Energy Conservation Law Research Articles

Unitarity violation in field theories of Lee–Wick’s complex ghost

Abstract Theories with fourth-order derivatives, including the Lee–Wick finite QED model and quadratic gravity, have a better UV behavior, but the presence of negative metric ghost modes endangers unitarity. Noticing that the ghost acquires a complex mass by radiative corrections, Lee and Wick, in particular, claimed that such complex ghosts would never be created by collisions of physical particles because of energy conservation, so that the physical S-matrix unitarity must hold. We investigate the unitarity problem faithfully, working in the operator formalism of quantum field theory. When complex ghosts participate, a complex delta function (a generalization of the Dirac delta function) appears at each interaction vertex, which enforces a specific conservation law of complex energy. Its particular property implies that the naive Feynman rule is wrong if the four-momenta are assigned to the internal lines after taking account of the conservation law in advance. We show that complex ghosts are actually created and unitarity is violated in such fourth-order derivative theories. We also find a definite energy threshold below which ghosts cannot be created: The theories are unitary and renormalizable below the threshold.

Mode-matching technique for analyzing scattering in elastic shell chambers: Applications in trifurcated waveguide systems

This study presents a comprehensive investigation into the behavior of elastic shell chambers used for noise control and vibration mitigation in engineering applications. The study focuses on the analysis of fluid–structure coupled waves in a cylindrical waveguide system with trifurcated structures and membrane discs. The mode-matching technique is employed to analyze the scattering characteristics of the elastic chamber shell. Numerical simulations and analytical techniques are used to explore the interplay between material properties, geometric configurations, and loading conditions. The Galerkin formulation is utilized to model the response of membrane bridging discs and elastic shell regions. Linear algebraic systems are solved numerically to obtain the scattering amplitudes, and the convergence of the obtained solution is assessed. The energy conservation law and transmission loss are analyzed to evaluate the accuracy and convergence behavior of the system. The numerical results provide insights into the scattering behavior of the structure, showing the influence of frequency, chamber radius, and edge conditions. The findings highlight the importance of parameter selection and boundary conditions in guiding structures and provide a basis for design optimization.

Flow and heat transfer analysis of laminar flow in hypersonic aircraft with variable specific heat capacity at small attack angles

Purpose As to different angles of attack and nonlinear problems caused by high temperatures in coexisting hypersonic aircraft, people mainly rely on fluid software for research but lack analysis of flow mechanisms. Owing to computational difficulties, few people use numerical algorithms to combine them for discussion. Hence, this study aims to make a deep inquiry into the laminar flow and heat transfer of compressible Newtonian fluid in hypersonic aircraft with small attack angles. Design/methodology/approach In this paper, on the basis of mass, momentum and energy conservation laws, the governing equations of the hypersonic boundary layer are established. Viscosity, specific heat capacity and thermal conductivity are considered nonlinear functions concerning temperature. In virtue of the MacCormack finite difference method, the stationary numerical solutions are solved directly, and the validity of the algorithm is verified. Findings The results demonstrate that at Mach number 5, compared to the 0° attack angle, the maximum temperature near-wall at the 3° attack angle increases by about 25%. An enjoyable phenomenon is discovered, where the position corresponding to the maximum wall shear force shifts back as the attack angle and Mach number increase. The relationship between the near-wall maximum temperature versus attack angle and Mach number is fitted through numerical calculation results. Originality/value Empirical formulas can be used to estimate heat transfer characteristics at small attack angles, which will guide the design of aircraft thermal protection systems.

MHD peristaltic flow of hybrid nanomaterial between compliant walls with slippage and radiation

In this paper, we have discussed the MHD peristaltic flow of Al2O3 − Cu/H2O hybrid nanomaterial in a channel whose walls are taken to be compliant in nature. We also examined the effects of joule heating, thermal slip boundary conditions, thermal radiation, hall current, porous medium, heat source/sink, and viscous dissipation. The flow rotates at a constant angular velocity. The main aim of this work is to study the effects of various physical parameters on the peristaltic flow of a hybrid nanofluid in a rotating channel with complaint walls and heat transfer. The model is presented by using the conservation laws of mass, momentum, and energy along with boundary conditions. Selected variables have been used to simplify the nonlinear equation and the hypotheses of large wavelengths and small Reynolds numbers. The simplified form of the system of equations is solved using Adam’s Bashforth method, which is a multistep predictor–corrector method. To explore the potential applications of hybrid nanofluids in biomedical engineering, nanotechnology, and industrial processes, the effects of emerging parameters on both axial and secondary velocities and the temperature profile are analyzed with the help of graphs. The flow and temperature profiles are influenced by the hall effect, magnetic field, thermal slip, thermal radiation, viscous dissipation, porous medium, and heat source/sink parameters. We find that both velocities increase with hall effect and first-order slippage but decrease with magnetic field parameter. The temperature of the nanoparticles increases with dissipation effects but decreases with thermal radiation.

Computational Fluid Mechanics with Phase Transitions by Particle Methods

A computational method of simulations for processes of heterogeneous hydrodynamics with take of phase transitions will be discussed. The method is based on relevant approximation of conservation laws for mass, momentum, and energy in integral and differential forms. The time and spatial approximation is natural and numerical simulations are realized as direct computer experiments. It is supposed that the fluids are compressible and non-viscous. Heterogeneities of the fluids are considered as small drops or particles of one fluid within other fluid. Total number of the drops may be large enough and the drops may have phase transitions. Therefore, simulations of the main fluid with small transited drops dynamics are considered. The particle dynamics will be modelled as in the particle-in-cell method, and in the main fluid as in the large particle method. This approach makes it possible to simulate phase transitions under certain assumptions about heterogeneous fluids. The calculation algorithm of this method is implemented as a computer simulation of the dynamics of a multiphase carrier fluid containing particles that can undergo, for example, graphite-diamond phase transitions. Such transitions are modelled on the basis of the theory of phase transformations and the laws of thermodynamics. In fact, the method is a combination of the Harlow's particle-in-cell method, Belotserkovskii's large particles method and Bakhvalov's homogenization method. A modification of this method has also been developed to take into account the effects of viscosity when simulating the dynamics of a multiphase fluid in porous media. A model of the motion of such a liquid in a porous medium is obtained by freezing the motion of particles of the corresponding size in the presented method. The method will certainly be promising for numerical simulations of absorption and diffusion processes in complex fluids with phase transitions.

Double reduction order method based conservative compact schemes for the Rosenau equation

In this paper, fourth-order compact difference schemes are derived, analyzed and tested at length for both one- and two-dimensional Rosenau equations under the spatial periodic boundary conditions on the basis of the double reduction order method and bilinear compact operator. We prove that these schemes satisfy mass and energy conservation law via the help of the energy method. In addition, the uniquely solvable, unconditional convergence and stability are all obtained with the convergence order four in space and order two in time under the L∞-norm. Several numerical examples are presented to support the theoretical results.

Field emission in vacuum resonant tunneling heterostructures with high current densities

We analyse the steady-state thermal regime of a one-dimensional triode resonant tunnelling structure. The high currents generated by resonant tunnelling produce a large amount of heat that could damage the structure. Establishing the conditions under which it can operate at optimum efficiency is therefore a problem of great relevance for applications. The tunnel current is found via eigenvalues of the Schrödinger equation in quantum wells. By calculating the current generated in the device and using the energy conservation law in the electrodes, the temperature reached is obtained for different types of electrodes and the importance of heat conduction and thermal radiation is analysed. In the cases discussed, conduction is dominant. When the electrode material is copper, the temperature reached is similar to that of the thermostat for a wide range of electrode lengths, whereas when the cathode material is diamond-graphite and the anode material is copper, the temperature increases significantly as a function of length. The results obtained allow the temperature to be controlled for optimum performance of the field-emitting triode structures.

Conservative Fourier spectral method for a class of modified Zakharov system with high-order space fractional quantum correction

In this paper, we consider the Fourier spectral method and numerical investigation for a class of modified Zakharov system with high-order space fractional quantum correction. First, the numerical scheme of the system is developed with periodic boundary condition based on the Crank–Nicolson/leap-frog methods in time and the Fourier spectral method in space. Moreover, it is shown that the scheme preserves simultaneously mass and energy conservation laws. Second, we analyze stability and convergence of the numerical scheme. Last, the numerical experiments are given, and the results show the correctness of theoretical results and the efficiency of the conservative scheme.

Analysis of the energy transfer process for multiple scattering problems involving lossy media

The energy transfer process for acoustic propagation and scattering in inhomogeneous, lossy media is rigorously investigated. Two problems are considered: an arbitrarily composed cluster of lossy scatterers, excited by a single point source and a layered, lossy medium excited by an internal point-source distribution. Energy conservation laws and optical theorems are established. The connection of active intensity with the scattering cross section and the relation between reactive intensity and Lagrangian density are determined. Furthermore, the influence of the losses of the involved media to the kinetic energy is unveiled. Reductions to lossless media and near-zero frequency values are derived.

Effect of Magnetic and Thermal Parameters on the Reflected Waves in Generalized Magneto Thermoelastic Materials

The present paper is concerned with the problem of reflection of homogeneous plane waves from the free surface of a generalized magneto thermoelastic half-space. The phase speeds of corresponding to longitudinal, transverse and thermal waves are obtained and are independent of angle of propagation. The amplitude and energy ratios corresponding to the reflected waves are obtained theoretically and numerically with the help of boundary conditions. The effects of magnetic and thermal parameters on the reflected waves are examined. The results hold the conservation law of energy.

Analysis of heat transfer in [formula omitted]-immiscible layers of a horizontal Jeffrey fluid film flow

This paper deals with theoretical analysis of heat transfer in n-immiscible layers of a horizontal Jeffrey fluid film, driven by a heated plate and surface tension gradient. The formulation of the horizontal n-immiscible layers is based on mass, momentum, and energy conservation laws. The resulting systems of coupled linear ordinary differential equations are solved to obtain exact solutions for velocity, temperature, volume flow rate, shear stress, and rate of heat transfer. The effects of flow control parameters of interest, such as the inverse capillary number C, thermal conductivity of fluid χ, and Brinkmann number Br, on the velocity and temperature of the 5-immiscible layers, are investigated through graphical analysis. It is observed that increasing C leads to an increase in the velocity of all 5-immiscible layers. The temperature of all 5-immiscible layers also rises with increasing values of C, χ, and Br. The analysis of these 5-immiscible layers provides significant knowledge and understanding that may be applied to systems with a higher or lower number of immiscible layers utilizing the expressions derived for n-immiscible layers of a fluid film. Moreover, a comparison between immiscible layers of Newtonian fluid and Jeffrey fluid films is made in terms of velocity and temperature.

Coercivity properties of the canonical energy in double null gauge on the 4-dimensional Schwarzschild exterior

In this paper, we study the canonical energy associated with solutions to the linearised vacuum Einstein equation on a stationary spacetime. The main result of this paper establishes, in the context of the 4-dimensional Schwarzschild exterior, a direct correspondence between the conservation law satisfied by the canonical energy and the conservation laws deduced by Holzegel for gravitational perturbations in double null gauge. Since the latter exhibit useful coercivity properties (leading to energy and pointwise boundedness statements) we obtain coercivity results for the canonical energy in the double null gauge as a corollary. More generally, the correspondence suggests a systematic way to uncover coercivity properties in the conservation laws for the canonical energy on Kerr.

Propagation and reflection of thermoelastic wave in a rotating nonlocal fractional order porous medium under Hall current influence

This investigation relates to the research on Hall current on propagation and reflection of elastic waves through non-local fractional-order thermoelastic rotating medium with voids. The system is split up into longitudinal and transverse components using the Helmholtz vector rule. It is observed that, through the frequency dispersion relation four coupled quasi-waves exist in the medium. The rotating solid modifies the nature of purely longitudinal and transverse waves toward the quasi-type waves. All the propagating waves are dispersive as they depend upon angular frequency. The quasi-longitudinal wave qP and quasi-transverse wave qSV faces cut-off frequencies. The nonlocal parameter affect all the waves except the quasi void wave. Analytically, the reflection coefficients of the wave are computed using suitable boundary conditions. MATLAB software is used to perform numerical computations for a chosen solid material. The amplitude ratios and the speed of propagation of the wave are plotted graphically for rotational frequency, nonlocal, fractional order, and Hall current parameter. The significant effect of the physical parameters on the computed results has been observed. The cut-off frequency of the waves is also presented graphically. The energy conservation law is proved in the form of energy ratios. The earlier findings in the literature are obtained as special case in the absence of rotation, Hall current parameter and porous voids.

Idea „ekonomii przyrody ożywionej” jako próba wyjaśnienia jej jedności, harmonii, ciągłości i stabilności

Attempts to explain the “phenomenon” of the stability and unity of nature were the subject of philosophical reflections and then of natural science research. The purpose of formulated concepts was to capture and describe the mechanisms of the perceived harmony of nature, for instance, in archaic myths personifying nature or in ancient Ionian philosophy. In modern times, these ideas were expressed in the form of a principle analogous to the contemporary “energy conservation law” and “the chain of being,” and finally they were covered in Linnaeus’s work under the common name “oeconomia naturae.” These ideas were reformulated by Darwin in his theory in which he concluded that this stability and harmony can be described using the term “economy of nature.” Such an approach to natural phenomena, allowing observation of new relationships between various elements of nature, made it possible to mathematize the sciences of animate nature. Changes in the perception of nature (philosophy of nature) had their consequences in the methodology of the natural sciences. Darwin’s theory reinterprets all earlier ideas, reducing their sense to the balance between costs and benefits, losses and profits. The contents of the article focus on discussing the concepts of Linnaeus and Darwin, treating previous ideas as introduction to the actual issues.

Investigation of dissipative heat transfer and peristaltic pumping on MHD Casson fluid flow in an inclined channel filled with porous medium

A theoretical investigation is performed for free convective peristaltic pumping of a Casson fluid through an inclined porous wavy channel. The flow is subjected to uniform magnetic field in the transverse direction. In addition, the energy equation contains porous and viscous dissipation effects. The governing flow problem is modeled for Casson fluid with the help of conservation laws of mass, momentum, and energy under the long wavelength assumption. Using a regular perturbation method, we obtained the analytical expressions for the axial velocity, temperature, pressure rise per one wavelength, and heat transfer rate. The consequences of various effects on the flow quantities are demonstrated in the form of graphical representations and discussed in detail. The findings reveal that the rise in the thermal Grashof number and permeability parameter leads to an increment in the velocity and thermal fields. The heat transfer rate strengthened when the Casson parameter and magnetic parameter were increased. The pressure rise exhibits an enhancing trend for the Brinkmann number and permeability parameter. Further, we observed a decreasing behavior on streamlines for increasing magnetic field strength. Moreover, the obtained findings are applicable to a variety of fields in the bioengineering and medical sciences, such as targeted drug delivery, heart-lung machines, MRI, cancer therapy, power conversion devices, and micromanufacturing processes.

An efficient phase-field model for fatigue fracture in viscoelastic solids using cyclic load decomposition and damage superposition

Accurate and efficient evaluations of fatigue fracture is of great importance for the design and evaluation of viscoelastic materials in critical applications subject to cyclic load. In this study, an efficiency-enhanced phase-field model for viscoelastic fatigue fracture is proposed, allowing for fast evaluations of high-cycle fatigue damage. Based on the Boltzmann superposition principle, the cyclic fatigue load is decomposed into a mean load and a zero-mean cyclic load. The response of the mean load is solved numerically, while the response of the zero-mean cyclic load is solved analytically. The phase-field driving force is obtained analytically by combining the responses of the two independent parts, and the phase-field evolution is calculated numerically. In addition, both the dissipated energy and the elastic energy are decomposed using the volumetric-deviatoric decomposition to avoid unrealistic damage under the compression portion of the cyclic load. The proposed efficiency-enhanced model satisfies the energy conservation law as it does not require the fracture toughness degradation or additional fatigue energy treatments. The computational efficiency of the overall fatigue fracture can be greatly improved by leveraging the analytical solution for the response associated with the cyclic load. Numerical investigations are performed, and comparisons with the conventional cycle-by-cycle computation method are made. The results show that the proposed method can reduce the exponential computational demand to a constant or a linear one while achieving an accuracy comparable to that of the conventional method. The effectiveness of the proposed method is further demonstrated using an actual rubber component with testing data.

Combined effects of Joule heating and binary chemical reaction of MHD Williamson nanofluid on Darcy–Forchheimer porous medium past unsteady stretching cylinder

In this study, the convective transport phenomena of Williamson nanofluid flow with variable thermal conductivity on Darcy–Forchheimer porous medium past unsteady stretching cylindrical sheet is presented. The conservation laws of mass, momentum, energy and concentration are used to formulate the governing boundary value problem of the flow regime. The flow is expressed with a couple of nonlinear partial differential equations. An appropriate similarity transformation and techniques are used to transform the couple of partial differential equations into a system of initial value problems. The system of initial value problems is then solved numerically using the Runge–Kutta fourth order with the shooting technique. The Python programming tool is used to carry out the computation. The influence of unsteady parameter, thermal and concentration Biot numbers, thermal conductivity parameter and other parameters on velocity, temperature and concentration profiles of the nanofluid are examined. The responses of the three transfer rates (i.e momentum, mass and heat) to many pertinent parameters are also investigated. Most flows in industries are in a controlled manner hence the cylindrical geometry is used to study the flow regime. The results of the study show that the convective mass transfer is initiated with a rise in thermal and concentration Biot numbers whereas the convective heat transfer is motivated and demotivated with a rise in thermal and concentration Biot numbers, respectively. Larger values of the unsteady parameter on the other hand creates substantial wall friction to the motion of the nanofluid. Further, the numerical method used is found in excellent agreement with some earlier works under common assumptions.

Muti-objective optimization on energy consumption, CO2 emission and production cost for iron and steel industry

Due to high material density, high energy consumption density and CO2 emission density, it is not only difficult but significant to clarify the relationship between energy consumption, the CO2 emission and the production cost in different conditions. However, the previous researches rarely refer how to balance the energy consumption, the CO2 emission and the production cost after the fluctuation of material, energy and carbon price as well as what will happen to them if production structure changes. Therefore, based on the conservation law of mass and energy, to study iron and steel manufacturing process (ISMP), this paper, taking carbon price into consideration, establishes a muti-optimization model of energy consumption, CO2 emission and cost. After optimization with different objectives, the production cost per tonne of crude steel is reduced by 192.03 CNY (7.71%), the CO2 emission per tonne of crude steel is reduced by 224.22 kg (13.37%), and the energy consumption per tonne of steel is reduced by 51.20 kgce (9.10%). Moreover, based on the optimization results under different objectives, it is ironmaking process (coal ratio and ore ratio) and steelmaking process (amount of scrap steel) that has more impact on three above as well as ore blending and coal blending have a great influence on production cost but little effect on energy consumption and CO2 emission.

Numerical Computation of Natural Convection of Nanofluid in an Open Wavy Porous Cavity Heated Partially

In this work, we emphasise the heat transfer and fluid flow due to buoyancy force in a wavy open porous cavity, placed horizontally having filled with porous media and, its top wall is being kept open, whereas the right cold wall is wavy and, its left vertical wall is heated partially, keeping all other walls at thermally insulated. The non-dimensional ψ − θ formulation of mass, momentum, and energy conservation laws for porous media are solved by the standard finite difference scheme for a wide range of pertinent parameters such as nanoparticle volume fraction (0.05 ≤ Φ ≤ 0.2), Rayleigh-Darcy number (10 ≤ Ra ≤ 103), length of heat source (0.25 ≤ ε ≤ 1), and parameters controlling waviness of right wall (1 ≤ N ≤ 5) and amplitude (0.05 ≤ a ≤ 0.25). The simulated results are presented in the form of streamlines and isotherms; global and local Nusselt numbers are computed. Obtained results are analyzed and it is observed that the convection process is augmented at the presence of nanoparticle for low Ra but decreases at high Ra for all pertinent parameters; also, the wall waviness augments convection low Ra.

On stability and error bounds of an explicit in time higher-order vector compact scheme for the multidimensional wave and acoustic wave equations

We study a three-level explicit in time higher-order vector compact scheme, with additional n sought functions approximating second order non-mixed spatial derivatives of the solution, for an initial-boundary value problem for the n-dimensional wave equation and acoustic wave equation, with the variable speed of sound, n⩾1. We also approximate the solution at the first time level in a similar two-level manner, without using derivatives of the initial data as usual. For the first time, under the CFL-type conditions, new stability bounds in the standard and stronger mesh energy norms and the discrete energy conservation laws are presented, and the corresponding error bounds of the orders 4 and 3.5 are rigorously proved. Generalizations to the cases of the nonuniform meshes in space and time are described. Results of various numerical experiments are also included.