Unconditional Superconvergence Analysis of Energy Conserving Finite Element Methods for the Nonlinear Coupled Klein-Gordon Equations

In this paper,we consider the energy conserving numerical scheme for coupled nonlinear Klein-Gordon equations.We propose energy conserving finite element method and get the unconditional superconvergence resultO(h^(2)+Dt^(2))by using the error splitting technique and postprocessing interpolation.Numerical experiments are carried out to support our theoretical results.

ENERGY CONSERVATION FOR THE WEAK SOLUTIONS TO THE 3D COMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOW

In this paper,we establish some regularity conditions on the density and velocity fields to guarantee the energy conservation of the weak solutions for the three-dimensional compressible nematic liquid crystal flow in the periodic domain.

Exploration and Application Practice of Energy Conservation Theory and Method in Steel Manufacturing Process System

This article briefly discusses the theoretical basis and overall goals of energy conservation in the steel manufacturing process system.It is proposed that in the process of implementing system energy conservation,it is necessary to fully recognize and utilize the characteristics and functional advantages of the steel manufacturing process,pay more attention to energy quality,firmly grasp the overall goal of system optimization,focus on the integrated optimization of gas,steam,and waste heat systems,and propose the idea of constructing a"steel chemi-cal gas electricity heating cooling multi generation system".Based on practice,the main principles,models,and effects of implementing systematic energy conservation in steel enterprises have been proposed.

Energy Saving Analysis of Coal Gas Resource Utilization in Iron and Steel Enterprises

The article discusses the preparation of a gas balance sheet,as well as the recovery,storage,transporta-tion,and use of gas.An analysis was conducted on the occurrence and consumption quotas of various gas media,and specific energy-saving measures were elaborated for each process.This provides a theoretical reference for saving gas and reducing energy consumption in steel enterprises.

Optimal Superconvergence of Energy Conserving Local Discontinuous Galerkin Methods for Wave Equations

This paper is concerned with numerical solutions of the LDG method for 1D wave equations.Superconvergence and energy conserving properties have been studied.We first study the superconvergence phenomenon for linear problems when alternating fluxes are used.We prove that,under some proper initial discretization,the numerical trace of the LDG approximation at nodes,as well as the cell average,converge with an order 2k+1.In addition,we establish k+2-th order and k+1-th order superconvergence rates for the function value error and the derivative error at Radau points,respectively.As a byproduct,we prove that the LDG solution is superconvergent with an order k+2 towards the Radau projection of the exact solution.Numerical experiments demonstrate that in most cases,our error estimates are optimal,i.e.,the error bounds are sharp.In the second part,we propose a fully discrete numerical scheme that conserves the discrete energy.Due to the energy conserving property,after long time integration,our method still stays accurate when applied to nonlinear Klein-Gordon and Sine-Gordon equations.

A modified discrete element method for concave granular materials based on energy-conserving contact model

The development of a general discrete element method for irregularly shaped particles is the core issue of the simulation of the dynamic behavior of granular materials.The general energy-conserving contact theory is used to establish a universal discrete element method suitable for particle contact of arbitrary shape.In this study,three dimentional(3D)modeling and scanning techniques are used to obtain a triangular mesh representation of the true particles containing typical concave particles.The contact volumebased energy-conserving model is used to realize the contact detection between irregularly shaped particles,and the contact force model is refined and modified to describe the contact under real conditions.The inelastic collision processes between the particles and boundaries are simulated to verify the robustness of the modified contact force model and its applicability to the multi-point contact mode.In addition,the packing process and the flow process of a large number of irregular particles are simulated with the modified discrete element method(DEM)to illustrate the applicability of the method of complex problems.

THE ENERGY CONSERVATION OF VLASOV-POISSON SYSTEMS

We prove that energy conservation holds for weak solutions to classical VlasovPoisson systems with proper regularity.In particular,there exists a solution that conserves energy with|v|^(m)f0∈L^(1)_(x,v)for m>9/4.

THE ENERGY CONSERVATION OF THE LANDAU-LIFSHITZ-BLOCH EQUATION

In this paper,we consider the three-dimensional Landau-Lifshitz-Bloch equation in the whole space,which can describe the micromagnetic dynamic behavior of material at all temperatures,especially near the Curie temperature.We establish a sufficient condition of energy conservation for when weak solutions of the Landau-Lifshitz-Bloch equation with the temperature higher than the Curie temperature and its gradient belong to the Besov space L_(loc)^(3);B_(p,c0)^(α)(R^(3)))for some α∈(1/2,1)and p=9/(3α+1).Moreover,we also use the dimensional homogeneity to explain that the restrictions on the indicators are reasonable.

Adaptive energy-preserving algorithms for guiding center system

We develop two types of adaptive energy preserving algorithms based on the averaged vector field for the guiding center dynamics,which plays a key role in magnetized plasmas.The adaptive scheme is applied to the Gauss Legendre’s quadrature rules and time stepsize respectively to overcome the energy drift problem in traditional energy-preserving algorithms.These new adaptive algorithms are second order,and their algebraic order is carefully studied.Numerical results show that the global energy errors are bounded to the machine precision over long time using these adaptive algorithms without massive extra computation cost.

Optimizing Storage for Energy Conservation in Tracking Wireless Sensor Network Objects

The amount of needed control messages in wireless sensor networks(WSN)is affected by the storage strategy of detected events.Because broadcasting superfluous control messages consumes excess energy,the network lifespan can be extended if the quantity of control messages is decreased.In this study,an optimized storage technique having low control overhead for tracking the objects in WSN is introduced.The basic concept is to retain observed events in internal memory and preserve the relationship between sensed information and sensor nodes using a novel inexpensive data structure entitled Ordered Binary Linked List(OBLL).Whenever an object passes over the sensor area,the recognizing sensor can immediately produce an OBLL along the object’s route.To retrieve the entire information,the OBLL can be traversed with logarithmic complexity which is much less than the traversing complexity of existing linked list structures.Performance evaluation and simulations were carried out to ensure that the suggested technique minimizes the number of messages and thus saving energy and extending the network life.

An IoT-Based Energy Conservation Smart Classroom System

With the increase of energy consumption worldwide in several domains such as industry,education,and transportation,several technologies played an influential role in energy conservation such as the Internet of Things(IoT).In this article,we describe the design and implementation of an IoT-based energy conser-vation smart classroom system that contributes to energy conservation in the edu-cation domain.The proposed system not only allows the user to access and control IoT devices(e.g.,lights,projectors,and air conditions)in real-time,it also has the capability to aggregate the estimated energy consumption of an IoT device,the smart classroom,and the building based on the energy consumption and cost model that we propose.Moreover,the proposed model aggregates the estimated energy cost according to the Saudi Electricity Company(SEC)rates.Furthermore,the model aggregates in real-time the estimated energy conservation percentage and estimated money-saving percentage compared to data collected when the system wasn't used.The feasibility and benefits of our system have been validated on a real-world scenario which is a classroom in the college of computer science and engineering,Taibah University,Yanbu branch.The results of the experimental studies are promising in energy conservation and cost-saving when using our proposed system.

Application Research and Case Analysis of Green Technology in Building Engineering under the Direction of Energy Conservation Demands

With the rapid development of the economy,the scale of construction projects in China is gradually expanding.In terms of construction technology,continuous innovation is being made to meet the needs of sustainable development strategies,and green energy conservation technologies have emerged.It has a brand new design concept,and advocates for maximum energy conservation and environmental protection,fundamentally promoting the rational use of resources and space,and preventing the expansion of air and land pollution.First of all,a brief explanation is given on the current development status of green energy conservation technology in this paper.Secondly,through the introduction and analysis of energy conservation technologies and related building cases,the in-depth research on energy conservation measures of buildings is conducted.Finally,the prospects of green energy conservation technologies are proposed based on the current development status in China.This paper has certain reference value for its related engineering and theoretical research.

Assessment of the Implementation of Energy Conservation Opportunities Arising from Energy Audits;A Study of Four-Star and Five-Star Hotels in Nairobi Kenya

This study assesses the implementation of energy conservation opportunities in four-star and five-star hotels in Nairobi. The Covid-19 pandemic had a significant impact on the Hospitality Industry. Currently, there is a growing inclination to furnish guests with superior and sustainable services in an energy-efficient and eco-friendly way. Comprehensive research was conducted from energy audits gathered from the establishments and contracted auditing companies, on top of this, hotel staff were given digital questionnaires. To add to the data, the researcher surveyed the hotels with engineering managers. The Energy Audits found that all 10 hotels had adopted Energy Conservation Opportunities (ECOs). After further analysis, the mean adoption rate of Energy Conservation Opportunities (ECOs) during the past three years was 55.83%, which was below the aim of 100%. According to studies, hotel staff manages energy to cut costs. The researcher found that hotels use up a lot of energy. However, they have conservation potential, depending on government policies, costs, ease of implementation, and management commitment to sustainable practices. Essentially, Energy Conservation Opportunities (ECOs) reduce energy expenditures and boost reliable revenues, especially during high energy prices and uncertainty.

Energy Consumption Analysis and Optimization of Electric Submersible Pump System

Electric submersible pumps account for a considerable proportion in the development of the Bohai Oilfield. Improving the system efficiency of the electric submersible pump wells, ensuring that the units operate in the high-efficiency zone, is essential. Analysis shows that the efficiency of the electric submersible pump system depends on the wear and tear of each component of the submersible pump equipment, the setting of operational parameters, and more importantly, the production status and daily management level of the oil well. Therefore, improving the structural performance of the submersible pump product, optimizing the parameters setting of the oil well, strengthening daily management, establishing a scientific management system, and improving the production management process and system can effectively improve the production efficiency and economic benefits of the oil well, and further achieve the goal of energy saving and emission reduction. In addition, it is necessary to actively promote the concept and technology of energy saving and emission reduction, encourage oilfield enterprises to explore effective measures to reduce the energy consumption of the electric submersible pump system by strengthening the scientific management system, and achieve a green, low-carbon, and high-quality development of oilfield production to achieve the unity of economic benefits, social benefits, and environmental benefits. This article applies the above measures in the P oilfield to achieve energy optimization of submersible electric pump systems, reducing the daily power consumption of single well submersible electric pump systems by 371 kWh per day, increasing the submersible electric pump's lifespan by 200 days, generating considerable project benefits.

A Local Macroscopic Conservative(LoMaC)Low Rank Tensor Method with the Discontinuous Galerkin Method for the Vlasov Dynamics

In this paper,we propose a novel Local Macroscopic Conservative(LoMaC)low rank tensor method with discontinuous Galerkin(DG)discretization for the physical and phase spaces for simulating the Vlasov-Poisson(VP)system.The LoMaC property refers to the exact local conservation of macroscopic mass,momentum,and energy at the discrete level.The recently developed LoMaC low rank tensor algorithm(arXiv:2207.00518)simultaneously evolves the macroscopic conservation laws of mass,momentum,and energy using the kinetic flux vector splitting;then the LoMaC property is realized by projecting the low rank kinetic solution onto a subspace that shares the same macroscopic observables.This paper is a generalization of our previous work,but with DG discretization to take advantage of its compactness and flexibility in handling boundary conditions and its superior accuracy in the long term.The algorithm is developed in a similar fashion as that for a finite difference scheme,by observing that the DG method can be viewed equivalently in a nodal fashion.With the nodal DG method,assuming a tensorized computational grid,one will be able to(i)derive differentiation matrices for different nodal points based on a DG upwind discretization of transport terms,and(ii)define a weighted inner product space based on the nodal DG grid points.The algorithm can be extended to the high dimensional problems by hierarchical Tucker(HT)decomposition of solution tensors and a corresponding conservative projection algorithm.In a similar spirit,the algorithm can be extended to DG methods on nodal points of an unstructured mesh,or to other types of discretization,e.g.,the spectral method in velocity direction.Extensive numerical results are performed to showcase the efficacy of the method.

Application of Key Technologies in Green School Buildings: Taking Sino-German Future City Primary School as an Example

Green building is a manifestation of the response to the national“dual carbon”strategy.With the large-scale promotion of green buildings,the country has successively issued multiple evaluation standards for green buildings.Schools are places for preaching,teaching,and solving doubts,and the campus environment plays an important role in improving students’learning efficiency and promoting their physical and mental health.This article is based on the“Green Building Evaluation Standards”GB/T 50378-2019,analyzing and exploring the integration and application of key technologies in green schools,providing reference for green building designers.

Analysis of Oxygen Consumption in Lead and Zinc Metallurgy

This article analyzes the role of oxygen in lead zinc metallurgy,including shortening the metallurgical process,promoting energy conservation and environmental protection,improving metallurgical strength,enhancing raw material adaptability,and enhancing comprehensive recovery efficiency.This article introduces different lead zinc metallurgical processes and their oxygen consumption characteristics,including oxygen enriched side blowing lead smelting,oxygen bottom blowing lead smelting,oxygen enriched top blowing lead smelting,flash smelting lead,oxygen pressure leaching zinc smelting,and atmospheric pressure oxygen leaching zinc smelting.It is pointed out that oxygen enhanced metallurgy is the direction for the transformation and upgrading of lead zinc metallurgy.

On the energy conservation and critical velocities for the propagation of a "steady-shock" wave in a bar made of cellular material

The propagation of shock waves in a cellular bar is systematically studied in the framework of continuum solids by adopting two idealized material models, viz. the dynamic rigid, perfectly plastic, locking （D-R-PP-L） model and the dynamic rigid, linear hardening plastic, locking （D-R-LHP-L） model, both considering the effects of strain-rate on the material properties. The shock wave speed relevant to these two models is derived. Consider the case of a bar made of one of such material with initial length L 0 and initial velocity v i impinging onto a rigid target. The variations of the stress, strain, particle velocity, specific internal energy across the shock wave and the cease distance of shock wave are all determined analytically. In particular the ＂energy conservation condition＂ and the ＂kinematic existence condition＂ as proposed by Tan et al. （2005） is re-examined, showing that the ＂energy conservation condition＂ and the consequent ＂critical velocity＂, i.e. the shock can only be generated and sustained in R-PP-L bars when the impact velocity is above this critical velocity, is incorrect. Instead, with elastic deformation, strain-hardening and strain-rate sensitivity of the cellular materials being considered, it is appropriate to redefine a first and a second critical impact velocity for the existence and propagation of shock waves in cellular solids. Starting from the basic relations for shock wave propagating in D-R-LHP-L cellular materials, a new method for inversely determining the dynamic stress-strain curve for cellular materials is proposed. By using e.g. a combination of Taylor bar and Hopkinson pressure bar impact experimental technique, the dynamic stress-strain curve of aluminum foam could bedetermined. Finally, it is demonstrated that this new formulation of shock theory in this one-dimensional stress state can be generalized to shocks in a one-dimensional strain state, i.e. for the case of plate impact on cellular materials, by simply making proper replacements of the elastic and plastic constants.

A Moored Underwater Energy Conservation System for Profiling Measurement

There is a need to obtain the hydrologic data including ocean current, wave, temperature and so on in the South China Sea. A new profiling instrument which does not suffer from the damage due to nature forces or incidents caused by passing ships, is under development to acquire data from this area. This device is based on a taut single point mid-water mooring system. It incorporates a small, instrumented vertically profiling float attached via an electromechanical cable to a winch integral with the main subsurface flotation. On a pre-set schedule, the instrument float with sensors is winched up to the surface if there is no ship passing by, which is defined by an on-board miniature sonar. And it can be. inunediately winched down to a certain depth if the sonar sensor finds something is coming. Since, because of logistics, the area can only be visited once for a long time and a minimum of 10 times per day profiles are desired, energy demands are severe. To respond to these concerns, the system has been designed to conserve a substantial portion of the potential energy lost during the ascent phase of each profile and subsequently use this energy to pull the instrument down. Compared with the previous single-point layered measuring mode, it is advanced and economical. At last the paper introduces the test in the South China Sea.

Generalised energy conservation law for chaotic phenomena

Chaotic phenomena are increasingly being observed in all fields of nature,where investigations reveal that a natural phe nomenon exhibits nonlinearities and attempts to reveal their deep underlying mechanisms.Chaos is normally understood as“a state of disorder”,for which there is as yet no universally accepted mathematical definition.A commonly used concept states that,for a dynamical system to be classified as chaotic,it must have the following properties:be sensitive to initial conditions,show topological transitivity,have densely periodical orbits etc.Revealing the rules that govern chaotic motion is thus an important unsolved task for exploring nature.W e present herein a generalised energy conservation law governing chaotic phenomena.Based on two scalar variables,viz.generalised potential and kinetic energies defined in the phase space describing nonlinear dynamical systems,we find that chaotic motion is periodic motion with infinite time period whose time-averaged generalised potential and kinetic energies are conserved over its time period.This implies that,as the averaging time is increased,the time-averaged generalised potential and kinetic energies tend to constants while the time-averaged energy flows,i.e.,their rates of change with time,tend to zero.Numerical simulations on reported chaotic motions,such as the forced van der Pol system,forced Duffing system,forced smooth and discontinuous oscillator,Lorenz’s system,and Rossler's system,show the above conclusions to be correct according to the results presented herein.This discovery may indicate that chaotic phenomena in nature could be controlled because,even though their instantaneous states are disordered,their long-time averages can be predicted.