Estimation Of Dissipation Research Articles

Optimal decay of the Boltzmann equation

The Boltzmann equation is a typical example of partially dissipative equations, where the linearized collision operator is positive definite with respect to the microscopic part and the dissipation of the hydrodynamic part is discovered from the coupling structure between the transport operator and the linearized collision operator. Guo and Wang (Comm. Partial Differential Equations, 37, 2012) developed a general energy method for proving the optimal time decay rates of the solution to such type of equations in the whole space; however, the decay rate of the highest order spatial derivatives of the solution is not optimal. In this paper, by incorporating the high‐low frequency decomposition in the energy estimates, both linearly and nonlinearly, we prove the optimal decay rates of any high order spatial derivatives of the low frequency part of the solution to the Boltzmann equation and the almost exponential decay rate of the high frequency part, which imply in particular the optimal decay rate of the highest order spatial derivatives of the solution. Moreover, the velocity‐weighted assumption of the initial data required in Guo and Wang (Comm. Partial Differential Equations, 37, 2012) is removed by capturing the time‐weighted dissipation estimates via the time‐weighted energy method. The method can be applied to the compressible Navier–Stokes equations and many partially dissipative equations in kinetic theory and fluid dynamics.

Design-Level Seismic Estimation of Self-Centering Energy Dissipation–Braced Frame Structures with Partial Recentering Capacity

Design-Level Seismic Estimation of Self-Centering Energy Dissipation–Braced Frame Structures with Partial Recentering Capacity

The logarithmic Sobolev inequality on the Heisenberg group and applications to the uncertainty inequality and heat equation

We consider the logarithmic Sobolev inequality on the Heisenberg group. One can derive the logarithmic Sobolev inequality from the Sobolev inequality, and we consider an application to the uncertainty inequality on the Heisenberg group. Moreover, one can also obtain a dissipative estimate of a solution of the heat equation on the Heisenberg group from the logarithmic Sobolev inequality.

Information-theoretical limit on the estimates of dissipation by molecular machines using single-molecule fluorescence resonance energy transfer experiments.

Single-molecule fluorescence resonance energy transfer (FRET) experiments are commonly used to study the dynamics of molecular machines. While in vivo molecular processes often break time-reversal symmetry, the temporal directionality of cyclically operating molecular machines is often not evident from single-molecule FRET trajectories, especially in the most common two-color FRET studies. Solving a more quantitative problem of estimating the energy dissipation/entropy production by a molecular machine from single-molecule data is even more challenging. Here, we present a critical assessment of several practical methods of doing so, including Markov-model-based methods and a model-free approach based on an information-theoretical measure of entropy production that quantifies how (statistically) dissimilar observed photon sequences are from their time reverses. The Markov model approach is computationally feasible and may outperform model free approaches, but its performance strongly depends on how well the assumed model approximates the true microscopic dynamics. Markov models are also not guaranteed to give a lower bound on dissipation. Meanwhile, model-free, information-theoretical methods systematically underestimate entropy production at low photoemission rates, and long memory effects in the photon sequences make these methods demanding computationally. There is no clear winner among the approaches studied here, and all methods deserve to belong to a comprehensive data analysis toolkit.

Large Scale Turbulent Round Free Jet Far Field Investigations Using Shake-The-Box 3D Lagrangian Particle Tracking

In this study, we utilize the Shake-The-Box (STB) Lagrangian Particle Tracking (LPT) algorithm to conduct large-scale measurements in the far field of a turbulent jet. We confirm self-similar mean velocity and Reynold stress profiles across two fields of view (FOVs) spanning 90 to 240 nozzle diameters in streamwise direction. Furthermore, the utilization of a novel version of the data assimilation scheme FlowFit enables the visualization of instantaneous realizations of coherent structures in terms of Q-values. The results indicate that the structures are predominantly tube rather than hairpin-like. The high number of tracked particles and the extensive measurement range allow for the estimation of mean dissipation as a function of the distance from the nozzle using structure functions. A comparison of results derived from longitudinal and transverse approaches with those obtained using the velocity-acceleration structure function indicates that the latter provides more accurate results due to its validity in anisotropic flows. However, the findings also indicate that the anisotropy diminishes downstream. The determination of mean dissipation and acceleration enables the investigation of the validity of the Heisenberg-Yaglom relation in this anisotropic flow. Nevertheless, acceleration is a highly intermittent value, which hinders capturing all relevant events to measure its variance accurately. This paper presents the difficulties encountered in the tracking and filtering of the trajectories, offering a perspective on potential future solutions to the problem.

Design of QCA based memory cell using a novel majority voter with physical validation

Quantum Dot Cellular Automata (QCA) is a unique transistor less paradigm which effectively uses change in cell polarization to perform logical operations with high speed, low power and high intricacy. In recent years, the need of high performance memory cell is increased for improving the system performance. This paper presents the design of a QCA based memory cell with read write capabilities. In recent past, most of the QCA circuits are designed using the conventional three input majority voter. The conventional three input majority gate is not fault tolerant. Thus, we need an alternative design which can serve as the majority voter and also shows the fault tolerance. Moreover, the design of three input majority voter is not much addressed . In this paper, an alternative, simple structure of three input majority voter is presented which is better than the conventional one in terms of fault tolerance. In addition to this, the proposed three input majority voter is power aware and efficient to realize various digital circuits. The correctness of the proposed majority voter is validated through the physical proof. Moreover, the proposed gate is subjected to cell displacement defect to investigate the testability. The proposed gate is further used to implement rudimentary elements such as XOR gate, multiplexer and D latch. Finally, the design of Random Access Memory (RAM) cell with read, write, set and reset capabilities is proposed using the presented majority voter. The proposed circuits are further subjected to comprehensive analyses for estimation of cost functions and energy dissipation. The investigation of presented circuits manifests the use of proposed majority voter for next generation computing circuits.

Bounds on the rates of statistical divergences and mutual information via stochastic thermodynamics.

Statistical divergences are important tools in data analysis, information theory, and statistical physics, and there exist well-known inequalities on their bounds. However, in many circumstances involving temporal evolution, one needs limitations on the rates of such quantities instead. Here, several general upper bounds on the rates of some f-divergences are derived, valid for any type of stochastic dynamics (both Markovian and non-Markovian), in terms of information-like and/or thermodynamic observables. As special cases, the analytical bounds on the rate of mutual information are obtained. The major role in all those limitations is played by temporal Fisher information, characterizing the speed of global system dynamics, and some of them contain entropy production, suggesting a link with stochastic thermodynamics. Indeed, the derived inequalities can be used for estimation of minimal dissipation and global speed in thermodynamic stochastic systems. Specific applications of these inequalities in physics and neuroscience are given, which include the bounds on the rates of free energy and work in nonequilibrium systems, limits on the speed of information gain in learning synapses, as well as the bounds on the speed of predictive inference and learning rate. Overall, the derived bounds can be applied to any complex network of interacting elements, where predictability and thermodynamics of network dynamics are of prime concern.

A New Formulation For Vegetation Induced Damping Under Waves And Currents Based On Their Standing Biomass

Estimation of the flow energy dissipation induced by an ecosystem that accounts for its characteristics (i.e. biomechanical properties, morphology, density) and the incident hydrodynamic conditions is crucial if ecosystem-based coastal protection measurements want to be implemented. Characterization of a vegetated ecosystem by measuring leaf traits, biomechanical properties of plants and the number of individuals per unit area involves a lot of effort and is case-specific. Previous studies have shown that wave height attenuation positively correlates with standing biomass (Maza et al., 2022) highlighting the crucial role played by this variable that can be used to estimate the ecosystem wave damping capacity without using calibration coefficients. In addition, this variable has been already characterized for many ecosystems and it can be estimated by aerial images (Doughty and Cavanaugh, 2019) and remote sensing techniques. However, this new approach has not been extended to conditions where waves and currents are simultaneously present. These conditions are very relevant to habitats like saltmarshes that are commonly affected by tidal currents or wave-induced currents flowing simultaneously with wind or swell waves. Then, to further explore this new approach based on the ecosystem standing biomass, a new set of experiments using real vegetation with contrasting morphology and biomechanical properties, and subjected to different combinations of waves and currents, is proposed. The obtained standing biomass-attenuation relationships will help to quantify the expected coastal protection provided by different vegetated ecosystems based on their standing biomass under the combined effect of waves and currents.

Top-down characterization of resource use in LCA: from problem definition of resource use to operational characterization factors for resource inaccessibility of elements in a short-term time perspective

PurposeWhen resources are extracted and used by society, they are not necessarily lost for future generations. Therefore, recent publications on impact assessment of abiotic resource use in life cycle assessment focus on a decreased accessibility of resources due to dissipation, rather than depletion. In a previous study, dissipation was defined as a function of the global change in accessible stock due to human actions, and the global amount of the accessible stock, assuming a very long-term time perspective (more than 500 years). In this paper, a short-term time perspective (25 years) is adopted.MethodsThe same generic characterization model is used, but different choices are outlined to derive characterization factors for a short-term perspective (25 years). To illustrate how the short term might be approached, a preliminary set of characterization factors is developed, based on assumptions and estimates.ResultsThe problem of resource use is defined as follows: the decrease of accessibility on a global level of primary and/or secondary elements over the short term due to the net result of compromising actions (i.e., emissions, dissipation in the technosphere, occupation in use, and exploration for new stocks). Characterization factors are derived based on assumptions, like the following: the accessible stock is based on present estimates of accessible stocks in the environment and the technosphere; estimates of accessible stocks in the technosphere are based on past extractions and generic recycling rates; all flows that are presently not recycled are assumed to be inaccessible. Finally, weighting between elements and the functions they have for the present society is based on the added value of the economic sector that is affected due to the decreased accessibility.Discussion and conclusionA preliminary set of characterization factors is proposed for 55 elements. They assess the impact of the present use of resources on the decreased accessibility in the short term due to emissions and dissipation in the technosphere. However, calculation of impact category scores is still hampered by a lack of appropriate data for dissipative flows in life cycle inventory databases. The presented calculations are based on several simplifications and proxies. A more detailed distinction of dissipative flows and estimates of stocks in the technosphere may be possible based on (dynamic) SFA modelling of elements in different applications. To derive a more mature set of characterization factors, it is recommended to use the presented model as a basis and further elaborate or replace the proxies.

Sufficient Criteria for Stabilization Properties in Banach Spaces

We study abstract sufficient criteria for cost-uniform open-loop stabilizability of linear control systems in a Banach space with a bounded control operator, which build up and generalize a sufficient condition for null-controllability in Banach spaces given by an uncertainty principle and a dissipation estimate. For stabilizability these estimates are only needed for a single spectral parameter and, in particular, their constants do not depend on the growth rate w.r.t. this parameter. Our result unifies and generalizes earlier results obtained in the context of Hilbert spaces. As an application we consider fractional powers of elliptic differential operators with constant coefficients in Lp(Rd)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_p(\\mathbb {R}^d)$$\\end{document} for p∈[1,∞)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p\\in [1,\\infty )$$\\end{document} and thick control sets.

Bayesian estimation of dissipation and sound speed in tube measurements using a transfer-function model.

This study discusses acoustic dissipation, which contributes to inaccuracies in impedance tube measurements. To improve the accuracy of these measurements, this paper introduces a transfer function model that integrates diverse dissipation prediction models. Bayesian inference is used to estimate the important parameters included in these models, describing dissipation originating from various mechanisms, sound speed, and microphone positions. By using experimental measurements and considering a hypothetical air layer in front of a rigid termination as the material under test, Bayesian parameter estimation allows a substantial enhancement in characterization accuracy by incorporating the dissipation and sound speed estimates. This approach effectively minimizes residual absorption coefficients attributed to both boundary-layer effects and air medium relaxation. The incorporation of dissipation models leads to a substantial reduction (to 1%) in residual absorption coefficients. Moreover, the use of accurately estimated parameters further enhances the accuracy of actual tube measurements of materials using the two-microphone transfer function method.

Joint-mode diffusion analysis of discontinuous Galerkin methods: Towards superior dissipation estimates for nonlinear problems and implicit LES

We present a new linear eigensolution analysis technique that provides superior estimates of dissipation distribution in wavenumber space for the discontinuous Galerkin (DG) method. The technique builds upon traditional dispersion-diffusion analyses that have been applied to spectral/hp element methods, but in particular is an improvement upon the non-modal eigenanalysis approach proposed by Fernandez et al. in [1]. The present technique takes into account the indirect effects that dispersion may have on dissipation, as recently discussed by Moura et al. in [2], in order to better represent dissipation itself. Also, a concept often used with dynamic mode decomposition (DMD) techniques is invoked to weight the relative contribution of the multiple diffusion curves that stem from temporal eigenanalysis. This allows for obtaining a single dissipation profile in wavenumber space, so that the proposed technique is named joint-mode analysis. Although the non-modal approach also provides a single diffusion curve, the joint-mode dissipation curve is shown to correlate significantly better with the energy spectrum of Burgers' turbulence at large and intermediate scales, which is particularly relevant for implicit large-eddy simulation (LES). The proposed technique is readily extensible to other spectral/hp element methods.

Enhanced dissipation and transition threshold for the Poiseuille-Couette flow

In this paper, we consider the hydrodynamic stability of the 2D Navier-Stokes equations on T×R around Poiseuille-Couette flow V=(y2,0)+a(y,0) with a∈(0,1). By means of the hypocoercivity method with time dependent weights and introducing a new estimate on the energy functional, we establish the enhanced dissipation estimates for the linearized Navier-Stokes equations. More precisely, for a⩽10−3ν14, we obtain a decay rate proportional to ν12, which is consistent with the Poiseuille flow. For a=10−3νs with s∈[0,14], the decay rate is proportional to ν1−2s. As an application of the linear estimates, we obtain the result of nonlinear stability transition threshold.

Global non-relativistic quasi-neutral limit for a two-fluid Euler-Maxwell system

This paper concerns a two-fluid Euler-Maxwell system for plasmas with two small parameters. We study the non-relativistic quasi-neutral limit for smooth solutions of the system in whole space R3. When the initial data are smooth and sufficiently close to constant equilibrium states, we give a rigorous justification of the limit for all time. The limit system is governed by a compressible Euler system. The proof is based on uniform energy estimates and various dissipative estimates of smooth solutions with respect to the parameters and time. A key step in these estimates is to control the quasi-neutrality of the velocities by using a projection operator.

Entropy dissipation estimates for the Landau equation with Coulomb potentials

Entropy dissipation estimates for the Landau equation with Coulomb potentials

Global convergence of a two-fluid non-isentropic Euler–Poisson system in one space dimension

In this paper, we study the global in time quasi-neutral limit for a two-fluid non-isentropic Euler–Poisson system in one space dimension. We prove that the system converges to the non-isentropic Euler equations as the Debye length tends to zero. This problem is studied for smooth solutions near the constant equilibrium state. To prove this result, we establish uniform energy estimates and various dissipation estimates with respect to the Debye length and the time. These estimates allow to pass to the limit to obtain the limit system by compactness arguments. In addition, the global convergence rate is obtained by use of stream function technique.

Detection of materially coherent eddies from satellite altimetry in the Bay of Bengal

Mesoscale eddies are a well-recognized feature of the global oceans, being of dynamical relevance to various ocean processes and of significance to transport of various species. In the last few decades, advancements in satellite observations of the sea surface have revealed mesoscale and sub-mesoscale eddy features in many parts of the ocean. An objective definition and detection of eddies has, however, remained a challenge, thus resulting in unreliable estimates of eddy formation, evolution and dissipation. In this study, we present an implementation of a Lagrangian averaged vorticity deviation (LAVD) based method to detect and characterize eddies in the Bay of Bengal (BoB), a freshwater-dominated semi-enclosed basin in the northern Indian Ocean. Systematic sensitivity studies are performed to identify parameter values that result in robust eddy detection in the BoB, and finite-time coherence in material transport associated with the LAVD-based eddies is demonstrated. LAVD-based eddy detection is then used to statistically characterize the Sri Lanka dome (SLD) eddy, an annual mesoscale cyclonic eddy of dynamical and physical importance in the southern BoB. Analysing satellite-based ocean surface currents from 27 years (1993–2019) of data, the inter-annual variability in the SLD formation, its spatio-temporal evolution and dissipation are elucidated. On an average, SLD has a lifetime of 15 weeks and a maximum area of 5 square degrees, with the longest lifetime of 38 weeks in 1996 and a maximum area of 12 square degrees in 1998. Long-lived SLDs are shown to spatially excurse into the BoB, potentially influencing large-scale transport of physical and biogeochemical properties. A potential correlation between large SLD lifetime and large variations in the monthly evolution of Dipole Mode Index and NINO3.4 is highlighted. An SSH-based Eulerian eddy detection method is also implemented to understand its efficacy in identifying materially coherent eddies in the BoB region. The paper concludes with a summary of our results, and a brief discussion of potential applications of LAVD-based eddy detection in the northern Indian Ocean.

An attempt to predict the heat build-up of filled elastomers under multiaxial fatigue

Elastomeric materials are well-known for their ability to dissipate mechanical energy into heat. Under cyclic loading, this dissipated energy, combined with the low thermal conductivity of these materials causes heat storage in the sample resulting in a rise of the material temperature. As this phenomenon induces negative effects on fatigue life, this heat build-up has been widely studied in recent years but a few for multiaxial loadings. In this paper, we propose to investigate the self-heating induced by multiaxial mechanical loading of Natural Rubber (NR). The goal of this research work is to find a suitable modeling to predict the heat build-up of elastomers under multiaxial cyclic loadings. The proposed model, based upon a weak coupling approach and which only requires an estimation of the energy dissipation during a cycle of loading, is used to predict the heat build-up evolution of 3 different specimen geometries under multiaxial cyclic mechanical loading for 2 materials: a natural rubber (NR) experimentally investigated in this work allowing to develop the model and a styrene-butadiene rubber (SBR) which heat build-up data are taken from the literature for further model validation. A satisfactory agreement between simulations and experiments is found, making this approach a useful tool for temperature evolution estimates during fatigue loading.

Global convergence in non-relativistic limits for Euler-Maxwell system near non-constant equilibrium

In this paper, we study the global-in-time convergence of non-relativistic limits from Euler-Maxwell systems to Euler-Poisson systems near non-constant equilibrium states by letting the reciprocal of the speed of light ν:=1/c→0. In previous studies, the dissipative estimates for the electric field E appear to be singular and the orders of singularities for divE and ∇×E are different, hence a div-curl decomposition should be considered in our case, and this makes it unclear the preservation of the anti-symmetric structure of the system and the global-in-time L2–estimate of the smooth solutions. To overcome these difficulties, we find a strictly convex entropy of the system that is valid for the case of non-constant equilibrium to obtain the global L2–estimate and use some induction arguments to close the estimates. It is worth mentioning that in our proof, very careful and accurate estimates of solutions are needed and we show that the electric field E is actually non-singular, which is vital and necessary for our proof.

Polyurethane shape memory polymer: structure characterization and estimation of energy storage and dissipation during the tension process

Polyurethane shape memory polymer: structure characterization and estimation of energy storage and dissipation during the tension process