Conditions For Extremum Research Articles

FORMING CAPABILITIES OF A PULSE MAGNETIC FIELD GENERATOR

Purpose. Determination of areas ratio of the parameters of the discharge circuit elements of the generator, which ensure the formation of magnetic field pulses of different shapes. Methodology. Numerical simulation using dimensionless variables that determine the nature of the transition process in the discharge circuit of the generator, and use the procedure for determining the pulse points of meeting the conditions of extremum and the transition through zero. Results. Obtained a description of the formation of the three specific areas of waveforms: oscillatory weakly damped oscillatory strongly damped and unipolar pulse with a monotonic rise and fall values. A relation to the choice of parameters of elements of the discharge circuit of the generator, which formed unipolar pulses with a monotonic rise and fall values. Originality. A completed and extended database that implements the mapping of the formal description of the pulse shape with a description of areas ratio parameters for high-voltage pulse discharge circuit test units, with respect to the pulses of current flowing in the formation of the magnetic field. Practical value. The relations obtained allow to select the parameters of the discharge circuit elements of the generator designed to generate test pulses of magnetic field.

A property diagram-based method for synthesis and parameter optimization of heat and mass transfer in moist air–water/aqueous solution systems

Coupled heat and mass transfer processes between moist air and water/aqueous solution commonly occur in absorption/desorption systems for air conditioning, thermal storage and energy conservation, which are always optimized from such two aspects as layout synthesis and parameter matching. This contribution introduces six sub-zones in the integrated property diagram of moist air and aqueous solution according to the differences of temperatures, absolute humidities and relative humidities between moist air and water/aqueous solution, and describes different heat and mass transfer characteristics between them in each sub-zone, which favor the construction of different optimal layouts and their corresponding systems to make full use of heat and mass transfer potentials. Based on the optimal layouts, a quantitative method for the system parameter matching is further proposed based on the conditional extremum method in mathematics. The optimized results of a typical liquid regeneration system show that utilization of the proposed optimization method gives the optimal allocation of mass flow rates of all working fluids to minimize the total mass flow rate with a constant required mass transfer quantity and increasing the inlet temperatures of moist air, liquid desiccant and regeneration medium reduce the total mass flow rate of all working fluids.

Boundary Element Approach in Impedance Cloaking Problem

The cloaking problem is considered for a 2-D wave scattering model in an unbounded homogenous medium containing an impenetrable covered (cloaked) boundary. The control is a surface impedance which enters the boundary condition as a coefficient. The problem is reduced to the inverse extremal problem of choosing the surface impedance. The solvability of the original scattering problem for 2-D Helmholtz equation and of the extremal problem is proved. Optimality system describing the necessary extremum conditions is derived. The algorithm for numerical solving of the control problem based on the optimality system and boundary element method is designed.

Optimization Method in 2-D Problems of Material Body Cloaking

We consider the control problem for two-dimensional model of the electromagnetic field which describes the scattering E-polarized electromagnetic waves in an infinite homogeneous medium containing permeable dielectric obstacle with a partially covered (for masking) boundary. The role of control function is played by surface conductivity entering the impedance boundary condition on the covered part of the boundary and the index of refraction of the dielectric obstacle. We prove the solvability of the control problem, derive the optimality system which describes the necessary conditions of an extremum and develop an efficient numerical algorithm for the solution of the control problem.

A Residual Thermodynamic Analysis of Inert Wear and Attrition, Part 2: Applications

Some differential relations of inert wear- and attrition work mechanisms, derived in a parallel paper, are here applied. The consideration of relevant and suitable boundary conditions is called for. For ductile- and brittle-type target materials, one may often establish a direct- or proportional connection between the relevant sub-process work mechanism – referred to as wear work or attrition work – and corresponding net resulting wear- or attrition rates. Kinetic theory can be supportive in estimating model coefficients. In addition, additional thermodynamic considerations may be necessary, in order to estimate behavior at extremum conditions. The direct connection is demonstrated for the differential process of ductile wear, which encompasses most types of macroscopic-scale ductile erosion and 2-body- and 3-body ductile abrasion situations. The direct connection is also demonstrated for brittle erosion, and for impact wear. It is shown that the size effect on ductile erosion and abrasion – a hitherto not understood phenomenon – can also be explained by this connection.

Distribution optimization of circulating water in air-cooled heat exchangers for a typical indirect dry cooling system on the basis of entransy dissipation

The flow and heat transfer of air-cooled heat exchangers play important roles in the performance of indirect dry cooling systems in power plants, so it is of benefit to the design and operation of a typical indirect dry cooling system to optimize the thermo-flow characteristics of air-cooled heat exchangers. The entransy dissipation method is applied to the performance optimization of air-cooled heat exchangers in this paper. Two irreversible heat transfer processes in air-cooled heat exchangers, the heat transfer between circulating water and cooling air and the mixing of circulating water, are taken into account and analyzed by means of the entransy dissipation method. The total entransy dissipation rate, which connects the geometrical parameters of air-cooled heat exchanger sectors and the heat capacity rates of the fluids to the heat flow rate in every sector, is obtained. Based on the mathematical relation and the conditional extremum method, an optimization equation group is derived, by which the air-cooled heat exchanger with known air-side parameters is optimized, showing that the entransy dissipation based optimization approach can contribute to the distribution optimization of circulating water in air-cooled heat exchangers of a typical indirect dry cooling system.

Energy balance and robustness adjustable topology control algorithm for wireless sensor networks

In wireless sensor networks, the interference around the application environment may cause the actual distance between any pair of nodes to fail to be measured accurately. Enclosure graph (EG) model uses this distance between nodes as its weight to construct the topology, which does not fully consider the interference. Consequently it will lead to a large amount of energy consumption induced by the application environment. Even it shortens the survival time. According to the feature of network energy inequality in a wireless sensor network and the defect of EG, we first introduce the adjustable factor of node degree, establish a model of communication metric and a model for the node actual survival time. Then according to the demand of network energy equalization and maximum network lifetime, we quantitatively analyze the network node degree, and achieve its regular pattern. In accordance with this regular pattern and sufficient conditions of function extremum, the maximum node energy consumption and the maximum node actual survival time are deduced. And the corresponding optimal node degree is achieved. Finally, according to the above model, in this paper we propose an energy balance and robustness adjustable topology control algorithm for wireless sensor networks. Theoretical analyses show that this algorithm can guarantee that the network is connected and the link of the network is bi-directionally connected. Experiments show that the network takes advantage of this optimal node degree to obtain the high robustness, thus guaranteeing that the information can be transferred unfailingly. This algorithm can effectively balance the node energy, improve the node survival time, enhance the network robustness, and prolong the network's lifetime.

A thermal resistance-based method for the optimal design of central variable water/air volume chiller systems

Varying water/air volume (VWV/VAV) favors the performance improvement of central chiller systems. However, due to the lack of an intrinsic relation connecting these design parameters to the requirements, both the operating parameters of variable speed pumps/fans (VSP/VSF) and the structural parameters of heat exchangers are usually designed empirically or semi-empirically, which offers a huge potential for energy conservation. Therefore, through analyzing the heat transfer processes in each heat exchanger of a central VWV/VAV chiller system by the entransy-dissipation-based thermal resistance (EDTR) and studying the fluid flow processes by the characteristics of VSPs/VSFs and pipeline pressure drops, respectively, we yield the formulas connecting the areas of each heat exchanger and the rotating speeds of each VSP/VSF directly to the design requirements. Combining these formulas with the conditional extremum method gives several optimization equations corresponded to different optimization objectives. Simultaneously solving these equations directly gives the optimal area allocation of each heat exchanger and the operating parameters of VSPs and VSFs, which successfully avoid the limitation of the trial-and-error method. Finally, a simple central VWV/VAV chiller system is taken as an example to illustrate the applications of the newly proposed optimization method.

Using the method of artificial immune systems to seek the suboptimal program control of deterministic systems

Determination of the suboptimal programmed control for the continuous deterministic systems by the use of the method of artificial immune systems for search of the conditional global extremum was proposed. An algorithm to solve it which underlies the corresponding software was generated, and a modification of the method was suggested to enhance its efficiency. Examples of solutions of the model problems were given, and the method of artificial immune systems was compared with its modification, as well as with other metaheuristic methods.

Spectral compression and modulation of second harmonic generation by Fresnel-inspired binary phase shaping

The second harmonic generation (SHG) process is investigated theoretically using the quantum mechanics method of coherent control. Based on the extremum conditions for the SHG intensity at the center frequency, a Fresnel-inspired binary phase shaping scheme is proposed for tailoring the fundamental pulse. The SHG spectrum can be compressed into a narrowband signal with lower background by modulating the relative phases between the frequency components within the fundamental pulse, inducing constructive interference at the center frequency and destructive interference elsewhere. Multipeak second harmonic signals can also be obtained by properly modulating various interference pathways. These results have potential applications in high resolution nonlinear spectroscopy, microscopy, and information coding.

Analysis of 2-D Impedance Cloaking Problem Based on Boundary Element Method

Control problems are considered for a two-dimensional model describing wave scattering in an unbounded homogenous medium containing an impenetrable covered (cloaked) boundary. The control is a surface impedance which enters the boundary condition as a coefficient. The solvability of the original scattering problem for 2-D Helmholtz equation and of the control problem is proved. Optimality system dгescribing the necessary extremum conditions are derived. The algorithm for numerical solving of the control problem based on the optimality system and boundary element method is designed.

A Method to Determine Relative Vehicle Positioning for Safety Warning

Determining relative vehicle positioning for vehicle safety warning services requires high level of accuracy. Positioning based on general satellite information has a large margin of error due to cost constraints. This paper proposes a method to determine relative vehicle position for vehicle safety warning, based on conditional extremum and relative vehicle history positioning. Special attention is paid to improve not only the computational efficiency but also the accuracy of determining the relative position of two vehicles or a vehicle and reference frame. Field test results demonstrate the significance of improved accuracy in determining relative vehicle position. Theoretical analysis and realistic systematic tests provide useful insights into potential applications in safety warning.

Quantum focusing and coherent control of nonresonant two-photon absorption in frequency domain.

We theoretically investigate the nonresonant two-photon absorption (TPA) process in a two-level atom induced by a weak chirped pulse in the frequency domain. According to the extremum condition of the two-photon transition probability (TPTP) at the transition center frequency, we propose a Fresnel-inspired pulse tailoring scheme for TPA that is significantly different from that of Broers etal. [Phys. Rev. A46, 2749 (1992)]. Using this scheme, the TPTP can be focused or eliminated completely by constructively or destructively modulating various pathways of the quantum interference. Our results are a significant improvement on those obtained by Broers etal. and will have potential applications in selective two-photon microscopy and spectroscopy.

An entransy dissipation-based optimization principle for solar power tower plants

The entransy theory, which can be used to optimize the heat transfer network of a solar power tower system (SPTS) and improve its energy efficiency, was introduced in this paper. Firstly, the irreversibility of the heat transfer processes in a SPTS was analyzed and the total entransy dissipation equation of a SPTS was derived. Then, two types of optimization problems (reducing the total circulating flow rate or the total heat-exchanging area) of a SPTS were solved with conditional extremum model based on the formulas of total entransy dissipation. Finally, the entransy dissipation-based optimization principle was applied to a simple SPTS without re-heater and a complex SPTS with a re-heater. The results showed that under the chosen calculation conditions the minimum total thermal conductance was 19306.03 W K−1 for a SPTS without re-heater when the total heat capacity rate of heat transfer fluid (HTF) was 3200 W K−1. The minimum total thermal conductance was about 7.9% lower than the value predicted based on the typical outlet temperature of a receiver. This meant that the total heat exchange area or initial investment could be effectively reduced under the prescribed total HTF circulating flow rate. We also studied the variation trends of the two optimized results including minimum total HTF heat capacity rate and minimum total thermal conductance. The minimum total HTF heat capacity rate decreased with the given total thermal conductance, the minimum total thermal conductance decreased first and then increased with the given total HTF heat capacity rate. We also found that for a SPTS with a re-heater, the mixing temperature and the mixing position of HTF had significant effects on the two types of optimization problems.

A global optimization method for regenerative air refrigeration systems

The air refrigeration systems always involve such physical processes as heat transfer processes in heat exchangers, compression processes in compressors and expansion processes in expanders. This contribution proposes a theoretical global optimization method for regenerative air refrigeration systems and introduces the entransy theory to analyze the heat transfer processes in the hot-end heat exchanger, the cold-end heat exchanger and the regenerator. Integration of the heat transfer analyses and the thermodynamic analyses for the compression and expansion processes yields a mathematical model to describe the physical relation between the design requirements and the unknown design parameters, i.e. the heat transfer area of each heat exchanger and the heat capacity rate and the intermediate temperature of the air. Based on this model, the optimization can be converted into a conditional extremum problem. That is, solving the problem via the Lagrange multiplier method offers an optimization equation group, which directly leads to the optimal values of all the unknown parameters. Finally, this optimization method is validated through an optimization case to minimize the total thermal conductance of all the heat exchangers in a typical regenerative air refrigeration system.

Control of boundary impedance in two-dimensional material-body cloaking by the wave flow method

Control problems are considered for a two-dimensional electromagnetic field model describing electromagnetic wave scattering in a unbounded homogeneous medium containing an anisotropic permeable inclusion with a partially covered (cloaked) boundary. The control is a function involved in the impedance boundary condition on the covered part of the boundary. The solvability of the original mixed transmission problem for the two-dimensional Helmholtz equation and of the control problems is proved. Optimality systems describing necessary extremum conditions are derived. The uniqueness and stability of optimal solutions with respect to certain perturbations of the cost functional and the incident wave are established.

An optimization method for gas refrigeration cycle based on the combination of both thermodynamics and entransy theory

A thermodynamic cycle usually consists of heat transfer processes in heat exchangers and heat-work conversion processes in compressors, expanders and/or turbines. This paper presents a new optimization method for effective improvement of thermodynamic cycle performance with the combination of entransy theory and thermodynamics. The heat transfer processes in a gas refrigeration cycle are analyzed by entransy theory and the heat-work conversion processes are analyzed by thermodynamics. The combination of these two analysis yields a mathematical relation directly connecting system requirements, e.g. cooling capacity rate and power consumption rate, with design parameters, e.g. heat transfer area of each heat exchanger and heat capacity rate of each working fluid, without introducing any intermediate variable. Based on this relation together with the conditional extremum method, we theoretically derive an optimization equation group. Simultaneously solving this equation group offers the optimal structural and operating parameters for every single gas refrigeration cycle and furthermore provides several useful optimization criteria for all the cycles. Finally, a practical gas refrigeration cycle is taken as an example to show the application and validity of the newly proposed optimization method.

A theoretical global optimization method for vapor-compression refrigeration systems based on entransy theory

The vapor-compression refrigeration systems have been one of the essential energy conversion systems for humankind and exhausting huge amounts of energy nowadays. Surrounding the energy efficiency promotion of the systems, there are lots of effectual optimization methods but mainly relied on engineering experience and computer simulations rather than theoretical analysis due to the complex and vague physical essence. We attempt to propose a theoretical global optimization method based on in-depth physical analysis for the involved physical processes, i.e. heat transfer analysis for condenser and evaporator, through introducing the entransy theory and thermodynamic analysis for compressor and expansion valve. The integration of heat transfer and thermodynamic analyses forms the overall physical optimization model for the systems to describe the relation between all the unknown parameters and known conditions, which makes theoretical global optimization possible. With the aid of the mathematical conditional extremum solutions, an optimization equation group and the optimal configuration of all the unknown parameters are analytically obtained. Eventually, via the optimization of a typical vapor-compression refrigeration system with various working conditions to minimize the total heat transfer area of heat exchangers, the validity and superior of the newly proposed optimization method is proved.

The dynamical analysis of a new chaotic system and simulation

In this paper, we make a study of dynamical properties of a nonlinear monetary system (1.1) towards the solution of the localization problem of compact invariant sets of the system (1.1). Here, a localization signifies a description of a set containing all compact invariant sets of (1.1) in terms of equalities and inequalities defined in the state space R3. Our approach is based on using the first-order extremum conditions and is realized with the help of the iterative theory. We claim that all compact invariant sets of this system are located in the intersection of a ball with two frusta, and we also compute its corresponding parameters of the system. In addition, localization with the help of a two-parameter set of parabolic cylinders is described. Numerical simulation is consistent with the results of theoretical calculation. Copyright © 2013 John Wiley & Sons, Ltd.

The Practicability of Pluralistic Nr-E-V Distribution and a Comparison of it with Singular Statistical Distribution

This paper, based on the maximum entropy and conditional extremum, deals with the practicability of Nr-E-V distribution of the pluralistic single-phase system. Whats more, in the paper other kinds of distributions formulas of probability and partition function have been derived from Nr-E-V distribution. Finally, the thermodynamics function of partition function, internal energy, entropy and pressure of E distribution are derived from the example of pluralistic ideal gas composed of single-atomic molecule.