Weak Dissipation Research Articles

A Sufficient Condition for the Kolmogorov 4/5 Law for Stationary Martingale Solutions to the 3D Navier–Stokes Equations

We prove that statistically stationary martingale solutions of the 3D Navier-Stokes equations on $\mathbb{T}^3$ subjected to white-in-time (colored-in-space) forcing satisfy the Kolmogorov 4/5 law (in an averaged sense and over a suitable inertial range) using only the assumption that the kinetic energy is $o(\nu^{-1})$ as $\nu \rightarrow 0$ (where $\nu$ is the inverse Reynolds number). This plays the role of a weak anomalous dissipation. No energy balance or additional regularity is assumed (aside from that satisfied by all martingale solutions from the energy inequality). If the force is statistically homogeneous, then any homogeneous martingale solution satisfies the spherically averaged 4/5 law pointwise in space. An additional hypothesis of approximate isotropy in the inertial range gives the traditional version of the Kolmogorov law. We demonstrate a necessary condition by proving that energy balance and an additional quantitative regularity estimate as $\nu \rightarrow 0$ imply that the 4/5 law (or any similar scaling law) cannot hold.

Warm DBI inflation with constant sound speed

We study inflation with the Dirac–Born–Infeld (DBI) noncanonical scalar field in both the cold and warm scenarios. We consider the Anti-de Sitter warp factor f(phi )=f_{0}/phi ^{4} for the DBI inflation and check viability of the quartic potential V(phi )=lambda phi ^{4}/4 in light of the Planck 2015 observational results. In the cold DBI setting, we find that the prediction of this potential in the r-n_s plane is in conflict with Planck 2015 TT, TE, EE + low P data. This motivates us to focus on the warm DBI inflation with constant sound speed. We conclude that in contrary to the case of cold scenario, the r-n_s result of warm DBI model can be compatible with the 68% CL constraints of Planck 2015 TT, TE, EE + low P data in the intermediate and high dissipation regimes, whereas it fails to be observationally viable in the weak dissipation regime. Also, the prediction of this model for the running of the scalar spectral index dn_s/dln k is in good agreement with the constraint of Planck 2015 TT, TE, EE + low P data. Finally, we show that the warm DBI inflation can provide a reasonable solution to the swampland conjecture that challenges the de Sitter limit in the standard inflation.

Nonlinear dust magnetosonic waves in collisional plasma

The excitations and damping of nonlinear dust magnetosonic waves in dissipative plasma are investigated. The dynamics of negatively charged dust particles is considered. The dissipation is taken due to dust neutral collisions. The ions and electrons are inertialess on dust dynamic scale. The temperature of ions and electrons is also taken into account. The linear dispersion charteristics of dust magnetosonic waves are discussed for different values of plasma parameters. For this purpose we have derived Damped Korteweg de Vries (DKdV) equation by applying the reductive perturbation method. For weak dissipation the analytical solution of DKdV is presented. For the numerical solution, we apply a two-level finite difference scheme with the help of the Runge-Kutta method. The effects of variations of different plasma parameters on the damping of nonlinear dust magnetosonic solitary wave structures are discussed.

Full-Scale Tests on the Horizontal Hysteretic Behavior of a Single-Span Timber Frame

ABSTRACT In a column-beam-bracket (CBB) sets timber frame, the columns are connected with beams using mortise-tenon joints and the columns rest directly on stone bases. To study the horizontal hysteretic behavior of such structures, a single-span full-scale model was constructed. By analyzing the load-displacement hysteretic curves, envelope curves, and dissipation capacity under different vertical loads, it is found that the timber frame is a self-centering structure with high ductility and weak hysteretic energy dissipation, the rotational deformation of the timber frame is mainly caused by the column rotation. The column rotation and the frictional sliding of components are the primary factors causing the significant stiffness degradation of the timber frame. The frictional sliding is also the major source of initial energy dissipation. The vertical loads show a linear growth relationship with the elastic stiffness and maximum horizontal force for each stage in the simplified four-stage linear model.

Variability of Internal Wave‐Driven Mixing and Stratification in Canadian Arctic Shelf and Shelf‐Slope Waters

AbstractOur understanding of ocean mixing is challenged by its patchy, episodic nature and a scarcity of direct measurements, especially in the Arctic Ocean. In this study, we exploit a historical record of nearly 3,000 conductivity‐temperature‐depth profiles collected in the shelf and shelf‐slope waters of the Canadian Arctic Ocean from 2002 to 2016 to characterize the variability of 28,872 internal wave‐driven turbulent dissipation and mixing rate estimates from a finescale parameterization. We find that these estimates of wave‐driven dissipation rates and associated diapycnal diffusivities are generally low, but exhibit wide variability, each spanning several orders of magnitude. We further find that stratification plays a significant role in modulating the mixing rate both vertically and regionally within the study domain. Dissipation rate and diffusivity estimates display a weak seasonal cycle, but no evidence of statistically significant interannual trends over this period. Exceptionally large localized temporal variability appears to dominate other potential underlying patterns. The presence of strong upper ocean stratification combined with predominately weak dissipation rate estimates implies that many regions in the Canadian Arctic Ocean are likely in a molecular or buoyancy‐controlled mixing regime. Even when the concept of a turbulent‐enhanced diffusivity is potentially relevant, most turbulent heat flux estimates out of the Atlantic Water thermocline are smaller than the average value required to close the standardly assumed Arctic Ocean heat budget. In contrast, we find evidence for isolated occurrences of anomalously large heat fluxes, which may disproportionately contribute to the liberation of Atlantic Water heat toward the surface sea ice pack.

Exponential Stability for the Generalized Korteweg-de Vries Equation in a Finite Interval with Weak Damping

The aim of this paper is to consider the generalized Korteweg-de Vries equation in a finite interval with a very weak localized dissipation. We obtain the globally uniformly exponentially stability of this equation. The main difficulty in this context comes from the structure of nonlinear term and the lack of regularity.

Ergodic BSDE with unbounded and multiplicative underlying diffusion and application to large time behaviour of viscosity solution of HJB equation

We study ergodic backward stochastic differential equations (EBSDEs), for which the underlying diffusion is assumed to be multiplicative and of linear growth. The fact that the forward process has an unbounded diffusion is balanced with an assumption of weak dissipativity for its drift. Moreover, the forward equation is assumed to be non-degenerate. We study the existence and uniqueness of EBSDEs and we apply our results to an ergodic optimal control problem. In particular, we show the large time behaviour of viscosity solution of Hamilton–Jacobi–Bellman equation with an exponential rate of convergence when the underlying diffusion is multiplicative and unbounded.

Periodic traveling waves in a generalized BBM equation with weak backward diffusion and dissipation terms

In this paper, we consider a generalized BBM equation with weak backward diffusion, dissipation and Marangoni effects, and study the existence of periodic and solitary waves. Main attention is focused on periodic and solitary waves on a manifold via studying the number of zeros of some linear combination of Abelian integrals. The uniqueness of the periodic waves is established when the equation contains one coefficient in backward diffusion and dissipation terms, by showing that the Abelian integrals form a Chebyshev set. The monotonicity of the wave speed is proved, and moreover the upper and lower bounds of the limiting wave speeds are obtained. Especially, when the equation involves Marangoni effect due to imposed weak thermal gradients, it is shown that at most two periodic waves can exist. The exact conditions are obtained for the existence of one and two periodic waves as well as for the co-existence of one solitary and one periodic waves. The analysis is mainly based on Chebyshev criteria and asymptotic expansions of Abelian integrals near the solitary and singularity.

Effective quantum Zeno dynamics in dissipative quantum systems

We investigate the time evolution of an open quantum system described by a Lindblad master equation with dissipation acting only on a part of the degrees of freedom ${\cal H}_0$ of the system, and targeting a unique dark state in ${\cal H}_0$. We show that, in the Zeno limit of large dissipation, the density matrix of the system traced over the dissipative subspace ${\cal H}_0$, evolves according to another Lindblad dynamics, with renormalized effective Hamiltonian and weak effective dissipation. This behavior is explicitly checked in the case of Heisenberg spin chains with one or both boundary spins strongly coupled to a magnetic reservoir. Moreover, the populations of the eigenstates of the renormalized effective Hamiltonian evolve in time according to a classical Markov dynamics. As a direct application of this result, we propose a computationally-efficient exact method to evaluate the nonequilibrium steady state of a general system in the limit of strong dissipation.

Decoherence in the quantum Ising model with transverse dissipative interaction in the strong-coupling regime

We study the decoherence dynamics of a quantum Ising lattice of finite size with a transverse dissipative interaction, namely the coupling with the bath is assumed perpendicular to the direction of the spins interaction and parallel to the external transverse magnetic field. In the limit of small transverse field, the eigenstates and spectrum are obtained by a strong coupling expansion, from which we derive the Lindblad equation in the Markovian limit. At temperature lower than the energy gap and for weak dissipation, the decoherence dynamics can be restricted to take only the two degenerate ground states and the first excited subspace into account. The latter is formed by pairs of topological excitations (domain walls or kinks), which are quantum delocalized along the chain due to the small magnetic field. We find that some of these excited states form a relaxation-free subspace, i.e. they do not decay to the ground states. We also discuss the decoherence dynamics for an initial state formed by a quantum superposition of the two degenerate ground states corresponding to the orthogonal classical, ferromagnetic states.

Holographic transports from Born\u2013Infeld electrodynamics with momentum dissipation

We study the Einstein-axions AdS black hole from Born–Infeld electrodynamics. Various DC transport coefficients of the dual boundary theory are analytically computed. The DC electric conductivity depends on the temperature, which is a novel property comparing to that in RN-AdS black hole. The effects of Born-Infeld parameter on the transport coefficients are analyzed. Also, we study the AC electric conductivity from Born–Infeld electrodynamics with momentum dissipation. For weak momentum dissipation, the low frequency behavior satisfies the standard Drude formula and the electric transport is coherent for various correction parameter. While for stronger momentum dissipation, the modified Drude formula is applied and we observe a crossover from coherent to incoherent phase. Moreover, the Born–Infeld correction amplifies the incoherent behavior. Finally, we study the non-linear conductivity in probe limit and compare our results with those observed in (i)DBI model.

Dynamical quantum phase transition for mixed states in open systems

Based on a kinematic approach in defining a geometric phase for a density matrix, we define the generalized Loschmidt overlap amplitude (GLOA) for an open system for arbitrary quantum evolution. The GLOA reduces to the Loschmidt overlap amplitude (LOA) with a modified dynamic phase for unitary evolution of a pure state, with the argument of the GLOA well-defined by the geometric phase, thus possessing similar physical interpretation to that of the LOA. The rate function for the GLOA exhibits non-analyticity at a critical time, which corresponds to the dynamical quantum phase transition. We observe that the dynamical quantum phase transition related to GLOA is not destroyed under a finite temperature and weak enough dissipation. In particular, we find that a new type of dynamical quantum phase transition emerges in a dissipation system. The proposed GLOA provides a powerful tool in the investigation of a dynamical quantum phase transition in an arbitrary quantum system, which not only can characterize the robustness of the dynamical quantum phase transition but also can be used to search for new transitions.

Existence for elastodynamic Griffith fracture with a weak maximal dissipation condition

We consider a model of elastodynamics with fracture evolution, based on energy-dissipation balance and a maximal dissipation condition. We prove an existence result in the case of planar elasticity with a free crack path, where the maximal dissipation condition is satisfied among suitably regular competitor cracks.

Optimal initialization of a quantum system for an efficient coherent energy transfer

For an energy transfer network, the irreversible depletion of excited electron energy occurs through either an efficient flow into an outer energy sink or an inefficient decay. With a small decay rate, the energy transfer efficiency is quantitatively reflected by the average life time of excitation energy before being trapped in the sink where the decay process is omitted. In the weak dissipation regime, the trapping time is analyzed within the exciton population subspace based on the secular Redfield equation. The requirement of the noise-enhanced energy transfer is obtained, where the trapping time follows an exact or approximate 1/Γ-scaling of the dissipation strength Γ. On the opposite side, optimal initial system states are conceptually constructed to suppress the 1/Γ-scaling of the trapping time and maximize the coherent transfer efficiency. Our theory is numerically testified in four models, including a biased two-site system, a symmetric three-site branching system, a homogeneous one-dimensional chain, and an 8-chromophore FMO protein complex.

Resonance-induced energy localization in a weakly dissipative nonlinear chain.

This work investigates the emergence of resonance and resonance-induced localization in a weakly dissipative chain of coupled anharmonic oscillators under the influence of a harmonic force applied at one end of the chain. The dynamics of the chain is studied assuming 1:1 (fundamental) resonance, when the response of each nonlinear oscillator has a dominant harmonic component with the frequency close to the frequency of the external excitation. It is shown that weak dissipation in a strongly nonlinear chain may be a key factor preventing large-amplitude resonance. The resulting process in the dissipative system represents resonance-induced large-amplitude oscillations of a part of the chain adjacent to the actuator and escape from resonance of the distant oscillators. Conditions of the emergence of resonance and energy localization are derived. The obtained solutions indicate that the maximal concentration of energy on the excited oscillator arises together with equipartition of energy among the other resonant oscillators. An agreement between the analytical and numerical results is demonstrated.

On the effect of the thermostat in non-equilibrium molecular dynamics simulations.

The numerical investigation of the statics and dynamics of systems in non-equilibrium in general, and under shear flow in particular, has become more and more common. However, not all the numerical methods developed to simulate equilibrium systems can be successfully adapted to out-of-equilibrium cases. This is especially true for thermostats. Indeed, even though thermostats developed to work under equilibrium conditions sometimes display good agreement with rheology experiments, their performance rapidly degrades beyond weak dissipation and small shear rates. Here we focus on gauging the relative performances of three thermostats, Langevin, dissipative particle dynamics, and Bussi-Donadio-Parrinello under varying parameters and external conditions. We compare their effectiveness by looking at different observables and clearly demonstrate that choosing the right thermostat (and its parameters) requires a careful evaluation of, at least, temperature, density and velocity profiles. We also show that small modifications of the Langevin and DPD thermostats greatly enhance their performance in a wide range of parameters.

Tidal Dissipation in the System WASP-46

The change in the orbital period of the system WASP-46 due to quasi-static and dynamical tidal interactions is investigated. Various dissipation mechanisms are studied. In the case of quasi-static tides, dissipation is assumed to occur due to turbulent viscosity, while in the case of dynamical tides, two limiting cases are considered: the regime of moderately large dissipation and the regime of weak dissipation due to radiative viscosity. The change in the orbital period of WASP-46 is calculated and compared with observations. The regime of moderately large dissipation is shown to describe best the observations.

Simultaneous Observations of Polar Mesosphere Winter Echoes and Cosmic Noise Absorptions in a Common Volume by the PANSY Radar (69.0°S, 39.6°E)

AbstractThis study focuses on the one‐to‐one relationship between the morphology of polar mesosphere winter echo (PMWE) and cosmic noise absorption (CNA) as determined by measurements made with a single atmospheric radar, the Program of the Antarctic Syowa mesosphere‐stratosphere‐troposphere/incoherent scatter (PANSY) radar. CNA was calculated using the noise level in radar signal data collected during May 2013, including data of a solar proton event on 23 May. Using PMWE and CNA data in a common volume, their temporal variations and relation were examined in detail. PMWE altitude was clearly anticorrelated with CNA magnitude in a statistical sense: When a large CNA exceeding 0.50 dB took place, PMWE seemed to concentrate around 65 km and disappear above 70 km. The electron density behind the PMWE was estimated by using the ionospheric model for the auroral zone for the solar proton event. PMWE occurrence roughly coincided with a high electron density in the model, except that no PMWE was observed above 70 km at 0730 UT despite the electron density being higher than 108 m−3. Additionally, the estimated radar volume reflectivity with the Schmidt number Sc less than or equal to 1 is qualitatively consistent with the observed PMWE. Although weak turbulent energy dissipation rate can also play a dominant role in the observed PMWE decay, a plausible mechanism was small Sc or reduction of Sc that is equal to an increase in electron diffusivity resulting from an unusually high electron density, which significantly reduced radar volume reflectivity above 70 km.

Experimental study of the stability and dynamics of a two-dimensional ideal vortex under external strain

The dynamics of two-dimensional (2-D) ideal fluid vortices is studied experimentally in the presence of an irrotational strain flow. Laboratory experiments are conducted using strongly magnetized pure electron plasmas, a technique which is made possible by the isomorphism between the drift–Poisson equations describing plasma dynamics transverse to the field and the 2-D Euler equations describing an ideal fluid. The electron plasma system provides an excellent opportunity to study the dynamics of a 2-D Euler fluid due to weak dissipation and weak 3-D effects, simple diagnosis and precise control. The plasma confinement apparatus used here was designed specifically to study vortex dynamics under the influence of external flow by applying boundary conditions in two dimensions. Additionally, vortex-in-cell simulations are carried out to complement the experimental results and to extend the parameter range of the studies. It is shown that the global dynamics of a quasi-flat vorticity profile is in good quantitative agreement with the theory of a piecewise-constant elliptical patch of vorticity, including the equilibria, dynamical orbits and stability properties. Deviations from the elliptical patch theory are observed for non-flat vorticity profiles; they include inviscid damping of the orbits and modified stability limits. The dependence of these phenomena on the flatness of the initial profile is discussed. The relationship of these results to other theoretical, numerical and experimental studies is also discussed.

Coupled drift shock and soliton in collisional ambiplasma with nonthermal effects of electrons and positrons

In the present article coupled drift-ion acoustic mode is investigated in four component collisional, magnetized, and inhomogeneous ambiplasma consisting of positive and negative ions, non-thermal electrons and positrons. Linear dispersion relation for the coupled mode is derived with effect of nothermality and particle concentration. In the presence of weak dispersion and dissipation a KdV-Burger equation is derived in nonlinear regime, for coupled acoustic-drift shock and soliton. Using Tanh-method the solution for double layers in the system is derived. The results are numerically highlighted for ambi plasma at early universe and space plasma. Further more keeping in view the non thermal behavior of ambiplasma in space, a kappa distributed approach is used for these calculations.