Energy Conservation Constraints Research Articles

Applying the starquake model to study the formation of elastic mountains on spinning neutron stars

Abstract When a neutron star is spun-up or spun-down, the changing strains in its solid elastic crust can give rise to sudden fractures known as starquakes. Early interest in starquakes focused on their possible connection to pulsar glitches. While modern glitch models rely on pinned superfluid vorticity rather than crustal fracture, starquakes may nevertheless play a role in the glitch mechanism. Recently, there has been interest in the issue of starquakes resulting in non-axisymmetric shape changes, potentially linking the quake phenomenon to the building of neutron star mountains, which would then produce continuous gravitational waves. Motivated by this issue, we present a simple model that extends the energy minimisation-based calculations, originally developed to model axisymmetric glitches, to also include non-axisymmetric shape changes. We show that the creation of a mountain in a quake necessarily requires a change in the axisymmetric shape too. We apply our model to the specific problem of the spin-up of an initially non-rotating star, and estimate the maximum mountain that can be built in such a process, subject only to the constraints of energy and angular momentum conservation.

Poles, shocks, and tygers: The time-reversible Burgers equation.

We construct a formally time-reversible, one-dimensional forced Burgers equationby imposing a global constraint of energy conservation, wherein the constant viscosity is modified to a fluctuating state-dependent dissipation coefficient. The system exhibits dynamical properties which bear strong similarities with those observed for the Burgers equationand can be understood using the dynamics of the poles, shocks, and truncation effects, such as tygers. A complex interplay of these give rise to interesting statistical regimes ranging from hydrodynamic behavior to a completely thermalized warm phase. The end of the hydrodynamic regime is associated with the appearance of a shock in the solution and a continuous transition leading to a truncation-dependent state. Beyond this, the truncation effects such as tygers and the appearance of secondary discontinuity at the resonance point in the solution strongly influence the statistical properties. These disappear at the second transition, at which the global quantities exhibit a jump and attain values that are consistent with the establishment of a quasiequilibrium state characterized by energy equipartition among the Fourier modes. Our comparative analysis shows that the macroscopic statistical properties of the formally time-reversible system and the Burgers equationare equivalent in all the regimes, irrespective of the truncation effects, and this equivalence is not just limited to the hydrodynamic regime, thereby further strengthening the Gallavotti's equivalence conjecture. The properties of the system are further examined by inspecting the complex space singularities in the velocity field of the Burgers equation. Furthermore, an effective theory is proposed to describe the discontinuous transition.

A Theory of Maximum Entropy Production and Its Application to Microwave Remote Sensing—Simultaneous Retrieval of Soil Moisture and Vegetation Water Content

AbstractA theory of maximum entropy production (MEP) for electromagnetic wave propagation in dielectric materials is proposed and applied to simultaneously retrieving soil moisture (SM) and vegetation water content (VWC) from L‐band microwave brightness temperature (TB). One representation of the MEP principle states that a non‐equilibrium system corresponds to such a configuration of energy fluxes that minimizes a dissipation function under the constraint of energy conservation. The dissipation function for radiative transfer is formulated as an analogy of that for heat transfer. A new physical parameter, radiative inertia as an analogy of thermal inertia, is introduced to characterize radiative attenuation in dielectric media. The radiative inertia is parameterized in terms of the penetration depth of electromagnetic waves as a function of the complex dielectric constant. The MEP based retrieval algorithm predicts SM and VWC by minimizing the dissipation function under the constraint of the conservation of radiative energy. The retrievals of SM and VWC based on the MEP theory were validated against field observations in tropical and temperate forested regions of the Amazon and North America. The proof‐of‐concept analysis demonstrates the capability of the MEP algorithm for simultaneous retrievals of SM and VWC even for dense canopy (e.g., VWC > 5 kg m−2). The MEP method is a new theoretical framework for developing innovative remote sensing algorithms of the Earth system not limited to microwave observations.

Tourism eco-efficiency and its influencing factors under the constraint of energy conservation and emissions reduction in China

Tourism eco-efficiency and its influencing factors under the constraint of energy conservation and emissions reduction in China

Mode-resolved phonon transmittance using lattice dynamics: Robust algorithm and statistical characteristics

Lattice dynamics (LD) enables the calculation of mode-resolved transmittance of phonons passing through an interface, which is essential for understanding and controlling the thermal boundary conductance (TBC). However, the original LD method may yield unphysical transmittance over 100% due to the absence of the constraint of energy conservation. Here, we present a robust LD algorithm that utilizes linear algebra transformations and projection gradient descent iterations to ensure energy conservation. Our approach demonstrates consistency with the original LD method on the atomically smooth Si/Ge interface and exhibits robustness on rough Si/Ge interfaces. The evanescent modes and localized effects at the interface are revealed. In addition, bottom-up analysis of the phonon transmittance shows that the anisotropy in the azimuth angle can be ignored, while the dependency on the frequency and polar angle can be decoupled. The decoupled expression reproduces the TBC precisely. This work provides comprehensive insights into the mode-resolved phonon transmittance across interfaces and paves the way for further research into the mechanism of TBC and its relation to atomic structures.

A physics investigation on impedance matching theory in microwave absorption film. II. Problem analyses

In Part I of this work published previously, it was proved from the transmission-line theory that impedance matching (IM) theory should be replaced by wave cancellation theory, film is different from the material, and the phase effects from interfaces should be considered in quarter wavelength theory. In this Part, it is shown that energy penetration for a film cannot be defined and IM is flawed because it cannot be proved theoretically or shown to be consistent with experimental data. The multi-absorption peaks in a film originate from wave cancellation under the constraint of energy conservation rather than from the resonances from the material.

An iterative mass-to-drag ratio estimation method for ballistic targets

Ballistic target tracking and identification is a key task for missile defense systems. A vital problem in target track and recognition is how to estimate the target mass-to-drag ratio fast and accurately. Based on the constraints of energy conservation, this paper proposes an iterative mass-to-drag ratio estimation method. This algorithm first estimates the position and velocity of the target using unscented Kalman filter, and then estimates the mass-to-drag ratio of the target by using energy conservation. By iterating, the final value is outputted. The simulation results show that this method can estimate the mass-to-drag ratio of the target at a high altitude, which provides a precise way for mass-to-drag ratio estimation.

Equivalence of nonequilibrium ensembles: Two-dimensional turbulence with a dual cascade.

We examine the conjecture of equivalence of nonequilibrium ensembles for turbulent flows in two dimensions in a dual-cascade setup. We construct a formally time-reversible Navier-Stokes equationin two dimensions by imposing global constraints of energy and enstrophy conservation. A comparative study of the statistical properties of its solutions with those obtained from the standard Navier-Stokes equationsclearly shows that a formally time-reversible system is able to reproduce the features of a two-dimensional turbulent flow. Statistical quantities based on one- and two-point measurements show an excellent agreement between the two systems for the inverse- and direct-cascade regions. Moreover, we find that the conjecture holds very well for two-dimensional turbulent flows with both conserved energy and enstrophy at finite Reynolds number.

Formulations of the elastodynamic equations in anisotropic and multiphasic porous media from the principle of energy conservation

Abstract Elastodynamic equations have been formulated with Newton's second law of motion, Lagrange's equation, or Hamilton's principle for over 150 years. In this work, contrary to classical continuum mechanics, a novel strategic methodology is proposed for formulating general mechanical equations using the principle of energy conservation. First, based on Hamilton's principle, Hamilton's equations, Lagrange's equation, and the elastodynamic equation of motion are derived in arbitrarily anisotropic and multiphasic porous elastic media, for the first time. Secondly, these equations are all formulated using the principle of energy conservation for the related media. Both formulation results using the two kinds of principles are compared and validated by each other. The advantages of our methodology lie in that the elastodynamic equation of motion, Lagrange's equation, and Hamilton's equations in continuum mechanics are directly formulated using a simple constraint of energy conservation without introducing variational concepts. It is easy to understand and has clear physical meanings. Our methodology unlocks the physics essences of Hamilton's principle in continuum mechanics, which is a consequence of the principle of energy conservation. Although the linear stress–strain constitutive relation is considered, our methodology can still be used in a nonlinear dynamical system. The methodology also paves an alternative way of treating other complex continuous dynamical systems in a broad sense. In addition, as an application, the continuity conditions at various medium interfaces are also revisited and extended using our proposed approach, which explains the law of reflections and refractions.

The coupled deep neural networks for coupling of the Stokes and Darcy–Forchheimer problems

We present an efficient deep learning method called coupled deep neural networks (CDNNs) for coupling of the Stokes and Darcy–Forchheimer problems. Our method compiles the interface conditions of the coupled problems into the networks properly and can be served as an efficient alternative to the complex coupled problems. To impose energy conservation constraints, the CDNNs utilize simple fully connected layers and a custom loss function to perform the model training process as well as the physical property of the exact solution. The approach can be beneficial for the following reasons: Firstly, we sample randomly and only input spatial coordinates without being restricted by the nature of samples. Secondly, our method is meshfree, which makes it more efficient than the traditional methods. Finally, the method is parallel and can solve multiple variables independently at the same time. We present the theoretical results to guarantee the convergence of the loss function and the convergence of the neural networks to the exact solution. Some numerical experiments are performed and discussed to demonstrate performance of the proposed method.

Thermal effects on collective modes in disordered s -wave superconductors

We investigate the effect of thermal fluctuations on the two-particle spectral function for a disordered $s$-wave superconductor in two dimensions, focusing on the evolution of the collective amplitude and phase modes. We find three main effects of thermal fluctuations: (1) the phase mode is softened with increasing temperature, reflecting the decrease of superfluid stiffness; (2) remarkably, the nondispersive collective amplitude modes at finite energy near $\mathbf{q}=[0,0]$ and $\mathbf{q}=[\ensuremath{\pi},\ensuremath{\pi}]$ survive even in the presence of thermal fluctuations in the disordered superconductor; and (3) the scattering of the thermally excited fermionic quasiparticles leads to low-energy incoherent spectral weight that forms a strongly momentum-dependent background halo around the phase and amplitude collective modes and broadens them. Due to momentum and energy conservation constraints, this halo has a boundary which disperses linearly at low momenta and shows a strong dip near the $[\ensuremath{\pi},\ensuremath{\pi}]$ point in the Brillouin zone.

The Energy Potential of Harvested Wood Fuel by Refugees in Northern Uganda.

For the last three decades, Uganda has lost considerable natural vegetation cover in the refugee settlements and buffer zones due to the high demand for wood fuel and timber. It is worthy to note that the supplies of wood fuel are more likely to dwindle in the near future. This study explored the determinants of harvested wood-fuel choices and their energy potential. It also examined the implemented energy conservation measures and constraints faced by the refugees both in Palorinya and Imvepi refugee settlements in Northern Uganda. The data were collected by conducting household interviews and collection of wood species samples for energy potential laboratory analysis. Findings indicate that the major sources of wood fuel were firewood, charcoal, briquettes, and biomass fuels. The major refugee choices that determined wood-fuel collection included the family size of the house hold, culture, method of cooking, type of food cooked, high poverty levels, and availability of family labour (P ≤ 0.05). The sampled wood tree species had the highest energy potential were Celtis durandii (5,837 kcal/kg), Parkinsonia aculeata (5,771 kcal/kg), Delonix regia (5,153 kcal/kg), and Bligihia unijugata (5,034 kcal/kg). Access to wood fuel by the households was mainly constrained by limited household income levels, long distances trekked, and inadequate awareness about wood fuel sources and availability. To conserve wood fuel, the refugees deploy several measures including the use of mobile solar gadgets for cooking and lighting, taking up agroforestry, use of briquettes, adoption of energy-saving cooking stoves, and establishment of new woodlots. Therefore, to reverse this trend, the Ugandan government and development partners should prioritise energy investments by supporting cheaper energy alternatives such as mobile solar gadgets and energy-saving cooking technologies, and establishment of woodlots.

An Energy Conservative hp-method for Liouville\u2019s Equation of Geometrical Optics

Liouville’s equation on phase space in geometrical optics describes the evolution of an energy distribution through an optical system, which is discontinuous across optical interfaces. The discontinuous Galerkin spectral element method is conservative and can achieve higher order of convergence locally, making it a suitable method for this equation. When dealing with optical interfaces in phase space, non-local boundary conditions arise. Besides being a difficulty in itself, these non-local boundary conditions must also satisfy energy conservation constraints. To this end, we introduce an energy conservative treatment of optical interfaces. Numerical experiments are performed to prove that the method obeys energy conservation. Furthermore, the method is compared to the industry standard ray tracing. The numerical experiments show that the discontinuous Galerkin spectral element method outperforms ray tracing by reducing the computation time by up to three orders of magnitude for an error of 10^{-6}.

Model Kinetic Equations for Multiply Ionized Gas Mixtures

Model kinetic equations are proposed for the description of ionized monoatomic gas mixture flows. The mixtures are assumed enough rarefied to be treated as ideal gases after multiple ionization steps. The model equations contain the equilibrium distribution functions for the components of the gas mixtures under consideration like it was done in BGK equations and their well-known generalizations. However, in this paper the new forms of the equilibrium distribution functions are used which correspond to the entropy maximum under the constraints of momentum, total energy, nuclei and electrons (both bound and free) conservation. It is shown that the derived model equations allow us to study the local equilibrium flows of the ionized gases and the transport processes of energy, nuclei and electrons in the non-equilibrium conditions.

Distributed Finite-Time Bipartite Consensus for Multiagent System with Event-Triggered Control

This paper investigates the distributed finite-time event-triggered bipartite consensus control for multiagent systems over antagonistic networks. Under the constraint of energy conservation, a distributed nonlinear finite-time control protocol only depending upon local information is proposed coupled with event-triggered strategies, where controllers of agents at triggered instants are only updated to reduce the computation. It is proved that when the antagonistic network is structurally balanced with a spanning tree, a necessary and sufficient condition is established to guarantee all agents to reach consensus values with identical magnitude but opposite signs. More interestingly, the settling time depending on the initial state is obtained over the whole process. Comparing to asymptotic control algorithms, the proposed control method has better disturbance rejection properties and convergence rate. Simulations are given to demonstrate the effectiveness of the theoretical results.

Energy consumption, environmental pollution, and technological innovation efficiency: taking industrial enterprises in China as empirical analysis object.

Facing increasingly serious environmental problems, technological innovation has become the key for industrial enterprises to coordinate energy conservation and emission reduction constraints and achieve steady growth of the industrial economy. Considering the impact of energy consumption and environmental pollution on the technological innovation efficiency of industrial enterprises, this paper incorporates industrial energy consumption, pollution control, and wastewater and exhaust emissions into the technical inefficiency equation. Based on the panel data of industrial enterprises in 30 provinces and autonomous regions in China from 2009 to 2016, the stochastic frontier analysis (SFA) model is used to study the effect of energy consumption and environmental pollution on technological innovation efficiency of industrial enterprises. The research results show that reducing energy consumption and increasing pollution treatment investment both have a significant driving effect on the improvement of industrial enterprises' technological innovation efficiency. Industrial wastewater and exhaust emissions have the opposite effect; unreasonable input mode of pollution control and personnel allocation have hindered the improvement of industrial enterprises' technological innovation efficiency. The average annual trend of technological innovation efficiency in industrial enterprises shows a curve of first rising, then falling, and rising again. The average values of Chongqing, Zhejiang, and Hunan rank in the top three, and the average values of Qinghai, Heilongjiang, and Inner Mongolia rank the bottom three. The average values of other provinces are higher than 0.9, and the difference is small. A suitable incentive mechanism should be established for industrial enterprises to save energy and reduce emissions and strengthen pollution control, improve the training program for environmental protection technical personnel, and provide important support for improving the green competitiveness of industrial enterprises.

Implosion-explosion in supernovae

We sketch a scenario for the explosion of massive stars (supernovae) that differs from published scenarios of explosions as a two-step process, an initial gravitational core collapse followed by an expansion of matter after a bouncing on the core, which meet difficulties. Our simple model, based on fluid mechanics and stability properties of the equilibrium state, shows that one can have a simultaneous inward/outward motion in the early stage of the instability of the star. This shows up by slowly sweeping a saddle-center bifurcation found when considering equilibrium states associated with the constraint of energy conservation (microcanonical ensemble) instead of the constraint of a fixed temperature (canonical ensemble). After the weakly nonlinear Painlevé regime, we show that the strongly nonlinear regime displays a self-similar behavior of the core collapse. Finally, the expansion of the remnants is revisited as an isentropic process leading to shocks formation.

Energy-conservation constraints on cosmic string loop production and distribution functions

A network of cosmic strings would lead to gravitational waves which may be detected by pulsar timing or future interferometers. The details of the gravitational wave signal depend on the distribution of cosmic string loops, which are produced by intercommutations from the scaling network of long strings. We analyze the limits imposed by energy conservation, i.e., by the fact that the total amount of string flowing into loops cannot exceed the amount leaving the long strings. We show that some recent suggestions for the cosmic string loop production rate and distribution are ruled out by these limits. As a result, gravitational waves based on such suggestions, in particular "model 3" used in LIGO data analysis, are not to be expected.

Supernova implosion-explosion in the light of catastrophe theory

The present understanding of supernova explosion of massive stars as a two-step process, with an initial gravitational collapse toward the center of the star followed by an expansion of matter after a bouncing on the core, meets several difficulties. We show that it is not the only possible one: a simple model based on fluid mechanics, catastrophe theory, and stability properties of the equilibrium state shows that one can have also a simultaneous inward/outward motion in the early stage of the instability of the supernova described by a dynamical saddle-center bifurcation. The existence of this simultaneous inward/outward motion is sensitive to the model in such systems with long-range interactions. If a constant temperature is assumed (canonical ensemble), an overall inward motion occurs, but if one imposes with the same equation of state the constraint of energy conservation (microcanonical ensemble) there is an inward velocity field near the center of the star together with an outward velocity field in the rest of the star. We discuss the expansion stage of the remnants away from the collapsed core, and propose a new explanation for the formation of shock waves in the ejecta which differs from the usual Sedov-Taylor self-similar description.

Comparing the Performance of the Maximum Entropy Production Model With a Land Surface Scheme in Simulating Surface Energy Fluxes

AbstractHydrological projections under future climate change have been shown to be sensitive to the formulation of evapotranspiration. Many hydrological models still rely on empirical formulations of this flux, and hence do not take into account the surface energy budget. On the other hand, land surface schemes, which are used within the climate models to describe land hydrology and associated surface heat fluxes (SHF), rely on the energy conservation. Due to land surface schemes complexity, they are not suitable for integration in traditional hydrological models. A newly developed and relatively simple Maximum Entropy Production model, which operates under the constraint of energy conservation and allows for an appropriate partitioning of available energy into SHF, appears to be a good alternative for integration in hydrological models. However, the MEP's performances still need to be evaluated under various environmental conditions. This study aims to evaluate the SHF simulated by MEP using observations over a multiyear period from several carefully chosen snow‐free sites located in low‐latitude regions. Moreover, simulated fluxes were compared to those derived from the Canadian Land Surface Scheme (CLASS), which was run at the same sites. The analysis of simulated and observed fluxes associated with different water stress conditions suggests that the abilities of MEP and CLASS in estimating sensible and latent heat fluxes are comparable. It was also found that the MEP and CLASS fluxes are in a good agreement with observations. However, the simulated nocturnal fluxes show that both models are in less agreement with the observations.