Conservation Laws Research Articles

A criterion of dimensional design to improve flame spread resistance of magnesium alloy components

A criterion for predicting the flame spread time of stick-shaped Mg alloy samples was proposed based on the law of energy conservation. It is indicated that the flame spread time is mainly affected by the material and sample dimension. The initial temperature and ignition temperature of the control volume and the S/lc ratio (the cross-sectional area/cross-sectional circumference) of the sample are decisive for the flame spread time. The flame spread time is proportional to the ΔH (the energy required to heat a unit mass of sample from initial temperature to ignition temperature) and the S/lc ratio, which is confirmed in three Mg alloys of Mg–8.5Al–0.5Zn–0.2Mn, Mg–2.7Nd– 0.4Zn–0.6Zr and Mg–4.0Y–3.3Nd–0.5Zr. For samples with the same dimension, the Mg–8.5Al–0.5Zn–0.2Mn alloy sample possesses the largest ΔH and the longest flame spread time. For samples with constant length and cross-sectional area, the sample with circular cross-section has the largest S/lc ratio and the best flame spread resistance in the same alloy.

Supernatural Belief in ‘Scientific’ Worldviews?

Abstract A ‘scientific worldview’ is commonly seen as contradictory to belief in supernatural forces, and there is little research on the supernatural beliefs of individuals who identify with science. In this article, we investigate the supernatural explanations of science-oriented individuals in domains of fundamental concern (suffering, death, and origins), and how supernatural causality is reconciled with belief in science. The open-ended responses of 387 Finns were analysed. The results show that science-oriented Finns endorsed both religion-related and more secular supernatural beliefs (such as belief in evolution as a purposeful process). Following the coexistence model, science-oriented Finns applied synthetic and target-dependent reasoning. In addition, many who invoked supernatural explanations integrated supernatural causality with science. Two forms of integrated reasoning were found: 1) supernatural agency as the ultimate cause and scientific theory as the proximate cause, and 2) a similarity-based heuristic, as seen in afterlife beliefs appealing to the law of conservation of energy.

Визуализация течений вязкой несжимаемой жидкости, соответствующих точным решениям уравнений Навье-Стокса

The work visualizes flows corresponding to the exact solutions of the system of hydrodynamic equations previously published by the authors, consisting of the vector Navier-Stokes equation and the law of conservation of mass for an incompressible fluid. This work uses the MathGL library for the C/C++ language and ParaView for scientific visualization of the results of numerical and analytical calculations. Without the use of such means, it would be impossible to see that the fluid flow is stratified into invariant subregions, and the trajectories of motion of fluid particles are wound on torus-shaped surfaces. Most of the scientific works on the study of hydrodynamic equations cover the results of calculations and do not address the questions of the existence of exact analytical solutions. At the same time, these calculations are performed with a specially selected set of fitting parameters unique to the equipment used and the computer software used. Questions about trust in the results of such calculations, their verification with exact solutions and the creation of a bank of test examples of applied problems in order to certify the applicability of the calculation results in practice become relevant.

Economic Development Drives Massive Global Estuarine Loss in the Anthropocene

AbstractEstuaries have great ecological and economic value and sustain both population and economic growth. Global‐scale analyses suggest that human activities drive estuarine area change but these projections neglect direct human‐estuary interactions and socio‐economic feedbacks. Here, we quantified area changes of 2,396 estuaries in response to recent human impacts (e.g., land reclamation, estuarine dam construction) and economic development between 1984 and 2019, and find that estuarine area shrank by 5,372 km2 whereas upland submergence created 5,015 km2 of estuarine area elsewhere. Approximately 44% (n = 1,046) of today's estuaries have been directly altered through land reclamation, estuarine dam construction, or a combination of both, and ∼250,000 acres (1,027 km2) of estuarine area have been directly converted to urban or agricultural fields. Nearly 90% (923 km2) of land reclamation occurred in Asia linked to recent advances in economic development during the middle‐income stage. Additional historical mapping and 5‐year interval analyses revealed that while human alterations were insignificant during the low‐income stages, estuaries were predominantly altered during their middle‐income stages, where estuarine degradation is a common consequence of economic growth. However, this trend stabilizes in high‐income countries with the adaption of conservation laws and policies. Together, our results indicate that large‐scale estuarine loss can be avoided by preserving estuaries in low‐ and mid‐income countries in the early stages of economic development.

An operator-splitting numerical scheme for relativistic magnetohydrodynamics

We describe a novel operator-splitting approach to numerical relativistic magnetohydrodynamics designed to expand its applicability to the domain of ultra-high magnetisation. In this approach, the electromagnetic field is split into the force-free component, governed by the equations of force-free degenerate electrodynamics (FFDE), and the perturbation component, governed by the perturbation equations derived from the full system of relativistic magnetohydrodynamics (RMHD). The combined system of the FFDE and perturbation equations is integrated simultaneously, for which various numerical techniques developed for hyperbolic conservation laws can be used. At the end of every time-step of numerical integration, the force-free and the perturbation components of the electromagnetic field are recombined and the result is regarded as the initial value of the force-free component for the next time-step, whereas the initial value of the perturbation component is set to zero. To explore the potential of this approach, we build a 3rd-order WENO code, which was used to carry out 1D and 2D test simulations. Their results show that this operator-splitting approach allows us to bypass the stiffness of RMHD in the ultra-high-magnetisation regime where the perturbation component becomes very small. At the same time, the code performs very well in problems with moderate and low magnetisation too.

An Entropy Stable Essentially Oscillation-Free Discontinuous Galerkin Method for Hyperbolic Conservation Laws

An Entropy Stable Essentially Oscillation-Free Discontinuous Galerkin Method for Hyperbolic Conservation Laws

Steady-state selection in multi-species driven diffusive systems

We introduce a general method to determine the large-scale non-equilibrium steady-state properties of one-dimensional multi-species driven diffusive systems with open boundaries, generalizing thus the max-min current principle known for systems with a single type of particles. This method is based on the solution of the Riemann problem of the associated system of conservation laws. We demonstrate that the effective density of a reservoir depends not only on the corresponding boundary hopping rates but also on the dynamics of the entire system, emphasizing the interplay between bulk and reservoirs. We highlight the role of Riemann variables in establishing the phase diagram of such systems. We apply our method to three models of multi-species interacting particle systems and compare the theoretical predictions with numerical simulations.

Improved hybrid approach of monotonic upstream-centered scheme for conservation laws and discontinuity sharpening technique for steady and unsteady flows

In finite-volume methods, monotonic upstream-centered schemes for conservation laws (MUSCL) offer second-order spatial accuracy but tend to produce highly dissipative solutions for density discontinuity and weak shock waves. To address this limitation within a second-order framework, a novel strategy for hybridizing MUSCL with the tangent of the hyperbola interface capturing technique for both steady and unsteady compressible flows is presented. This hybridization optimizes the process based on the degree of nonlinearity and discontinuity around the target cells, providing a novel method to sharply resolve weak shock waves and robustly compute strong shock waves within the hybrid scheme. The proposed scheme sharply captures exceedingly weak shock waves that conventional MUSCL fails to resolve accurately due to excessive numerical dissipation. Furthermore, for resolving small vortices induced by instability at slip lines, computational results demonstrate high-resolution surpassing fifth-order spatial accuracy schemes within this second-order spatial accuracy framework with less computational cost. Moreover, the scheme exhibits commendable convergence and robustness when applied to steady-state problems featuring strong shock waves. This scheme offers a more precise and high-resolution alternative to conventional MUSCL for compressible flow computations, as it requires no additional stencil for reconstruction, unlike conventional fifth-order schemes.

The Principle of Operation of an Engine That Draws Energy from the Electrogravitational Vacuum

Abstract: The principle of operation of a fuel-free electromagnetic engine is presented, in which the relativistic charged particles of the electrogravitational vacuum serve as a driving force. The crossed electric and magnetic fields in the engine’s working chamber lead to the Lorentz force, which results in asymmetric fluxes of charged vacuum particles in this chamber. The subsequent interaction of these particle fluxes with the charged matter of the chamber walls leads to the appearance of the resultant thrust force. The parameters of the charged particles of the electrogravitational vacuum can be determined using the theory of the infinite hierarchical nesting of matter and the theory of similarity. Taking this into account, the motion trajectories of the charged particles in the working chamber and the forces created by the particles are determined. When the engine is running, the laws of conservation of energy and momentum are fully satisfied; in particular, the engine increases its momentum due to the change in the total momentum of the fluxes of the vacuum’s charged particles. Keywords: Fuel-free engine, Force field, Electromagnetic interaction, Electrogravitational vacuum.

An emission model for inhalable chemicals from children's play mats based on partition coefficients

Inhalable chemicals found in children's play mats can be slowly released into indoor environments and consequently threaten human health. In this study, the partition coefficients of seven inhalable chemicals between play mats and air were calculated by headspace gas chromatography-mass spectrometry based on the law of conservation of mass and the principle of equilibrium of headspace bottles. Furthermore, an emission source model for the residual ratio of the inhalable chemicals in play mats was established. Most substances found in play mats have large partition coefficients owing to the complex void structure of the mats, which adsorbs a large number of organic pollutants. The partition coefficient is not only related to the boiling point and environmental temperature, but also the specific material and the adsorption of the organic pollutant onto the material. The emission source model for children's play mats developed in this study can characterize the decay of the inhalable chemicals over time. The data showed that after eight days of placing the play mat in a ventilated environment, the residual ratio of seven inhalable chemicals did not exceed 15 %.

Symmetry-based study and dynamics of casual bulk viscous matter-dominated universe

The dynamics of cosmological expansion is studied for a spatially flat matter-dominated universe filled with barotropic casual bulk viscous fluid. The evolution equation for the Hubble parameter is derived using Friedmann equations and conservation law for the viscous fluid, in which the viscous pressure is modeled by truncated version of the full Israel-Stewart theory of bulk viscosity. We use a Lie symmetry-based approach to study the evolution of the expansion rate of the Universe. The model equation possesses eight-parameter Lie symmetry generators and gives two different analytic group invariant solutions for the Hubble parameter. Expressions for various important cosmological parameters are obtained and values are estimated analytically for the explanation of the evolution dynamics of the Universe. The interesting features of the obtained symmetry-based solutions are that, one satisfies the present acceleration of the Universe, while the other could not support present accelerating phase, rather represents a universe dominated by non-viscous stiff fluid. We make useful checks on the observational constraints on the model parameters from the latest released observational data. The accelerating phase of the current universe is investigated using observational bounds and compared the model under investigation with the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM model. The evolutionary cosmic phases obtained from the analysis of the Lie symmetry-based solutions correspond to the association with the critical points in the equivalent phase space. These interesting features are investigated and analyzed using dynamical systems approach.

Description of community behavior regarding the trade mode of babirusa (Babyroussa babirussa Celebensis Deniger), a protected endemic animal circulating at the Langowan traditional market, Minahasa Regency, North Sulawesi of Indonesia

Introduction and aim: The babirusa (Babyrousa babyrussa Celebensis Deniger) is a genetic resource of immeasurable value, even though it has held protected status for nearly 60 years. Unfortunately, its status remains declared as endangered due to factors such as forest encroachment in the North Sulawesi region. This research aims to investigate the behaviours of community collectors, traders, and consumers concerning their level of interest in babirusa meat, which continues to circulate in the Langowan traditional market, Minahasa Regency. The findings of this study can provide valuable recommendations for the government to formulate new policies and regulations. Methods: The research employed a survey method, focusing on the community of collectors, traders, and buyers of babirusa meat in the Langowan traditional market, Minahasa Regency, and its surroundings. Results: The results from the field survey were then juxtaposed with the outcomes of sensory test analyses conducted by several panellists at the Animal Products Technology Laboratory. Until now, babirusa meat remains a sought-after commodity for Minahasa residents in the Langowan area and its surroundings. This indicates that despite the existence of government regulations in the form of Conservation Law No. 5 of 1990, there is still evidence of the covert sale of protected babirusa meat in the Langowan traditional market, Minahasa Regency, North Sulawesi province of Indonesia. In conclusion: The local individuals in the Langowan traditional market of Minahasa Regency who purchase and consume babirusa meat are predominantly under 50 years old, with a higher representation of males with the majority holds of elementary school education, and their primary occupation of farmers. Public awareness of the endemic babirusa is remarkably high. The sensory test results indicated that babirusa meat is perceived as highly attractive in terms of colour, possesses a distinctive meaty aroma, rough texture, excellent taste, and high tenderness. This positive perception is linked to the understanding that babirusa meat has its own benefits, leading to a genuine liking for this unique meat. Implications: There exists a notable public awareness of babirusa as an endemic animal. The overall acceptability of babirusa meat was noteworthy, reinforcing its significance as an endemic animal in North Sulawesi. Specifically, the Langowan traditional market has been a focal point for the buying and selling of babirusa meat. This practice, which was more prevalent before 1990, continues to be carefully executed in the Langowan market being protected for the next sustainability of this endemic animals.

Conservation laws, exact solutions and stability analysis for time-fractional extended quantum Zakharov–Kuznetsov equation

Conservation laws, exact solutions and stability analysis for time-fractional extended quantum Zakharov–Kuznetsov equation

Analysis of Magnetohydrodynamic Free Convection in Micropolar Fluids over a Permeable Shrinking Sheet with Slip Boundary Conditions

The convective micropolar fluid flow over a permeable shrinking sheet in the presence of a heat source and thermal radiation with the magnetic field directed towards the sheet has been studied in this paper. The mathematical formulation considers the partial slip condition at the sheet, allowing a realistic representation of the fluid flow near the boundary. The governing equations for the flow, heat, and mass transfer are formulated using the conservation laws of mass, momentum, angular momentum, energy, and concentration. The resulting nonlinear partial differential equations are transformed into a system of ordinary differential equations using suitable similarity transformations. The numerical solutions are obtained using robust computational techniques to examine the influence of various parameters on the velocity, temperature, and concentration profiles. The impact of slip effects, micropolar fluid characteristics, and permeability parameters on the flow features and heat transfer rates are thoroughly analyzed. The findings of this investigation offer valuable insights into the behavior of micropolar fluids in free convection flows over permeable shrinking sheets with slip, providing a foundation for potential applications in various industrial and engineering processes. Key findings include the observation that the velocity profile overshoots for assisting flow with decreasing viscous force and rising magnetic effects as opposed to opposing flow. The thermal boundary layer thickness decreases due to buoyant force but shows increasing behavior with heat source parameters. The present result agrees with the earlier findings for specific parameter values in particular cases.

On the singular limit problem in nonlocal balance laws: Applications to nonlocal lane-changing traffic flow models

We present a convergence result from nonlocal to local behavior for a system of nonlocal balance laws. The velocity field of the underlying conservation laws is diagonal. In contrast, the coupling to the remaining balance laws involves a nonlinear right-hand side that depends on the solution, nonlocal term, and other factors. The nonlocal operator integrates the density around a specific spatial point, which introduces nonlocality into the problem. Inspired by multi-lane traffic flow modeling and lane-changing, the nonlocal kernel is discontinuous and only looks downstream. In this paper, we prove the convergence of the system to the local entropy solutions when the nonlocal operator (chosen to be of an exponential type for simplicity) converges to a Dirac distribution. Numerical illustrations that support the main results are also presented.

Universality in coupled stochastic Burgers systems with degenerate flux Jacobian

In our contribution we study stochastic models in one space dimension with two conservation laws. One model is the coupled continuum stochastic Burgers equation, for which each current is a sum of quadratic nonlinearities, linear diffusion, and spacetime white noise. The second model is a two-lane stochastic lattice gas. As distinct from previous studies, the two conserved densities are tuned such that the flux Jacobian, a 2×2 matrix, has coinciding eigenvalues. In the steady state, spacetime correlations of the conserved fields and the time-integrated currents at the origin are investigated. For a particular choice of couplings, the dynamical exponent 3/2 is confirmed. Furthermore, at these couplings, the continuum stochastic Burgers equation and lattice gas are demonstrated to be in the same universality class.

The formation of invariant optical soliton structures to electric-signal in the telegraph lines on basis of the tunnel diode and chaos visualization, conserved quantities: Lie point symmetry approach

This study critically examines the nonlinear Lonngren wave model, a mathematical representation used to describe waves in shallow water environments such as beaches, lakes, and rivers, as well as electrical signals in semiconductor materials like tunnel diodes. The symmetry generators take into account the Lie invariance criteria. A three-dimensional Lie algebra can be obtained by using the suggested methodology. It links translation symmetries in space and time, respectively, with conservation of mass and energy. The third symmetry pertains to scaling or dilation. Recognizing the constraints of the inverse scattering transform in addressing the Cauchy problem for this equation, the investigation adopts new auxiliary equation approach to ordinary differential equations. This approach yields closed-form analytical solutions for the wave model. The obtained solutions include a plane solution, mixed hyperbolic solution, periodic and mixed periodic solutions, mixed trigonometric solution, smooth soliton, trigonometric solution, mixed singular solution, complex solitary and singular solution. Furthermore, the study develops the Hamiltonian function of the dynamical system to discuss the total energy of the system in terms of its position and momentum. Chaos analysis is performed to describe periodic, quasi-periodic, and chaotic behaviours, and a sensitivity analysis highlights the model’s sensitivity to different wave numbers. Graphical representations of selected solutions are presented in both 3-D and 2-D, illustrating the behaviour under specific physical conditions. The study concludes by identifying a comprehensive set of local conservation laws for the nonlinear Lonngren wave equation, applicable to arbitrary constant coefficients, using conservation laws multipliers.

Scaling and Localization in Multipole-Conserving Diffusion.

We study diffusion in systems of classical particles whose dynamics conserves the total center of mass. This conservation law leads to several interesting consequences. In finite systems, it allows for equilibrium distributions that are exponentially localized near system boundaries. It also yields an unusual approach to equilibrium, which in d dimensions exhibits scaling with dynamical exponent z=4+d. Similar phenomena occur for dynamics that conserves higher moments of the density, which we systematically classify using a family of nonlinear diffusion equations. In the quantum setting, analogous fermionic systems are shown to form real-space Fermi surfaces, while bosonic versions display a real-space analog of Bose-Einstein condensation.

A new global smoothness indicator of fifth order weighted non-oscillatory scheme for hyperbolic conservation laws

A new global smoothness indicator of fifth order weighted non-oscillatory scheme for hyperbolic conservation laws

More on symmetry resolved operator entanglement

The ‘operator entanglement’ of a quantum operator O is a useful indicator of its complexity, and, in one-dimension, of its approximability by matrix product operators. Here we focus on spin chains with a global U(1) conservation law, and on operators O with a well-defined U(1) charge, for which it is possible to resolve the operator entanglement of O according to the U(1) symmetry. We employ the notion of symmetry resolved operator entanglement (SROE) introduced in Rath et al (2023 PRX Quantum 4 010318) and extend the results of the latter paper in several directions. Using a combination of conformal field theory and of exact analytical and numerical calculations in critical free fermionic chains, we study the SROE of the thermal density matrix ρβ=e−βH and of charged local operators evolving in Heisenberg picture O=eitHOe−itH . Our main results are: i) the SROE of ρβ obeys the operator area law; ii) for free fermions, local operators in Heisenberg picture can have a SROE that grows logarithmically in time or saturates to a constant value; iii) there is equipartition of the entanglement among all the charge sectors except for a pair of fermionic creation and annihilation operators.