gravity. In this paper we give a simple analytic formula of the Engle-Pereira-Rovelli-Livine fusion coefficients. We study the large spin asymptotics and show that they map SO(3) semiclassical intertwiners into SU(2)L × SU(2)R semiclassical intertwiners. This non-trivial property opens the possibility for an analysis of the semiclassical behavior of the model.
Use of asymptotic methods in vibration analysis
NASA Technical Reports Server (NTRS)
Ashley, H.
1978-01-01
The derivation of dynamic differential equations, suitable for studying the vibrations of rotating, curved, slender structures was examined, and the Hamiltonian procedure was advocated for this purpose. Various reductions of the full system are displayed, which govern the vibrating troposkien when various order of magnitude restrictions are placed on important parameters. Possible advantages of the WKB asymptotic method for solving these classes of problems are discussed. A special case of this method is used illustratively to calculate eigenvalues and eigenfunctions for a flat turbine blade with small flexural stiffness.
Vacuum Potential and its Asymptotic Variation
NASA Astrophysics Data System (ADS)
Dahal, Pravin
2016-09-01
The possible form of existence of dark energy is explained and the relation for its asymptotic variation is given. This has two huge implications in the understanding of the Universe. The first is that the theory predicts that the Universe should be in negative pressure state in the very early period as required for inflation and spontaneous symmetry breaking. The second is that the theory gives the reasonable answer to the astrophysical evidence of dark energy dominating the Universe. The author is presenting his research in the nature of dark energy. Some of the work is submitted for publication in the journal and is currently under review.
Asymptotic Representations of Quantum Affine Superalgebras
NASA Astrophysics Data System (ADS)
Zhang, Huafeng
2017-08-01
We study representations of the quantum affine superalgebra associated with a general linear Lie superalgebra. In the spirit of Hernandez-Jimbo, we construct inductive systems of Kirillov-Reshetikhin modules based on a cyclicity result that we established previously on tensor products of these modules, and realize their inductive limits as modules over its Borel subalgebra, the so-called q-Yangian. A new generic asymptotic limit of the same inductive systems is proposed, resulting in modules over the full quantum affine superalgebra. We derive generalized Baxter's relations in the sense of Frenkel-Hernandez for representations of the full quantum group.
Asymptotic Theory for Nonparametric Confidence Intervals.
1982-07-01
distributions. Ann. Math Statist. 14, 56-62. 24. ROY, S.N. and POTTHOFF, R.F. (1958). Confidence bounds on vector analogues of the "ratio of the mean" and...fl c,~_________ 14L TITLE feed &MV) S. TYPE or REPORT a PeftOo COVx:REC Asympeocic Theory for Nonaparuetric Technical Report Confidence Intevals 6...S..C-0S78 UNCLASSIFIED TŗU *uuuuumuuumhhhhmhhhm_4 ASYMPTOTIC THEORY FOR NONPARAMETRIC CONFIDENCE INTERVALS by Peter W. Glynn TECHNICAL REPORT NO. 63
Dissipative-particle-dynamics model of biofilm growth.
Xu, Zhijie; Meakin, Paul; Tartakovsky, Alexandre; Scheibe, Timothy D
2011-06-01
A dissipative-particle-dynamics 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.
Dissipative-particle-dynamics model of biofilm growth
NASA Astrophysics Data System (ADS)
Xu, Zhijie; Meakin, Paul; Tartakovsky, Alexandre; Scheibe, Timothy D.
2011-06-01
A dissipative-particle-dynamics 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.
Dissipative-particle-dynamics model of biofilm growth
Xu, Zhijie; Meakin, Paul; Tartakovsky, Alexandre M.; Scheibe, Timothy D.
2011-06-13
A dissipative particle dynamics (DPD) model for the quantitative simulation of biofilm growth controlled by substrate (nutrient) consumption, advective and diffusive substrate transport, and hydrodynamic interactions with fluid flow (including fragmentation and reattachment) is described. The model was used to simulate biomass growth, decay, and spreading. It predicts how the biofilm morphology depends on flow conditions, biofilm growth kinetics, the rheomechanical properties of the biofilm and adhesion to solid surfaces. The morphology of the model biofilm depends strongly on its rigidity and the magnitude of the body force that drives the fluid over the biofilm.
A Variational Approach to the Analysis of Dissipative Electromechanical Systems
Allison, Andrew; Pearce, Charles E. M.; Abbott, Derek
2014-01-01
We develop a method for systematically constructing Lagrangian functions for dissipative mechanical, electrical, and electromechanical systems. We derive the equations of motion for some typical electromechanical systems using deterministic principles that are strictly variational. We do not use any ad hoc features that are added on after the analysis has been completed, such as the Rayleigh dissipation function. We generalise the concept of potential, and define generalised potentials for dissipative lumped system elements. Our innovation offers a unified approach to the analysis of electromechanical systems where there are energy and power terms in both the mechanical and electrical parts of the system. Using our novel technique, we can take advantage of the analytic approach from mechanics, and we can apply these powerful analytical methods to electrical and to electromechanical systems. We can analyse systems that include non-conservative forces. Our methodology is deterministic, and does does require any special intuition, and is thus suitable for automation via a computer-based algebra package. PMID:24586221
A variational approach to the analysis of dissipative electromechanical systems.
Allison, Andrew; Pearce, Charles E M; Abbott, Derek
2014-01-01
We develop a method for systematically constructing Lagrangian functions for dissipative mechanical, electrical, and electromechanical systems. We derive the equations of motion for some typical electromechanical systems using deterministic principles that are strictly variational. We do not use any ad hoc features that are added on after the analysis has been completed, such as the Rayleigh dissipation function. We generalise the concept of potential, and define generalised potentials for dissipative lumped system elements. Our innovation offers a unified approach to the analysis of electromechanical systems where there are energy and power terms in both the mechanical and electrical parts of the system. Using our novel technique, we can take advantage of the analytic approach from mechanics, and we can apply these powerful analytical methods to electrical and to electromechanical systems. We can analyse systems that include non-conservative forces. Our methodology is deterministic, and does does require any special intuition, and is thus suitable for automation via a computer-based algebra package.
Pullback Asymptotic Behavior of Solutions for a 2D Non-autonomous Non-Newtonian Fluid
NASA Astrophysics Data System (ADS)
Liu, Guowei
2016-10-01
This paper studies the pullback asymptotic behavior of solutions for the non-autonomous incompressible non-Newtonian fluid in 2D bounded domains. Firstly, with a little high regularity of the force, the semigroup method and ɛ -regularity method are used to establish the existence of compact pullback absorbing sets. Then, with a minimal regularity of the force, by verifying the flattening property also known as the "Condition (C)", the author proves the existence of pullback attractors for the universe of fixed bounded sets and for the another universe given by a tempered condition. Furthermore, the regularity of pullback attractors is given.
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...
In this article, we consider the least-squares approach for estimating parameters of a spatial variogram and establish consistency and asymptotic normality of these estimators under general conditions. Large-sample distributions are also established under a sp...
Asymptotic behavior of a flat plate wake
NASA Technical Reports Server (NTRS)
Weygandt, James H.; Mehta, Rabindra D.
1989-01-01
An experimental study has been conducted to investigate the far-field, self-similar properties of a flat plate wake. A plane turbulent wake was generated at the trailing edge of a smooth splitter plate separating two legs of a Mixing Layer Wind Tunnel, with both initial boundary layers tripped. For the present study, both legs were operated at a free-steam velocity in the test section of 15 m/s, giving a Reynolds number based on wake momentum thickness of about 1750. Single profile measurements were obtained at five streamwise locations using a Pitot probe for the mean velocity measurements and a single cross-wire probe for the turbulence data, which included statistics up to third order. The mean flow data indicated a self-similar behavior beyond a streamwise distance equivalent to about 350 wake momentum thicknesses. However, the turbulence data show better collapse beyond a distance equivalent to about 500 momentum thicknesses, with all the measured peak Reynolds stresses achieving constant, asymptotic levels. The asymptotic mean flow behavior and peak primary stress levels agree well with theoretical predictions based on a constant eddy viscosity model. The present data also agree reasonably well with previous measurements, of which only one set extends into the self-similar region. Detailed comparisons with previous data are presented and discussed in this report.
Asymptotic modal analysis and statistical energy analysis
NASA Technical Reports Server (NTRS)
Dowell, Earl H.; Peretti, Linda F.
1990-01-01
The sound field of a structural-acoustic enclosure was subject to experimental analysis and theoretical description in order to develop an efficient and accurate method for predicting sound pressure levels in enclosures such as aircraft fuselages. Asymptotic Modal Analysis (AMA) is the method under investigation. AMA is derived from classical modal analysis (CMA) by considering the asymptotic limit of the sound pressure level as the number of acoustic and/or structural modes approaches infinity. Using AMA, results identical to those of Statistical Energy Analysis (SEA) were obtained for the spatially-averaged sound pressure levels in the interior. AMA is systematically derived from CMA and therefore the degree of generality of the end result can be adjusted through the choice of appropriate simplifying assumptions. For example, AMA can be used to obtain local sound pressure levels at particular points inside the enclosure, or to include the effects of varying the size and/or location of the sound source. AMA theoretical results were compared with CMA theory and also with experiment for the case where the structural-acoustic enclosure is a rectangular cavity with part of one wall flexible and vibrating, while the rest of the cavity is rigid.
Relaxing the parity conditions of asymptotically flat gravity
NASA Astrophysics Data System (ADS)
Compère, Geoffrey; Dehouck, François
2011-12-01
Four-dimensional asymptotically flat spacetimes at spatial infinity are defined from first principles without imposing parity conditions or restrictions on the Weyl tensor. The Einstein-Hilbert action is shown to be a correct variational principle when it is supplemented by an anomalous counterterm which breaks asymptotic translation, supertranslation and logarithmic translation invariance. Poincaré transformations as well as supertranslations and logarithmic translations are associated with finite and conserved charges which represent the asymptotic symmetry group. Lorentz charges as well as logarithmic translations transform anomalously under a change of regulator. Lorentz charges are generally nonlinear functionals of the asymptotic fields but reduce to well-known linear expressions when parity conditions hold. We also define a covariant phase space of asymptotically flat spacetimes with parity conditions but without restrictions on the Weyl tensor. In this phase space, the anomaly plays classically no dynamical role. Supertranslations are pure gauge and the asymptotic symmetry group is the expected Poincaré group.
Asymptotic equipartition and long time behavior of solutions of a thin-film equation
NASA Astrophysics Data System (ADS)
Carlen, Eric A.; Ulusoy, Süleyman
We investigate the large-time behavior of classical solutions to the thin-film type equation u=-()x. It was shown in previous work of Carrillo and Toscani that for non-negative initial data u that belongs to H(R) and also has a finite mass and second moment, the strong solutions relax in the L(R) norm at an explicit rate to the unique self-similar source type solution with the same mass. The equation itself is gradient flow for an energy functional that controls the H(R) norm, and so it is natural to expect that one should also have convergence in this norm. Carrillo and Toscani raised this question, but their methods, using a different Lyapunov functions that arises in the theory of the porous medium equation, do not directly address this since their Lyapunov functional does not involve derivatives of u. Here we show that the solutions do indeed converge in the H(R) norm at an explicit, but slow, rate. The key to establishing this convergence is an asymptotic equipartition of the excess energy. Roughly speaking, the energy functional whose dissipation drives the evolution through gradient flow consists of two parts: one involving derivatives of u, and one that does not. We show that these must decay at related rates—due to the asymptotic equipartition—and then use the results of Carrillo and Toscani to control the rate for the part that does not depend on derivatives. From this, one gets a rate on the dissipation for all of the excess energy.
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.
The Asymptotic Distribution of Mortality Rates in Competing Risks Analyses,
1979-12-01
For a sample of individuals from an animal or human population under observation in a clinical trial or life test, mortality rates are defined for...model, these mortality rates are shown to have an asymptotic normal distribution. An expression for the asymptotic correlation between a pair of... mortality rates is thus obtained and a necessary and sufficient condition for their asymptotic independence is investigated in some general situations with
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.
Asymptotic behaviour of solutions of semilinear parabolic equations
Egorov, Yu V; Kondratiev, V A
2008-04-30
The asymptotic behaviour of solutions of a second-order semilinear parabolic equation is analyzed in a cylindrical domain that is bounded in the space variables. The dominant term of the asymptotic expansion of the solution as t{yields}+{infinity} is found. It is shown that the solution of this problem is asymptotically equivalent to the solution of a certain non-linear ordinary differential equation. Bibliography: 8 titles.
Multicritical behavior in dissipative Ising models
NASA Astrophysics Data System (ADS)
Overbeck, Vincent R.; Maghrebi, Mohammad F.; Gorshkov, Alexey V.; Weimer, Hendrik
2017-04-01
We analyze theoretically the many-body dynamics of a dissipative Ising model in a transverse field using a variational approach. We find that the steady-state phase diagram is substantially modified compared to its equilibrium counterpart, including the appearance of a multicritical point belonging to a different universality class. Building on our variational analysis, we establish a field-theoretical treatment corresponding to a dissipative variant of a Ginzburg-Landau theory, which allows us to compute the upper critical dimension of the system. Finally, we present a possible experimental realization of the dissipative Ising model using ultracold Rydberg gases.
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.
Particle Acceleration in Dissipative Pulsar Magnetospheres
NASA Technical Reports Server (NTRS)
Kazanas, Z.; Kalapotharakos, C.; Harding, A.; Contopoulos, I.
2012-01-01
Pulsar magnetospheres represent unipolar inductor-type electrical circuits at which an EM potential across the polar cap (due to the rotation of their magnetic field) drives currents that run in and out of the polar cap and close at infinity. An estimate ofthe magnitude of this current can be obtained by dividing the potential induced across the polar cap V approx = B(sub O) R(sub O)(Omega R(sub O)/c)(exp 2) by the impedance of free space Z approx eq 4 pi/c; the resulting polar cap current density is close to $n {GJ} c$ where $n_{GJ}$ is the Goldreich-Julian (GJ) charge density. This argument suggests that even at current densities close to the GJ one, pulsar magnetospheres have a significant component of electric field $E_{parallel}$, parallel to the magnetic field, a condition necessary for particle acceleration and the production of radiation. We present the magnetic and electric field structures as well as the currents, charge densities, spin down rates and potential drops along the magnetic field lines of pulsar magnetospheres which do not obey the ideal MHD condition $E cdot B = 0$. By relating the current density along the poloidal field lines to the parallel electric field via a kind of Ohm's law $J = sigma E_{parallel}$ we study the structure of these magnetospheres as a function of the conductivity $sigma$. We find that for $sigma gg OmegaS the solution tends to the (ideal) Force-Free one and to the Vacuum one for $sigma 11 OmegaS. Finally, we present dissipative magnetospheric solutions with spatially variable $sigma$ that supports various microphysical properties and are compatible with the observations.
Scattering of traveling spots in dissipative systems.
Nishiura, Yasumasa; Teramoto, Takashi; Ueda, Kei-Ichi
2005-12-01
One of the fundamental questions for self-organization in pattern formation is how spatial periodic structure is spontaneously formed starting from a localized fluctuation. It is known in dissipative systems that splitting dynamics is one of the driving forces to create many particle-like patterns from a single seed. On the way to final state there occur many collisions among them and its scattering manner is crucial to predict whether periodic structure is realized or not. We focus on the colliding dynamics of traveling spots arising in a three-component system and study how the transition of scattering dynamics is brought about. It has been clarified that hidden unstable patterns called "scattors" and their stable and unstable manifolds direct the traffic flow of orbits before and after collisions. The collision process in general can be decomposed into several steps and each step is controlled by such a scattor, in other words, a network among scattors forms the backbone for scattering dynamics. A variety of input-output relations comes from the complexity of the network as well as high Morse indices of the scattor. The change of transition manners is caused by the switching of the network from one structure to another, and such a change is caused by the singularities of scattors. We illustrate a typical example of the change of transition caused by the destabilization of the scattor. A new instability of the scattor brings a new destination for the orbit resulting in a new input-output relation, for instance, Hopf instability for the scattor of peanut type brings an annihilation.
The aging of a surface and the evolution of conservative and dissipative nanoscale interactions.
Amadei, Carlo A; Tang, Tzu Chieh; Chiesa, Matteo; Santos, Sergio
2013-08-28
A method to monitor variations in the conservative and dissipative forces in dynamic atomic force microscopy is proposed in order to investigate the effects of exposing a surface to different sets of environmental conditions for prolonged periods of time. The variations are quantified by proposing and defining two metrics, one for conservative and another for dissipative interactions. Mica and graphite are chosen as model samples because they are atomically flat and easy to cleave. It is found that long term exposure to high relative humidity (RH), i.e., 90% > RH > 70%, affects the magnitude and distance dependencies of the forces, as quantified by the respective metrics, more drastically than the actual environmental conditions at which the samples are probed. Attenuated total reflectance infrared spectroscopy experiments further indicate that accumulation of water and carbonates on the surfaces with time is responsible for the variations in force measurements. This study has implications in surface functionality, reactivity, and longevity.
Dissipative structures and biological rhythms
NASA Astrophysics Data System (ADS)
Goldbeter, Albert
2017-10-01
Sustained oscillations abound in biological systems. They occur at all levels of biological organization over a wide range of periods, from a fraction of a second to years, and with a variety of underlying mechanisms. They control major physiological functions, and their dysfunction is associated with a variety of physiological disorders. The goal of this review is (i) to give an overview of the main rhythms observed at the cellular and supracellular levels, (ii) to briefly describe how the study of biological rhythms unfolded in the course of time, in parallel with studies on chemical oscillations, (iii) to present the major roles of biological rhythms in the control of physiological functions, and (iv) the pathologies associated with the alteration, disappearance, or spurious occurrence of biological rhythms. Two tables present the main examples of cellular and supracellular rhythms ordered according to their period, and their role in physiology and pathophysiology. Among the rhythms discussed are neural and cardiac rhythms, metabolic oscillations such as those occurring in glycolysis in yeast, intracellular Ca++ oscillations, cyclic AMP oscillations in Dictyostelium amoebae, the segmentation clock that controls somitogenesis, pulsatile hormone secretion, circadian rhythms which occur in all eukaryotes and some bacteria with a period close to 24 h, the oscillatory dynamics of the enzymatic network driving the cell cycle, and oscillations in transcription factors such as NF-ΚB and tumor suppressors such as p53. Ilya Prigogine's concept of dissipative structures applies to temporal oscillations and allows us to unify within a common framework the various rhythms observed at different levels of biological organization, regardless of their period and underlying mechanism.
Turbulence at high resolution: intense events in dissipation, enstrophy and acceleration
NASA Astrophysics Data System (ADS)
Yeung, P. K.; Zhai, X. M.; Sreenivasan, K. R.
2014-11-01
Access to the Blue Waters supercomputer under the NSF Track 1 Petascale Resource Allocations program has allowed us to conduct an 81923 simulation of forced isotropic turbulence, with Taylor-scale Reynolds number close to 1300, and grid spacing at about 1.5 Kolmogorov scales. Extreme fluctuations in dissipation and enstrophy (over 10,000 times the mean) are observed, and found to scale similarly and occur together. Conditional sampling based on both dissipation and enstrophy shows that such extreme events in these variables are directly associated with strong intermittency in the fluid particle acceleration, which reaches values well beyond 100 standard deviations. An attempt is made to characterize in detail the formation of events of intense dissipation and enstrophy, including the transport, production and dissipation terms in the dissipation and enstrophy transport equations, as well as the nature of local flow conditions in principal strain-rate axes. Statistics of dissipation and enstrophy averaged over 3D sub-domains of linear size in the inertial range are also available. Both high Reynolds number and good small-scale resolution are important factors in these results. Supported by NSF Grant ACI-1036170.
Asymptotic method for analysis of a conical shell under local loading
NASA Astrophysics Data System (ADS)
Nerubailo, B. V.; Ol'shanskii, V. P.
2007-06-01
Differential equations of the general theory describing the stress-strain state of conical shells are very complicated, and when computing the exact solution of the problem by analytic methods one encounters severe or even so far insurmountable difficulties. Therefore, in the present paper we develop an approach based on the method of asymptotic synthesis of the stressed state, which has already proved efficient when solving similar problems for cylindrical shells [1, 2]. We essentially use the fourth-order differential equations obtained by Kan [3], which describe the ground state and the boundary effect. Earlier, such equations have already been used to solve problems concerning force and thermal actions on weakly conical shells [4-6]. By applying the asymptotic synthesis method to these equations, we manage to obtain sufficiently accurate closed-form solutions.
The evolution of cross helicity in driven/dissipative two-dimensional magnetohydrodynamics
NASA Technical Reports Server (NTRS)
Ghosh, S.; Matthaeus, W. H.; Montgomery, D.
1988-01-01
The paper presents a series of incompressible two-dimensional simulations of driven/dissipative MHD turbulence where the amount of correlation between the kinetic and magnetic forcing is regulated, thereby controlling the amount of cross helicity injection. It is shown that correlated forcing provides a strong source of magnetofluid cross helicity. The clear appearance of the 'minority species effect,' which is the most striking and systematic effect during this driven dynamic alignment process, is discussed.
Dissipation and θ 13 in neutrino oscillations
NASA Astrophysics Data System (ADS)
Oliveira, R. L. N.; Guzzo, M. M.
2013-05-01
We obtain a complete survival and transition probability involving three neutrino flavors when dissipation effects in vacuum are taken into consideration. In an approach that presents decoherence and relaxation effects, we study the behavior of the probabilities obtained from complete positivity constraints. Making the von Neumann entropy increase in time, many cases can be obtained and studied with the Lindblad master equation with addition of only one or two parameters related to dissipation. New possibilities are obtained when we take into account two decoherence parameters with different magnitudes which are given by reactor and accelerator neutrino oscillation experiments. We also present a model with only one parameter that has an important symmetry property, which can be used when the effective matter potential is important. Furthermore, the dissipation effects can contribute to the appearance of neutrinos that can hide or imitate the θ 13 effects and we study these possibilities showing that dissipative effects have an important role in three-neutrino oscillations.
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.
Strongly nonlinear stress waves in dissipative metamaterials
NASA Astrophysics Data System (ADS)
Xu, Yichao; Nesterenko, Vitali F.
2017-01-01
We present the results of measurements and numerical simulations of stress wave propagation in a one-dimensional strongly nonlinear dissipative metamaterial composed of steel disks and Nitrile O-rings. The incoming bell shape stress wave is generated by the strikers with different masses. Numerical modeling including a viscous dissipative term to describe dynamic behavior of O-rings is developed to predict the wave amplitude, shape and propagation speed of stress waves. The viscous dissipation prevented the incoming pulse from splitting into trains of solitary waves typical for non-dissipative strongly nonlinear discrete systems. The linear momentum and energy from the striker were completely transferred into this strongly nonlinear "soft" metamaterial.
Dissipative 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.
Enhanced turbulence and energy dissipation at ocean fronts.
D'Asaro, Eric; Lee, Craig; Rainville, Luc; Harcourt, Ramsey; Thomas, Leif
2011-04-15
The ocean surface boundary layer mediates air-sea exchange. In the classical paradigm and in current climate models, its turbulence is driven by atmospheric forcing. Observations at a 1-kilometer-wide front within the Kuroshio Current indicate that the rate of energy dissipation within the boundary layer is enhanced by one to two orders of magnitude, suggesting that the front, rather than the atmospheric forcing, supplied the energy for the turbulence. The data quantitatively support the hypothesis that winds aligned with the frontal velocity catalyzed a release of energy from the front to the turbulence. The resulting boundary layer is stratified in contrast to the classically well-mixed layer. These effects will be strongest at the intense fronts found in the Kuroshio Current, the Gulf Stream, and the Antarctic Circumpolar Current, all of which are key players in the climate system.
Green's function asymptotics and sharp interpolation inequalities
NASA Astrophysics Data System (ADS)
Zelik, S. V.; Ilyin, A. A.
2014-04-01
A general method is proposed for finding sharp constants for the embeddings of the Sobolev spaces H^m(\\mathscr{M}) on an n-dimensional Riemannian manifold \\mathscr{M} into the space of bounded continuous functions, where m\\gt n/2. The method is based on an analysis of the asymptotics with respect to the spectral parameter of the Green's function of an elliptic operator of order 2m whose square root has domain determining the norm of the corresponding Sobolev space. The cases of the n-dimensional torus {T}^n and the n-dimensional sphere {S}^n are treated in detail, as well as certain manifolds with boundary. In certain cases when \\mathscr{M} is compact, multiplicative inequalities with remainder terms of various types are obtained. Inequalities with correction terms for periodic functions imply an improvement for the well-known Carlson inequalities. Bibliography: 28 titles.
Asymptotic Linear Stability of Solitary Water Waves
NASA Astrophysics Data System (ADS)
Pego, Robert L.; Sun, Shu-Ming
2016-12-01
We prove an asymptotic stability result for the water wave equations linearized around small solitary waves. The equations we consider govern irrotational flow of a fluid with constant density bounded below by a rigid horizontal bottom and above by a free surface under the influence of gravity neglecting surface tension. For sufficiently small amplitude waves, with waveform well-approximated by the well-known sech-squared shape of the KdV soliton, solutions of the linearized equations decay at an exponential rate in an energy norm with exponential weight translated with the wave profile. This holds for all solutions with no component in (that is, symplectically orthogonal to) the two-dimensional neutral-mode space arising from infinitesimal translational and wave-speed variation of solitary waves. We also obtain spectral stability in an unweighted energy norm.
Asymptotic charged BTZ black hole solutions
NASA Astrophysics Data System (ADS)
Hendi, S. H.
2012-03-01
The well-known (2 + 1)-dimensional Reissner-Nordström (BTZ) black hole can be generalized to three dimensional Einstein-nonlinear electromagnetic field, motivated from obtaining a finite value for the self-energy of a pointlike charge. Considering three types of nonlinear electromagnetic fields coupled with Einstein gravity, we derive three kinds of black hole solutions which their asymptotic properties are the same as charged BTZ solution. In addition, we calculate conserved and thermodynamic quantities of the solutions and show that they satisfy the first law of thermodynamics. Finally, we perform a stability analysis in the canonical ensemble and show that the black holes are stable in the whole phase space.
Chiral fermions in asymptotically safe quantum gravity.
Meibohm, J; Pawlowski, J M
2016-01-01
We study the consistency of dynamical fermionic matter with the asymptotic safety scenario of quantum gravity using the functional renormalisation group. Since this scenario suggests strongly coupled quantum gravity in the UV, one expects gravity-induced fermion self-interactions at energies of the Planck scale. These could lead to chiral symmetry breaking at very high energies and thus to large fermion masses in the IR. The present analysis which is based on the previous works (Christiansen et al., Phys Rev D 92:121501, 2015; Meibohm et al., Phys Rev D 93:084035, 2016), concludes that gravity-induced chiral symmetry breaking at the Planck scale is avoided for a general class of NJL-type models. We find strong evidence that this feature is independent of the number of fermion fields. This finding suggests that the phase diagram for these models is topologically stable under the influence of gravitational interactions.
The asymptotics of large constrained graphs
NASA Astrophysics Data System (ADS)
Radin, Charles; Ren, Kui; Sadun, Lorenzo
2014-05-01
We show, through local estimates and simulation, that if one constrains simple graphs by their densities ɛ of edges and τ of triangles, then asymptotically (in the number of vertices) for over 95% of the possible range of those densities there is a well-defined typical graph, and it has a very simple structure: the vertices are decomposed into two subsets V1 and V2 of fixed relative size c and 1 - c, and there are well-defined probabilities of edges, gjk, between vj ∈ Vj, and vk ∈ Vk. Furthermore the four parameters c, g11, g22 and g12 are smooth functions of (ɛ, τ) except at two smooth ‘phase transition’ curves.
Asymptotic properties of restricted naming games
NASA Astrophysics Data System (ADS)
Bhattacherjee, Biplab; Datta, Amitava; Manna, S. S.
2017-07-01
Asymptotic properties of the symmetric and asymmetric naming games have been studied under some restrictions in a community of agents. In one version, the vocabulary sizes of the agents are restricted to finite capacities. In this case, compared to the original naming games, the dynamics takes much longer time for achieving the consensus. In the second version, the symmetric game starts with a limited number of distinct names distributed among the agents. Three different quantities are measured for a quantitative comparison, namely, the maximum value of the total number of names in the community, the time at which the community attains the maximal number of names, and the global convergence time. Using an extensive numerical study, the entire set of three power law exponents characterizing these quantities are estimated for both the versions which are observed to be distinctly different from their counter parts of the original naming games.
Asymptotic analysis of loaded, unstable, cylindrical resonators
Chitanvis, S.M. )
1991-09-01
I show that the solution of the electromagnetic equations for a loaded cavity with a large Fresnel number {ital F} ({ital F}{gt}100) can be obtained analytically. This asymptotic solution is obtained as a perturbation of the geometrical-optics solution, with edge-diffraction effects appearing as ripples of order 1/({ital F}){sup 1/2}. The basic technique is to obtain a series expansion of the relevant integrals in powers of 1/({ital F}){sup 1/2}. This scheme works even better if the laser is operating in the saturated regime. This method of solution represents an extension of the method of Butts and Avizonis (J. Opt. Soc. Am. {bold 68}, 1072 (1978)), which is applicable to empty, cylindrical, unstable resonators.
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.
Asymptotically safe non-minimal inflation
NASA Astrophysics Data System (ADS)
Tronconi, Alessandro
2017-07-01
We study the constraints imposed by the requirement of Asymptotic Safety on a class of inflationary models with an inflaton field non-minimally coupled to the Ricci scalar. The critical surface in the space of theories is determined by the improved renormalization group flow which takes into account quantum corrections beyond the one loop approximation. The combination of constraints deriving from Planck observations and those from theory puts severe bounds on the values of the parameters of the model and predicts a quite large tensor to scalar ratio. We finally comment on the dependence of the results on the definition of the infrared energy scale which parametrises the running on the critical surface.
Universal Preparability of States and Asymptotic Completeness
NASA Astrophysics Data System (ADS)
Gohm, Rolf; Haag, Florian; Kümmerer, Burkhard
2017-05-01
We introduce a notion of universal preparability for a state of a system, more precisely: for a normal state on a von Neumann algebra. It describes a situation where from an arbitrary initial state it is possible to prepare a target state with arbitrary precision by a repeated interaction with a sequence of copies of another system. For B(H) we give criteria sufficient to ensure that all normal states are universally preparable which can be verified for a class of non-commutative birth and death processes realized, in particular, by the interaction of a micromaser with a stream of atoms. As a tool, the theory of tight sequences of states and of stationary states is further developed and we show that in the presence of stationary faithful normal states universal preparability of all normal states is equivalent to asymptotic completeness, a notion studied earlier in connection with the scattering theory of non-commutative Markov processes.
Chiral fermions in asymptotically safe quantum gravity
NASA Astrophysics Data System (ADS)
Meibohm, J.; Pawlowski, J. M.
2016-05-01
We study the consistency of dynamical fermionic matter with the asymptotic safety scenario of quantum gravity using the functional renormalisation group. Since this scenario suggests strongly coupled quantum gravity in the UV, one expects gravity-induced fermion self-interactions at energies of the Planck scale. These could lead to chiral symmetry breaking at very high energies and thus to large fermion masses in the IR. The present analysis which is based on the previous works (Christiansen et al., Phys Rev D 92:121501, 2015; Meibohm et al., Phys Rev D 93:084035, 2016), concludes that gravity-induced chiral symmetry breaking at the Planck scale is avoided for a general class of NJL-type models. We find strong evidence that this feature is independent of the number of fermion fields. This finding suggests that the phase diagram for these models is topologically stable under the influence of gravitational interactions.
Universality and asymptotic scaling in drilling percolation
NASA Astrophysics Data System (ADS)
Grassberger, Peter
2017-01-01
We present simulations of a three-dimensional percolation model studied recently by K. J. Schrenk et al. [Phys. Rev. Lett. 116, 055701 (2016), 10.1103/PhysRevLett.116.055701], obtained with a new and more efficient algorithm. They confirm most of their results in spite of larger systems and higher statistics used in the present Rapid Communication, but we also find indications that the results do not yet represent the true asymptotic behavior. The model is obtained by replacing the isotropic holes in ordinary Bernoulli percolation by randomly placed and oriented cylinders, with the constraint that the cylinders are parallel to one of the three coordinate axes. We also speculate on possible generalizations.
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]...
Rubidium-rich asymptotic giant branch stars.
García-Hernández, D A; García-Lario, P; Plez, B; D'Antona, F; Manchado, A; Trigo-Rodríguez, J M
2006-12-15
A long-debated issue concerning the nucleosynthesis of neutron-rich elements in asymptotic giant branch (AGB) stars is the identification of the neutron source. We report intermediate-mass (4 to 8 solar masses) AGB stars in our Galaxy that are rubidium-rich as a result of overproduction of the long-lived radioactive isotope (87)Rb, as predicted theoretically 40 years ago. This finding represents direct observational evidence that the (22)Ne(alpha,n)(25)Mg reaction must be the dominant neutron source in these stars. These stars challenge our understanding of the late stages of the evolution of intermediate-mass stars and would have promoted a highly variable Rb/Sr environment in the early solar nebula.
Nucleosynthesis in asymptotic giant branch stars
NASA Astrophysics Data System (ADS)
El Eid, Mounib F.
2014-05-01
The nucleosynthesis in asymptotic giant branch stars (briefly: AGB)is a challenging and fascinating subject in the theory of stellar evolution and important for observations as well. This is because about of half the heavy elements beyond iron are synthesized during thermal pulsation phases of these stars. Furthermore, the understanding of the production of the heavy elements and some light elements like carbon and fluorine represent a powerful tool to get more insight into the internal structure of these stars. The diversity of nuclear processing during the AGB phases may also motivate experimental activities in measuring important nuclear reactions. In this contribution, we emphasize several interesting feature of the nucleosynthesis in AGB stars which still needs further elaboration especially from theoretical point of view.
Nonlocality Induces Chains of Nested Dissipative Solitons.
Javaloyes, J; Marconi, M; Giudici, M
2017-07-21
Dissipative solitons often behave as quasiparticles, and they may form molecules characterized by well-defined bond distances. We show that pointwise nonlocality may lead to a new kind of molecule where bonds are not rigid. The elements of this molecule can shift mutually one with respect to the others while remaining linked together, in a manner similar to interlaced rings in a chain. We report experimental observations of these chains of nested dissipative solitons in a time-delayed laser system.
Nonlocality Induces Chains of Nested Dissipative Solitons
NASA Astrophysics Data System (ADS)
Javaloyes, J.; Marconi, M.; Giudici, M.
2017-07-01
Dissipative solitons often behave as quasiparticles, and they may form molecules characterized by well-defined bond distances. We show that pointwise nonlocality may lead to a new kind of molecule where bonds are not rigid. The elements of this molecule can shift mutually one with respect to the others while remaining linked together, in a manner similar to interlaced rings in a chain. We report experimental observations of these chains of nested dissipative solitons in a time-delayed laser system.
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.
Lattice quantum gravity and asymptotic safety
NASA Astrophysics Data System (ADS)
Laiho, J.; Bassler, S.; Coumbe, D.; Du, D.; Neelakanta, J. T.
2017-09-01
We study the nonperturbative formulation of quantum gravity defined via Euclidean dynamical triangulations (EDT) in an attempt to make contact with Weinberg's asymptotic safety scenario. We find that a fine-tuning is necessary in order to recover semiclassical behavior. Such a fine-tuning is generally associated with the breaking of a target symmetry by the lattice regulator; in this case we argue that the target symmetry is the general coordinate invariance of the theory. After introducing and fine-tuning a nontrivial local measure term, we find no barrier to taking a continuum limit, and we find evidence that four-dimensional, semiclassical geometries are recovered at long distance scales in the continuum limit. We also find that the spectral dimension at short distance scales is consistent with 3 /2 , a value that could resolve the tension between asymptotic safety and the holographic entropy scaling of black holes. We argue that the number of relevant couplings in the continuum theory is one, once symmetry breaking by the lattice regulator is accounted for. Such a theory is maximally predictive, with no adjustable parameters. The cosmological constant in Planck units is the only relevant parameter, which serves to set the lattice scale. The cosmological constant in Planck units is of order 1 in the ultraviolet and undergoes renormalization group running to small values in the infrared. If these findings hold up under further scrutiny, the lattice may provide a nonperturbative definition of a renormalizable quantum field theory of general relativity with no adjustable parameters and a cosmological constant that is naturally small in the infrared.
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
Calibrating conservative and dissipative response of electrically-driven quartz tuning forks.
Hao, Lifeng; Wang, Qi; Peng, Ping; Cao, Zhenxing; Jiao, Weicheng; Yang, Fan; Liu, Wenbo; Wang, Rongguo; He, Xiaodong
2017-03-01
Determining sensor parameters is a prerequisite for quantitative force measurement. Here we report a direct, high-precision calibration method for quartz tuning fork (TF) sensors that are popular in the field of nanomechanical measurement. In the method, conservative and dissipative forces with controlled amplitudes are applied to one prong of TF directly to mimic the tip-sample interaction, and the responses of the sensor are measured at the same time to extract sensor parameters. The method, for the first time, allows force gradient and damping coefficient which correspond to the conservative and dissipative interactions to be measured simultaneously. The calibration result shows surprisingly that, unlike cantilevers, the frequency shift for TFs depends on both the conservative and dissipative forces, which may be ascribed to the complex dynamics. The effectiveness of the method is testified by force spectrum measurement with a calibrated TF. The method is generic for all kinds of sensors used for non-contact atomic force microscopy (NC-AFM) and is an important improvement for quantitative nanomechanical measurement. Copyright © 2017 Elsevier B.V. All rights reserved.
Bayesian parametrization of coarse-grain dissipative dynamics models
NASA Astrophysics Data System (ADS)
Dequidt, Alain; Solano Canchaya, Jose G.
2015-08-01
We introduce a new bottom-up method for the optimization of dissipative coarse-grain models. The method is based on Bayesian optimization of the likelihood to reproduce a coarse-grained reference trajectory obtained from analysis of a higher resolution molecular dynamics trajectory. This new method is related to force matching techniques, but using the total force on each grain averaged on a coarse time step instead of instantaneous forces. It has the advantage of not being limited to pairwise short-range interactions in the coarse-grain model and also yields an estimation of the friction parameter controlling the dynamics. The theory supporting the method is exposed in a practical perspective, with an analytical solution for the optimal set of parameters. The method was first validated by using it on a system with a known optimum. The new method was then tested on a simple system: n-pentane. The local molecular structure of the optimized model is in excellent agreement with the reference system. An extension of the method allows to get also an excellent agreement for the equilibrium density. As for the dynamic properties, they are also very satisfactory, but more sensitive to the choice of the coarse-grain representation. The quality of the final force field depends on the definition of the coarse grain degrees of freedom and interactions. We consider this method as a serious alternative to other methods like iterative Boltzmann inversion, force matching, and Green-Kubo formulae.
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.
Dissipation in the deep interiors of Ganymede and Europa
NASA Astrophysics Data System (ADS)
Hussmann, Hauke; Shoji, Daigo; Steinbruegge, Gregor; Stark, Alexander; Sohl, Frank
2017-04-01
Jupiter's satellites are subject to strong tidal forces which result in variations of the gravitational potential and deformations of the satellites' surfaces on the diurnal tidal cycle. Tidal flexing in the deep interiors can be a significant heat source for the satellites' thermal-orbital evolution. Whereas typical structure models of Europa consist of a core, a silicate mantle, an ocean and an outer ice-I shell [1], pressures inside Ganymede are sufficient for high-pressure ice phases to occur between the silicate mantle and the ocean [2]. With current data it is unknown whether the deep interiors (i.e., Europa's silicate shell and Ganymede's silicate mantle and/or high-pressure ice layer) are dissipative. Other possibilities would be that the dissipation rates are in general very low (unlikely at least for Europa due to recent observations) or that dissipative processes are mainly occurring in the ice-I shell and/or ocean. Thus, for evaluations of the heating state of these satellites, it is important to measure the magnitude of the interior dissipation. However, observation of the interior layers such as high-pressure ice layers is more challenging than that of the surface ice-I layer. Here we suggest a method to constrain the dissipation states of the deep interiors of Ganymede and Europa by altimetry and gravity measurements from an orbiting or multi-flyby spacecraft. Tidal variations are generally described by the Love numbers k2 and h2 for the tide-induced potential variation due to internal mass redistribution and the radial surface displacement, respectively. The phase-lags of these complex numbers contain information about the rheological and dissipative states of the satellites. For the satellites we assume a decoupling of the outer ice-shell from the deep interior by a liquid subsurface water ocean. We show that, in this case, the phase-lag difference between the lags of k2 and h2 can provide information on the rheological and thermal state of the
Scattering in an external electric field asymptotically constant in time
Adachi, Tadayoshi; Ishida, Atsuhide
2011-06-15
We show the asymptotic completeness for two-body quantum systems in an external electric field asymptotically non-zero constant in time. One of the main ingredients of this paper is to give some propagation estimates for physical propagators generated by time-dependent Hamiltonians which govern the systems under consideration.
Asymptotic expansions for the reciprocal of the gamma function
NASA Astrophysics Data System (ADS)
Withers, Christopher S.; Nadarajah, Saralees
2014-05-01
Asymptotic expansions are derived for the reciprocal of the gamma function. We show that the coefficients of the expansion are the same, up to a sign change, as the asymptotic expansions for the gamma function obtained by exponentiating the expansions of its logarithm due to Stirling and de Moivre. Expressions for the coefficients are given in terms of Bell polynomials.
Gaussian and mean curvatures for discrete asymptotic nets
NASA Astrophysics Data System (ADS)
Schief, W. K.
2017-04-01
We propose discretisations of Gaussian and mean curvatures of surfaces parametrised in terms of asymptotic coordinates and examine their relevance in the context of integrable discretisations of classical classes of surfaces and their underlying integrable systems. We also record discrete analogues of the classical relation between the Gaussian curvature of hyperbolic surfaces and the torsion of their asymptotic lines.
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.
Reduction arguments for geometric inequalities associated with asymptotically hyperboloidal slices
NASA Astrophysics Data System (ADS)
Sle Cha, Ye; Khuri, Marcus; Sakovich, Anna
2016-02-01
We consider several geometric inequalities in general relativity involving mass, area, charge, and angular momentum for asymptotically hyperboloidal initial data. We show how to reduce each one to the known maximal (or time symmetric) case in the asymptotically flat setting, whenever a geometrically motivated system of elliptic equations admits a solution.
Internal spin angular momentum of an asymptotically flat spacetime
Randono, Andrew; Sloan, David
2009-08-15
In this paper we investigate the manner in which the internal spin angular momentum of a spinor field is encoded in the gravitational field at asymptotic infinity. The inclusion of internal spin requires us to reanalyze our notion of asymptotic flatness. In particular, the Poincare symmetry at asymptotic infinity must be replaced by a spin-enlarged Poincare symmetry. Likewise, the generators of the asymptotic symmetry group must be supplemented to account for the internal spin. In the Hamiltonian framework of first-order Einstein-Cartan gravity, the extra generator comes from the boundary term of the Gauss constraint in the asymptotically flat context. With the additional term, we establish the relations among the Noether charges of a Dirac field, the Komar integral, and the asymptotic Arnowitt-Deser-Misner-like geometric integral. We show that by imposing mild restraints on the generating functionals of gauge transformations at asymptotic infinity, the phase space is rendered explicitly finite. We construct the energy-momentum and the new total (spin+orbital) angular momentum boundary integrals that satisfy the appropriate algebra to be the generators of the spin-enlarged Poincare symmetry. This demonstrates that the internal spin is encoded in the tetrad at asymptotic infinity. In addition, we find that a new conserved and (spin-enlarged) Poincare invariant charge emerges that is associated with the global structure of a gauge transformation.
Internal spin angular momentum of an asymptotically flat spacetime
NASA Astrophysics Data System (ADS)
Randono, Andrew; Sloan, David
2009-08-01
In this paper we investigate the manner in which the internal spin angular momentum of a spinor field is encoded in the gravitational field at asymptotic infinity. The inclusion of internal spin requires us to reanalyze our notion of asymptotic flatness. In particular, the Poincaré symmetry at asymptotic infinity must be replaced by a spin-enlarged Poincaré symmetry. Likewise, the generators of the asymptotic symmetry group must be supplemented to account for the internal spin. In the Hamiltonian framework of first-order Einstein-Cartan gravity, the extra generator comes from the boundary term of the Gauss constraint in the asymptotically flat context. With the additional term, we establish the relations among the Noether charges of a Dirac field, the Komar integral, and the asymptotic Arnowitt-Deser-Misner-like geometric integral. We show that by imposing mild restraints on the generating functionals of gauge transformations at asymptotic infinity, the phase space is rendered explicitly finite. We construct the energy-momentum and the new total (spin+orbital) angular momentum boundary integrals that satisfy the appropriate algebra to be the generators of the spin-enlarged Poincaré symmetry. This demonstrates that the internal spin is encoded in the tetrad at asymptotic infinity. In addition, we find that a new conserved and (spin-enlarged) Poincaré invariant charge emerges that is associated with the global structure of a gauge transformation.
Echoes of asymptotic silence in causal set quantum gravity
NASA Astrophysics Data System (ADS)
Eichhorn, Astrid; Mizera, Sebastian; Surya, Sumati
2017-08-01
We explore the idea of asymptotic silence in causal set theory and find that causal sets approximated by continuum spacetimes exhibit behavior akin to asymptotic silence. We make use of an intrinsic definition of spatial distance between causal set elements in the discrete analogue of a spatial hypersurface. Using numerical simulations for causal sets approximated by \
Vortex formation and dynamics in two-dimensional driven-dissipative condensates
NASA Astrophysics Data System (ADS)
Hebenstreit, F.
2016-12-01
We investigate the real-time evolution of lattice bosons in two spatial dimensions whose dynamics is governed by a Markovian quantum master equation. We employ the Wigner-Weyl phase space quantization and derive the functional integral for open quantum many-body systems that determines the time evolution of the Wigner function. Using the truncated Wigner approximation, in which quantum fluctuations are only taken into account in the initial state whereas the dynamics is governed by classical evolution equations, we study the buildup of long-range correlations due to the action of non-Hermitean quantum jump operators that constitute a mechanism for dissipative cooling. Starting from an initially disordered state corresponding to a vortex condensate, the dissipative process results in the annihilation of vortex-antivortex pairs and the establishment of quasi-long-range order at late times. We observe that a finite vortex density survives the cooling process, which disagrees with the analytically constructed vortex-free Bose-Einstein condensate at asymptotic times. This indicates that quantum fluctuations beyond the truncated Wigner approximation need to be included to fully capture the physics of dissipative Bose-Einstein condensation.
Reliable dissipative control of high-speed train with probabilistic time-varying delays
NASA Astrophysics Data System (ADS)
Kaviarasan, B.; Sakthivel, R.; Shi, Y.
2016-12-01
This paper investigates the reliable dissipative control problem for high-speed trains (HSTs) under probabilistic time-varying sampling with a known upper bound on the sampling intervals. In particular, random variables obeying the Bernoulli distribution are considered to account for the probabilistic time-varying delays. Based on Lyapunov-Krasovskii functional approach which considers full use of the available information about actual sampling pattern, a new set of sufficient condition is established to guarantee that the HST can well track the desired speed and the relative spring displacement between the two neighbouring carriages is asymptotically stable and the corresponding error system is strictly ?-dissipative. The existence condition of the dissipativity-based reliable sampled-data controller is obtained in terms of a set of linear matrix inequalities which are delay-distribution-dependent, i.e. the solvability of the condition depends on not only the variation range of the delay but also the probability distribution of it. Moreover, different control processes for the HST system can be obtained from the proposed design procedure and hence it can reduce the time and cost. Finally, the effectiveness and benefits of the proposed control law is demonstrated through a numerical example by taking the experimental values of Japan Shinkansen HST.
Asymptotic Properties of Some Classes of Generalized Functions
NASA Astrophysics Data System (ADS)
Drozhzhinov, Yu N.; Zav'yalov, B. I.
1986-02-01
This paper studies the connection between the asymptotic and quasi-asymptotic properties at infinity of slowly increasing generalized functions with supports on the half-line and the asymptotic and quasi-asymptotic properties of the real parts of their Laplace and Fourier transforms in a neighborhood of the origin. The study is caried out in the scale of regularly varying self-similar functions. The results are applied to the study of the asymptotic properties of solutions of linear passive systems, and also to the study of the connection between Abel and Cesàro convergence (with respect to a self-similar weight) of the Fourier-Stieltjes series of nonnegative measures. Bibliography: 13 titles.
Eigenvalue spectrum of the spheroidal harmonics: A uniform asymptotic analysis
NASA Astrophysics Data System (ADS)
Hod, Shahar
2015-06-01
The spheroidal harmonics Slm (θ ; c) have attracted the attention of both physicists and mathematicians over the years. These special functions play a central role in the mathematical description of diverse physical phenomena, including black-hole perturbation theory and wave scattering by nonspherical objects. The asymptotic eigenvalues {Alm (c) } of these functions have been determined by many authors. However, it should be emphasized that all the previous asymptotic analyzes were restricted either to the regime m → ∞ with a fixed value of c, or to the complementary regime | c | → ∞ with a fixed value of m. A fuller understanding of the asymptotic behavior of the eigenvalue spectrum requires an analysis which is asymptotically uniform in both m and c. In this paper we analyze the asymptotic eigenvalue spectrum of these important functions in the double limit m → ∞ and | c | → ∞ with a fixed m / c ratio.
Asymptotic approximations to posterior distributions via conditional moment equations
Yee, J.L.; Johnson, W.O.; Samaniego, F.J.
2002-01-01
We consider asymptotic approximations to joint posterior distributions in situations where the full conditional distributions referred to in Gibbs sampling are asymptotically normal. Our development focuses on problems where data augmentation facilitates simpler calculations, but results hold more generally. Asymptotic mean vectors are obtained as simultaneous solutions to fixed point equations that arise naturally in the development. Asymptotic covariance matrices flow naturally from the work of Arnold & Press (1989) and involve the conditional asymptotic covariance matrices and first derivative matrices for conditional mean functions. When the fixed point equations admit an analytical solution, explicit formulae are subsequently obtained for the covariance structure of the joint limiting distribution, which may shed light on the use of the given statistical model. Two illustrations are given. ?? 2002 Biometrika Trust.
On the asymptotics of the α-Farey transfer operator
NASA Astrophysics Data System (ADS)
Kautzsch, J.; Kesseböhmer, M.; Samuel, T.; Stratmann, B. O.
2015-01-01
We study the asymptotics of iterates of the transfer operator for non-uniformly hyperbolic α-Farey maps. We provide a family of observables which are Riemann integrable, locally constant and of bounded variation, and for which the iterates of the transfer operator, when applied to one of these observables, is not asymptotic to a constant times the wandering rate on the first element of the partition α. Subsequently, sufficient conditions on observables are given under which this expected asymptotic holds. In particular, we obtain an extension theorem which establishes that, if the asymptotic behaviour of iterates of the transfer operator is known on the first element of the partition α, then the same asymptotic holds on any compact set bounded away from the indifferent fixed point.
Large gauge symmetries and asymptotic states in QED
NASA Astrophysics Data System (ADS)
Gabai, Barak; Sever, Amit
2016-12-01
Large Gauge Transformations (LGT) are gauge transformations that do not vanish at infinity. Instead, they asymptotically approach arbitrary functions on the conformal sphere at infinity. Recently, it was argued that the LGT should be treated as an infinite set of global symmetries which are spontaneously broken by the vacuum. It was established that in QED, the Ward identities of their induced symmetries are equivalent to the Soft Photon Theorem. In this paper we study the implications of LGT on the S-matrix between physical asymptotic states in massive QED. In appose to the naively free scattering states, physical asymptotic states incorporate the long range electric field between asymptotic charged particles and were already constructed in 1970 by Kulish and Faddeev. We find that the LGT charge is independent of the particles' momenta and may be associated to the vacuum. The soft theorem's manifestation as a Ward identity turns out to be an outcome of not working with the physical asymptotic states.
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
2017-05-01
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.
Dissipation-Induced d-Wave Pairing of Fermionic Atoms in an Optical Lattice
Diehl, S.; Daley, A. J.; Zoller, P.; Yi, W.
2010-11-26
We show how dissipative dynamics can give rise to pairing for two-component fermions on a lattice. In particular, we construct a parent Liouvillian operator so that a BCS-type state of a given symmetry, e.g., a d-wave state, is reached for arbitrary initial states in the absence of conservative forces. The system-bath couplings describe single-particle, number-conserving and quasilocal processes. The pairing mechanism crucially relies on Fermi statistics. We show how such Liouvillians can be realized via reservoir engineering with cold atoms representing a driven dissipative dynamics.
NASA Astrophysics Data System (ADS)
Jrad, Hanen; Dion, Jean Luc; Renaud, Franck; Tawfiq, Imad; Haddar, Mohamed
2016-10-01
This paper focuses on energy losses caused by inner damping and friction in an elastomeric rotational joint. A description of the design of a new experimental device intended to characterize dynamic stiffness in rotational elastomeric joint is presented. An original method based on Lagrange's equations, which allows accurately measuring forces and torques only with accelerometers, is proposed in order to identify dissipated energy in the rotational elastomeric joint. A rheological model developed taking into account dependence of the torque and the angular displacement (rotation). Experimental results and simulations used to quantify the dissipated energy in order to evaluate the damping ratio are presented and discussed.
Diffraction and Dissipation of Atmospheric Waves in the Vicinity of Caustics
NASA Astrophysics Data System (ADS)
Godin, O. A.
2015-12-01
A large and increasing number of ground-based and satellite-borne instruments has been demonstrated to reliably reveal ionospheric manifestations of natural hazards such as large earthquakes, strong tsunamis, and powerful tornadoes. To transition from detection of ionospheric manifestations of natural hazards to characterization of the hazards for the purposes of improving early warning systems and contributing to disaster recovery, it is necessary to relate quantitatively characteristics of the observed ionospheric disturbances and the underlying natural hazard and, in particular, accurately model propagation of atmospheric waves from the ground or ocean surface to the ionosphere. The ray theory has been used extensively to model propagation of atmospheric waves and proved to be very efficient in elucidating the effects of atmospheric variability on ionospheric signatures of natural hazards. However, the ray theory predicts unphysical, divergent values of the wave amplitude and needs to be modified in the vicinity of caustics. This paper presents an asymptotic theory that describes diffraction, focusing and increased dissipation of acoustic-gravity waves in the vicinity of caustics and turning points. Air temperature, viscosity, thermal conductivity, and wind velocity are assumed to vary gradually with height and horizontal coordinates, and slowness of these variations determines the large parameter of the problem. Uniform asymptotics of the wave field are expressed in terms of Airy functions and their derivatives. The geometrical, or Berry, phase, which arises in the consistent WKB approximation for acoustic-gravity waves, plays an important role in the caustic asymptotics. In addition to the wave field in the vicinity of the caustic, these asymptotics describe wave reflection from the caustic and the evanescent wave field beyond the caustic. The evanescent wave field is found to play an important role in ionospheric manifestations of tsunamis.
Acoustic Scattering from Ribs-Reinforced Plates - Asymptotic Solution
NASA Astrophysics Data System (ADS)
Seren, Cetin
The thesis deals with the development of analytic models for the prediction of the scattered acoustic field from an infinite elastic plate with single and multiple line force and line moment impedance dis- continuities due to an incident plane acoustic wave. The solution is in the form of a Fourier integral with a kernel having ten poles. The integral is evaluated by three methods. The first uses the Steepest Descent method (SDP), leading to a solution which decays as SQRT.(k(,0)r), where k(,0) is the acoustic wavenumber and r is the observer distance from the discontinuity. The second method uses conformal trans- formations and the modified saddle point method (MSP), where all ten poles of the integrand are factored out. This second method yields a solution which has complementary error functions and an asymptotic series in (k(,0)r). The third method employs a transformation of the integrand to effect an efficient and fastly convergent numerical integration algorithm. While the first method expects the diffracted pressures on the surface of the plate to be due to the residues of the kernel only, the other methods show non-vanishing contributions from the Fourier integral itself as well. In general, the MSP asymptotic series solution and the numerical integration yielded numerically identical results. However, while the SDP solution predicted a similar directivity function, it predicted numerically higher values than the MSP solution by as much as 20 dB for observers located close to the discontinuity. The three solu- tions converged for higher values of k(,0)r, the convergence being slower for higher frequencies, especially above the coincidence frequency. Both the integral contribution and the residue contribu- tion to the diffracted pressure along the surface were also compu- ted, and the integral contribution is shown to decay faster than the pressure at other locations by as much as 1/k(,0)r, depending on the incident wave frequency and the observer distance
NASA Astrophysics Data System (ADS)
Benaissa, Abbes; Benazzouz, Sohbi
2017-08-01
We consider the Timoshenko beam system with two dynamic control boundary conditions of fractional derivative type. We show that the system is not uniformly stable by a spectrum method and we establish the polynomial stability using the semigroup theory of linear operators and a result obtained by Borichev and Tomilov.
Jung, Gerhard; Schmid, Friederike
2016-05-28
Exact values for bulk and shear viscosity are important to characterize a fluid, and they are a necessary input for a continuum description. Here we present two novel methods to compute bulk viscosities by non-equilibrium molecular dynamics simulations of steady-state systems with periodic boundary conditions - one based on frequent particle displacements and one based on the application of external bulk forces with an inhomogeneous force profile. In equilibrium simulations, viscosities can be determined from the stress tensor fluctuations via Green-Kubo relations; however, the correct incorporation of random and dissipative forces is not obvious. We discuss different expressions proposed in the literature and test them at the example of a dissipative particle dynamics fluid.
Self-gravity and dissipation in polar rings
NASA Technical Reports Server (NTRS)
Dubinski, John; Christodoulou, Dimitris M.
1994-01-01
Studies of inclined rings inside galaxy potentials have mostly considered the influence of self-gravity and viscous dissipation separately. In this study, we construct models of highly inclined ('polar') rings in an external potential including both self-gravity and dissipation due to a drag force. We do not include pressure forces and thus ignore shock heating that dominates the evolution of gaseous rings inside strongly nonspherical potentials. We adopt an oblate spheroidal scale-free logarithmic potential with axis ratio q = 0.85 and an initial inclination of 80 deg for the self-gravitating rings. We find that stellar (dissipationless) rings suffer from mass loss during their evolution. Mass loss also drives a secular change of the mean inclination toward the poles of the potential. As much as half of the ring mass escapes in the process and forms an inner and an outer shell of precessing orbits. If the remaining mass is more than approximately 0.02 of the enclosed galaxy mass, rings remain bound and do not fall apart from differential precession. The rings precess at a constant rate for more than a precession period tau(sub p) finding the configuration predicted by Sparke in 1986 which warps at larger radii toward the poles of the potential. We model shear viscosity with a velocity-dependent drag force and find that nuclear inflow dominates over self-gravity if the characteristic viscous inflow time scale tau(sub vi) is shorter than approximately 25(tau(sub p)). Rings with (tau(sub vi))/(tau(sub p)) less than or approximately equal to 25 collapse toward the nucleus of the potential within one precession period independent of the amount of self-gravity. Our results imply that stars and gas in real polar rings exhibit markedly different dynamical evolutions.
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.
Dissipative structures, machines, and organisms: A perspective
NASA Astrophysics Data System (ADS)
Kondepudi, Dilip; Kay, Bruce; Dixon, James
2017-10-01
Self-organization in nonequilibrium systems resulting in the formation of dissipative structures has been studied in a variety of systems, most prominently in chemical systems. We present a study of a voltage-driven dissipative structure consisting of conducting beads immersed in a viscous medium of oil. In this simple system, we observed remarkably complex organism-like behavior. The dissipative structure consists of a tree structure that spontaneously forms and moves like a worm and exhibits many features characteristic of living organisms. The complex motion of the beads driven by the applied field, the dipole-dipole interaction between the beads, and the hydrodynamic flow of the viscous medium result in a time evolution of the tree structure towards states of lower resistance or higher dissipation and thus higher rates of entropy production. The resulting end-directed evolution manifests as the tree moving to locations seeking higher current, the current that sustains its structure and dynamics. The study of end-directed evolution in the dissipative structure gives us a means to distinguish the fundamental difference between machines and organisms and opens a path for the formulation of physics of organisms.
Ohmic Dissipation in Mini-Neptunes
NASA Astrophysics Data System (ADS)
Pu, Bonan; Valencia, Diana
2017-09-01
In the presence of a magnetic field and weakly ionizing winds, ohmic dissipation is expected to take place in the envelopes of Jovian and lower-mass planets alike. While the process has been investigated on the former, there have been no studies done on mini-Neptunes so far. From structure and thermal evolution models, we determine that the required energy deposition for halting the contraction of mini-Neptunes increases with planetary mass and envelope fraction. Scaled to the insolation power, the ohmic heating needed is small: ∼ {10}-5 orders of magnitude lower than for exo-Jupiters ∼ {10}-2. Conversely, from solving the magnetic induction equation, we find that ohmic energy is dissipated more readily for lower-mass planets and those with larger envelope fractions. Combining these two trends, we find that ohmic dissipation in hot mini-Neptunes is strong enough to inflate their radii (∼ {10}15 W for {T}{eq}=1400 {{K}}). The implication is that the radii of hot mini-Neptunes may be attributed in part to ohmic heating. Thus, there is a trade-off between ohmic dissipation and H/He content for hot mini-Neptunes, adding a new degeneracy for the interpretation of the composition of such planets. In addition, ohmic dissipation would make mini-Neptunes more vulnerable to atmospheric evaporation.
Energy dissipation in sheared granular flows
Karion, A.; Hunt, M.L.
1999-11-01
Granular material flows describe flows of solid particles in which the interstitial fluid plays a negligible role in the flow mechanics. Examples include the transport of coal, food products, detergents, pharmaceutical tablets, and toner particles in high-speed printers. Using a two-dimensional discrete element computer simulation of a bounded, gravity-free Couette flow of particles, the heat dissipation rate per unit area is calculated as a function of position in the flow as well as overall solid fraction. The computation results compare favorably with the kinetic theory analysis for rough disks. The heat dissipation rate is also measured for binary mixtures of particles for different small to large solid fraction ratios, and for diameter ratios of ten, five, and two. The dissipation rates increase significantly with overall solid fraction as well as local strain rates and granular temperatures. The thermal energy equation is solved for a Couette flow with one adiabatic wall and one at constant temperature. Solutions use the simulation measurements of the heat dissipation rate, solid fraction, and granular temperature to show that the thermodynamic temperature increases with solid fraction and decreases with particle conductivity. In mixtures, both the dissipation rate and the thermodynamic temperature increase with size ratio and with decreasing ratio of small to large particles.
Dissipative compensators for flexible spacecraft control
NASA Technical Reports Server (NTRS)
Joshi, S. M.; Maghami, P. G.
1990-01-01
The problem of controller design for flexible spacecraft is addressed. Model-based compensators, which rely on the knowledge of the system parameters to tune the state estimator, are considered. The instability mechanisms resulting from high sensitivity to parameter uncertainties are investigated. Dissipative controllers, which use collocated actuators and sensors, are also considered, and the robustness properties of constant-gain dissipative controllers in the presence of unmodeled elastic-mode dynamics, sensor/actuator nonlinearities, and actuator dynamics are summarized. In order to improve the performance without sacrificing robustness, a class of dissipative dynamic compensators is proposed and is shown to retain robust stability in the presence of second-order actuator dynamics if acceleration feedback is employed. A class of dissipative dynamic controllers is proposed which consists of a low-authority, constant-gain controller and a high-authority dynamic compensator. A procedure for designing an optimal dissipative dynamic compensator is given which minimizes a quadratic performance criterion. Such compensators offer the promise of better performance while still retaining robust stability.
Intermittent energy dissipation by turbulent reconnection
NASA Astrophysics Data System (ADS)
Fu, H. S.; Vaivads, A.; Khotyaintsev, Y. V.; André, M.; Cao, J. B.; Olshevsky, V.; Eastwood, J. P.; Retinò, A.
2017-01-01
Magnetic reconnection—the process responsible for many explosive phenomena in both nature and laboratory—is efficient at dissipating magnetic energy into particle energy. To date, exactly how this dissipation happens remains unclear, owing to the scarcity of multipoint measurements of the "diffusion region" at the sub-ion scale. Here we report such a measurement by Cluster—four spacecraft with separation of 1/5 ion scale. We discover numerous current filaments and magnetic nulls inside the diffusion region of magnetic reconnection, with the strongest currents appearing at spiral nulls (O-lines) and the separatrices. Inside each current filament, kinetic-scale turbulence is significantly increased and the energy dissipation, E' ṡ j, is 100 times larger than the typical value. At the jet reversal point, where radial nulls (X-lines) are detected, the current, turbulence, and energy dissipations are surprisingly small. All these features clearly demonstrate that energy dissipation in magnetic reconnection occurs at O-lines but not X-lines.
Dissipative compensators for flexible spacecraft control
NASA Technical Reports Server (NTRS)
Joshi, S. M.; Maghami, P. G.
1990-01-01
The problem of controller design for flexible spacecraft is addressed. Model-based compensators, which rely on the knowledge of the system parameters to tune the state estimator, are considered. The instability mechanisms resulting from high sensitivity to parameter uncertainties are investigated. Dissipative controllers, which use collocated actuators and sensors, are also considered, and the robustness properties of constant-gain dissipative controllers in the presence of unmodeled elastic-mode dynamics, sensor/actuator nonlinearities, and actuator dynamics are summarized. In order to improve the performance without sacrificing robustness, a class of dissipative dynamic compensators is proposed and is shown to retain robust stability in the presence of second-order actuator dynamics if acceleration feedback is employed. A class of dissipative dynamic controllers is proposed which consists of a low-authority, constant-gain controller and a high-authority dynamic compensator. A procedure for designing an optimal dissipative dynamic compensator is given which minimizes a quadratic performance criterion. Such compensators offer the promise of better performance while still retaining robust stability.
NASA Astrophysics Data System (ADS)
Bender, Carl M., Orszag, Steven A.
This book gives a clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory and explains how to use these methods to obtain approximate analytical solutions to differential and difference equations. These methods allow one to analyze physics and engineering problems that may not be solvable in closed form and for which brute-force numerical methods may not converge to useful solutions. The objective of this book is to teaching the insights and problem-solving skills that are most useful in solving mathematical problems arising in the course of modern research. Intended for graduate students and advanced undergraduates, the book assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations; develops local asymptotic methods for differential and difference equations; explains perturbation and summation theory; and concludes with a an exposition of global asymptotic methods, including boundary-layer theory, WKB theory, and multiple-scale analysis. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach the reader how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions; over 600 problems, of varying levels of difficulty; and an appendix summarizing the properties of special functions.
Optimal estimators and asymptotic variances for nonequilibrium path-ensemble averages
NASA Astrophysics Data System (ADS)
Minh, David D. L.; Chodera, John D.
2009-10-01
Existing optimal estimators of nonequilibrium path-ensemble averages are shown to fall within the framework of extended bridge sampling. Using this framework, we derive a general minimal-variance estimator that can combine nonequilibrium trajectory data sampled from multiple path-ensembles to estimate arbitrary functions of nonequilibrium expectations. The framework is also applied to obtain asymptotic variance estimates, which are a useful measure of statistical uncertainty. In particular, we develop asymptotic variance estimates pertaining to Jarzynski's equality for free energies and the Hummer-Szabo expressions for the potential of mean force, calculated from uni- or bidirectional path samples. These estimators are demonstrated on a model single-molecule pulling experiment. In these simulations, the asymptotic variance expression is found to accurately characterize the confidence intervals around estimators when the bias is small. Hence, the confidence intervals are inaccurately described for unidirectional estimates with large bias, but for this model it largely reflects the true error in a bidirectional estimator derived by Minh and Adib.
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.