Estimation Of Dissipation Research Articles

Libration- and Precession-driven Dissipation in the Fluid Cores of the TRAPPIST-1 Planets

The seven planets orbiting TRAPPIST-1 have sizes and masses similar to Earth and mean densities that suggest that their interior structures are comprised of a fluid iron core and rocky mantle. Here we use idealized analytical models to compute estimates of the viscous dissipation in the fluid cores of the TRAPPIST-1 planets induced by mantle libration and precession. The dissipation induced by the libration at orbital periods is largest for TRAPPIST-1b, of the order of 600 MW, and decreases with orbital distance, to values of 5–500 W for TRAPPIST-1h, depending on its triaxial shape. Extrapolating these results to the larger libration amplitudes expected at longer periods, dissipation may perhaps be as high as 1 TW in TRAPPIST-1b. Orbital precession induces a misalignment between the spin axes of the fluid core and mantle of a planet, the amplitude of which depends on the resonant amplification of its free precession and free core nutation. Assuming Cassini states, we show that the dissipation from this misalignment can reach a few TW for planets e and f. Our dissipation estimates are lower bounds, as we neglect ohmic dissipation, which may dominate if the fluid cores of the TRAPPIST-1 planets sustain magnetic fields. Our results suggest that dissipation induced by precession can be of the same order as tidal dissipation for the outermost planets, may perhaps be sufficient to supply the power to a generate a magnetic field in their liquid cores, and likely played an important role in the evolution of the TRAPPIST-1 system.

Estimation of the dissipation due to radiation damping for the pile embedded in soil: A closed-form solution

In the present work, the overall energy dissipation of a pile embedded in the soil, modeled as visco-elastic springs, is thoroughly investigated. The term dissipation is used to measure the rate of decay of amplitude of displacement response in the time domain. The estimation of dissipation in piles is necessary to understand how quickly a pile reaches its steady state or equilibrium under dynamic loads or in cases of free vibration, respectively. A higher level of dissipation indicates a shorter duration of transient vibration, which is a deserving trait for vibration mitigation in extreme events, such as earthquakes, storms, blasts, shocks, etc. The dispersion relation which is a function of wavenumber and free wave frequency is obtained for the pile embedded in the soil medium by implementing the generalized form of Bloch’s theorem. The dispersion relationship is solved in the free-wave approach, in which a real wave number yields a set of complex frequencies. For predicting the overall dissipation of the system from the complex frequency values, an analytical closed-form expression is proposed in this paper. Further, the predicted dissipation is validated with a finite element-based numerical model of the soil–pile system.

Model and method to predict the turbulent kinetic energy induced by tidal currents, application to the wave-induced turbulence

A prediction model for the turbulent kinetic energy (TKE) induced by tidal-currents is proposed as a function of the barotropic velocity only, along with a robust method evaluating the different parameters involved using Acoustic Doppler Current Profiler (ADCP) measurements from Alderney Race. We find that the model is able to reproduce correctly the TKE profiles with coefficients of correlation on average higher than 0.90 and normalised root-mean-square errors (NRMSE) less than 14%. Different profiles are also tested for the mean velocity, no satisfactory prediction model is found but we are able to have decent estimates of the velocity shear and friction velocity. Two applications are then carried out. First the turbulent budget terms are estimated and discussed. We identify the turbulent production and dissipation of TKE as the most important mechanisms, then we discuss the validity of several theoretical results derived for isotropic turbulence for this application. A strong departure for the estimation of the turbulent dissipation is notably found and explained by the turbulent anisotropy. At last the prediction model for the TKE is used to infer the wave-induced TKE. We show the importance of removing the tidal component, waves can have a strong influence down to mid-depth.

Large-time behavior of global solutions to the Cauchy problem of one-dimensional viscous and heat-conducting ionized gas

This paper is concerned with the Cauchy problem of one-dimensional viscous and heat-conducting ionized gas when the viscosity is a positive constant or depends on the density. According to Saha's ionization equation, the equations of state for the basic thermodynamic variables of an ionized gas depend also on the degree of ionization, which leads to the loss of concavity of the physical entropy in some small bounded domain. Such a property of the ionized gas together with the unboundedness of the domain under our consideration makes it hard to derive the desired dissipative estimates on the first-order spatial derivative of both the bulk velocity and the absolute temperature, thus making the problem more challenging.In this paper, for a class of constant non-vacuum equilibrium states with positive temperature, we succeed in deducing the desired uniform-in-time bounds on the above mentioned dissipative estimates on both the bulk velocity and the absolute temperature. Based on such an estimate, we can then establish the global existence of solutions to the Cauchy problem of one-dimensional viscous and heat-conducting ionized gas with positive constant or density-dependent viscosity and show that such a class of constant non-vacuum equilibrium states is time asymptotically nonlinear stable.

Finite-Time Dissipative Fuzzy State Estimation for Jump Systems With Mixed Cyber Attacks: A Probabilistic Event-Triggered Approach.

This article addresses the finite-time dissipative fuzzy state estimation for Markov jump systems under mixed cyber attacks. A probabilistic event-triggered mechanism (PETM) is proposed to reduce the unwanted network traffic by using the statistic information of network-induced delays. The dual asynchronizations characterized by asynchronous modes and mismatched premise variables are tackled simultaneously. Under the PETM, Takagi-Sugeno (T-S) fuzzy state estimators are first constructed based on the imperfect measurements subject to mixed cyber attacks and exogenous disturbances. Less conservative criteria relying on both fuzzy rules and jumping modes are established to achieve the strictly (Q,S,R) - ϑ -dissipative finite-time state estimation performance. Furthermore, a synthesis algorithm is derived to calculate the fuzzy state estimator gains by virtue of an improved matrix decoupling technique. Finally, two examples are utilized to validate the effectiveness and advantage of the proposed results.

An improved method for estimating the dissipation rate of turbulent kinetic energy using structure functions evaluated from the motion of finite-sized neutrally buoyant particles

Statistical relations used for estimating the dissipation rate of turbulent kinetic energy (TKE) in isotropic turbulence from the inertial subrange of Lagrangian temporal and spatial structure functions are extended here to the case of more realistic turbulence spectra that include low-frequency and low-wavenumber ranges. It is shown that using the traditional relations based only on the inertial subrange substantially underestimates the dissipation. The improved relations are better constrained by experimental data from which the dissipation is evaluated, enabling more accurate dissipation estimates. The concept is illustrated using laboratory data from water tank experiments of turbulence generated by an oscillating cylinder, where the dissipation is evaluated in three independent ways: from Lagrangian spectra and from Lagrangian temporal and spatial structure functions calculated from the motion of neutrally buoyant finite-sized particles. An additional correction to the relations for estimating the dissipation from the spatial structure functions is applied to take into account the filtering effect of the particles due to their finite size. It is found that, for these particular experiments, the TKE dissipation rate scales well with dimensionally consistent quantities built using the amplitude of the oscillation of the cylinder and the period of its motion, and the constant of proportionality in this scaling relation is determined using the method proposed here. Although the turbulence under consideration is quite anisotropic, the adopted theoretical framework, which assumes isotropic turbulence, seems to be applicable to the experimental data as long as the turbulence statistics are averaged over the three main flow directions.

Extreme value statistics of edge currents in Markov jump processes and their use for entropy production estimation

The infimum of an integrated current is its extreme value against the direction of its average flow. Using martingale theory, we show that the infima of integrated edge currents in time-homogeneous Markov jump processes are geometrically distributed, with a mean value determined by the effective affinity measured by a marginal observer that only sees the integrated edge current. In addition, we show that a marginal observer can estimate a fraction of the average entropy production rate in the underlying nonequilibrium process from the extreme value statistics in the integrated edge current. The estimated average rate of dissipation obtained in this way equals the above mentioned effective affinity times the average edge current. Moreover, we show that estimates of dissipation based on extreme value statistics can be significantly more accurate than those based on thermodynamic uncertainty ratios, as well as those based on a naive estimator obtained by neglecting nonMarkovian correlations in the Kullback-Leibler divergence of the trajectories of the integrated edge current.

BGK Model for Two-Component Gases Near a Global Maxwellian

In this paper, we establish the existence of the unique global-in-time classical solutions to the two-component Bhatnagar–Gross–Krook (BGK) model suggested in [C. Klingenberg, M. Pirner, and G. Puppo, Kinet. Relat. Models, 10 (2017), pp. 445–465] when the initial data is a small perturbation of global equilibrium. For this, we carefully analyze the dissipative nature of the linearized two-component relaxation operator and observe that the partial dissipation from the intraspecies and the interspecies linearized relaxation operators are combined in a complementary manner to give rise to the desired dissipation estimate of the model. We also observe that the convergence rate of the distribution function increases as the momentum-energy interchange rate between the different components of the gas increases.

Erratum to “optimal relaxation of bump-like solutions of the one-dimensional Cahn–Hilliard equation”

A dissipation estimate from the original article is corrected. The main result carries through unchanged, as explained below.

Current shear and turbulence during a near-inertial wave

Surface currents and turbulent mixing were observed during a near-inertial wave (NIW) using an accousting doppler current profiler (ADCP) and satellite-tracked drifters. Drifter trajectories sampled at three depth levels show characteristics of an Ekman solution superposed with the NIW. Velocity and dissipation estimates from the ADCP reveal strong shear with a distinct constant flux layer in between the roughness length and a critical depth at 4m. Below, a shear free slab layer performing an inertial oscillation is observed. Dissipation, as estimated from the vertical beam of the ADCP, peaks in the wave-enhanced friction layer when the current opposes the wind and wave direction. Below the constant flux layer, maximum turbulence is observed when the NIW is in a phase that is in opposite direction to the time-averaged current. During this phase, currents at various depths rapidly realign in the entire boundary layer.

Final state observability estimates and cost-uniform approximate null-controllability for bi-continuous semigroups

We consider final state observability estimates for bi-continuous semigroups on Banach spaces, i.e. for every initial value, estimating the state at a final time T>0 by taking into account the orbit of the initial value under the semigroup for tin [0,T], measured in a suitable norm. We state a sufficient criterion based on an uncertainty relation and a dissipation estimate and provide two examples of bi-continuous semigroups which share a final state observability estimate, namely the Gauß–Weierstraß semigroup and the Ornstein–Uhlenbeck semigroup on the space of bounded continuous functions. Moreover, we generalise the duality between cost-uniform approximate null-controllability and final state observability estimates to the setting of locally convex spaces for the case of bounded and continuous control functions, which seems to be new even for the case of Banach spaces.

Estimation of the power dissipation on the casing of DTT toroidal field coil during a fast plasma disruption

The aim of this paper is the computation of the power dissipated on the Toroidal Field Coil (TFC) casing of the Divertor Tokamak Test facility (DTT). The DTT Tokamak will be installed in Fascati (Italy), and is in an advanced design stage. The magnetic system will be realized with superconducting coils so that the correct dimensioning of the cooling system is mandatory. As a consequence, a detailed knowledge of the main sources of dissipation is required. Our attention will here be focused on the TFC casing and, in particular, on the dissipations due to the eddy currents induced on the casing by time-varying magnetic field during a Fast Plasma Disruption (FPD). A finite element model whose geometry has partly been imported into Ansys 2021/R2 SpaceClaim (TFC casing), and partly made in Ansys 2021/R2 DesignModeler (plasma, Vacuum Vessel (VV) and Stabilizing Plates (SP)), has been implemented in Ansys 2021/R2 Maxwell 3D to perform a transient analysis of the FPD event. The current induced on the TFC casing, as well as the total power losses, are the output of our computation to be used for the cooling system dimensioning. In order to estimate the heat rate to be removed during normal operation, the breakdown and Single Null (SN) scenarios have also been studied.

Observability for Non-autonomous Systems

We study non-autonomous observation systems , where is a strongly measurable family of closed operators on a Banach space and is a family of bounded observation operators from to a Banach space . Based on an abstract uncertainty principle and a dissipation estimate, we prove that the observation system satisfies a final-state observability estimate in for measurable subsets . We present applications of the above result to families of uniformly strongly elliptic differential operators as well as non-autonomous Ornstein–Uhlenbeck operators on with observation operators . In the setting of non-autonomous strongly elliptic operators, we derive necessary and sufficient geometric conditions on the family of sets such that the corresponding observation system satisfies a final-state observability estimate.

Improving estimation of entropy production rate for run-and-tumble particle systems by high-order thermodynamic uncertainty relation.

Entropy production plays an important role in the regulation and stability of active matter systems, and its rate quantifies the nonequilibrium nature of these systems. However, entropy production is hard to experimentally estimate even in some simple active systems like molecular motors or bacteria, which may be modeled by the run-and-tumble particle (RTP), a representative model in the study of active matters. Here we resolve this problem for an asymmetric RTP in one dimension, first constructing a finite-time thermodynamic uncertainty relation (TUR) for a RTP, which works well in the short observation time regime for entropy production estimation. Nevertheless, when the activity dominates, i.e., the RTP is far from equilibrium, the lower bound for entropy production from TUR turns out to be trivial. We address this issue by introducing a recently proposed high-order thermodynamic uncertainty relation (HTUR), in which the cumulant generating function of current serves as a key ingredient. To exploit the HTUR, we adopt a method to analytically obtain the cumulant generating function of the current we study, with no need to explicitly know the time-dependent probability distribution. The HTUR is demonstrated to be able to estimate the steady state energy dissipation rate accurately because the cumulant generating function covers higher-order statistics of the current, including rare and large fluctuations besides its variance. Compared to the conventional TUR, the HTUR could give significantly improved estimation of energy dissipation, which can work well even in the far from equilibrium regime. We also provide a strategy based on the improved bound to estimate the entropy production from a moderate amount of trajectory data for experimental feasibility.

Bayesian Parameter estimation of microphone positions, sound speed and dissipation for impedance tube measurements

With tube measurement widely used for acoustic measurements, calibration plays an important role in verifying and validating the measurement. This work applies a Bayesian method based on an air layer reflectance model to estimate the microphone positions, and sound speed in consideration of environmental effects on uncertainties of the normal incident impedance tube measurements. Bayesian theorem is applied to estimate the microphone positions and sound speed given the experimental data obtained from the transfer function method (TFM) in tube measurements. With a hypothetical air layer treated as material under test in front of a rigid backing in the tube, a parametric model is established for the TFM tube measurement to estimate the microphone positions using Bayesian inference. With the microphone positions accurately estimated, sound speed and losses due to tube interior boundary effects are also estimated within the same Bayesian framework. Bayesian analysis results show that Bayesian parameter estimation based on the air layer model is well suited in estimating the sound speed, microphone positions, and other parameters to ensure highly accurate tube measurements.

Final state observability in Banach spaces with applications to subordination and semigroups induced by Lévy processes

This paper generalizes the abstract method of proving an observability estimate by combining an uncertainty principle and a dissipation estimate. In these estimates we allow for a large class of growth/decay rates satisfying an integrability condition. In contrast to previous results, we use an iterative argument which enables us to give an asymptotically sharp estimate for the observation constant and which is explicit in the model parameters. We give two types of applications where the extension of the growth/decay rates naturally appear. By exploiting subordination techniques we show how the dissipation estimate of a semigroup transfers to subordinated semigroups. Furthermore, we apply our results to semigroups related to Lévy processes.

Observability and null-controllability for parabolic equations in $ L_p $-spaces

<p style='text-indent:20px;'>We study (cost-uniform approximate) null-controllability of parabolic equations in <inline-formula><tex-math id="M2">\begin{document}$ L_p( \mathbb{R}^d) $\end{document}</tex-math></inline-formula> and provide explicit bounds on the control cost. In particular, we consider systems of the form <inline-formula><tex-math id="M3">\begin{document}$ \dot{x}(t) = -A_px(t) + {\bf{1}}_ E u(t) $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M4">\begin{document}$ x(0) = x_0\in L_p ( \mathbb{R}^d) $\end{document}</tex-math></inline-formula>, with interior control on a so-called thick set <inline-formula><tex-math id="M5">\begin{document}$ E \subset \mathbb{R}^d $\end{document}</tex-math></inline-formula>, where <inline-formula><tex-math id="M6">\begin{document}$ p\in [1,\infty) $\end{document}</tex-math></inline-formula>, and where <inline-formula><tex-math id="M7">\begin{document}$ A $\end{document}</tex-math></inline-formula> is an elliptic operator of order <inline-formula><tex-math id="M8">\begin{document}$ m \in \mathbb{N} $\end{document}</tex-math></inline-formula> in <inline-formula><tex-math id="M9">\begin{document}$ L_p(\mathbb{R}^d) $\end{document}</tex-math></inline-formula>. We prove null-controllability of this system via duality and a sufficient condition for observability. This condition is given by an uncertainty principle and a dissipation estimate. Our result unifies and generalizes earlier results obtained in the context of Hilbert and Banach spaces. In particular, our result applies to the case <inline-formula><tex-math id="M10">\begin{document}$ p = 1 $\end{document}</tex-math></inline-formula>.</p>

Entropy dissipation estimates for the Boltzmann equation without cut-off

We prove the the entropy production of the Boltzmann equation, in the non cutoff regime, is bounded from below by a weighted $ L^p $ norm of the solution. The estimate holds for a wide range of potentials including soft potentials as well as very soft potentials. We discuss applications of this estimate for weak solutions of the Boltzmann equation. In particular, we obtain that weak solutions must be belong to the space $ L^1([0,T],L^p_q( \mathbb R^d)) $ for some precise exponents $ p $ and $ q $.

Control problem for quadratic parabolic differential equations with sparse sensor sets of finite volume or anisotropically decaying density

We prove observability and null-controllability for quadratic parabolic differential equations. The sensor set is allowed to be sparse and have finite volume if the generator has trivial singular space S. In the case of generators with singular space S ≠ {0} the sensor set is permitted to decay in directions determined by S. The proof is based on dissipation estimates for the quadratic differential operator with respect to spectral projections of partial harmonic oscillators and corresponding uncertainty relations.

A mechanism-based fate model of pesticide solutions on the plant surface under aerial application

ABSTRACT Pesticide residues on plant surfaces are a primary source of pesticide bioaccumulation in crops. In this context, we propose a mechanism-based model for understanding the pesticide fate on the plant surface following aerial application, taking into account fate modelling of the pesticide spray solution on the plant surface. Using chlorothalonil as an example, the simulation results revealed that the spray solution dissipated rapidly after aerial application, resulting in the formation of a saturated pesticide solution, which facilitated the diffusion process of the pesticide residue from the plant surface into the peel tissue. The proposed model generated higher simulated residue concentrations in the peel or pulp than the current model, owing to the proposed model’s assumption of rapid dissipation of the spray solution. This indicated that the proposed model specified the influence of the spray solution on the plant’s exposure to residues via the surface deposition pathway, whereas the current modelling approach presented a generic estimate of the residue dissipation on the plant surface that linked to the residue’s fate in the soil.