Gabor's Signal Expansion and Degrees of Freedom of a Signal

Gabor's expansion of a signal into a discrete set of properly shifted and modulated versions of an elementary signal is introduced, and a way to determine the expansion coefficients is derived. The way in which the expansion coefficients are transformed when the signal propagates through a linear system, is described; in particular, the basic coherent-optical system consisting of a 4farrangement with rectangular apertures in the input plane and the Fourier plane, is considered. As a result, the well-known property that a signal which is roughly limited both in space and in spatial frequency has a number of complex degrees of freedom which is equal to the space-bandwidth product, is re-established.     

Characterization of monolayer and bilayer (polymer/monolayer) structures for their use as a lubricant

To help to understand lubrication in order to design a good lubricant, a glass surface is modified by various monomolecular layers or bilayers (polymer on monolayer) and their effects on the coefficient of friction are examined. In a bilayer structure the monolayer is used as a binder between the polymer and the substrate. Monolayers are deposited by vapour phase deposition or the Langmuir-Blodgett technique. Polymers are spin coated after monolayer deposition. The coefficient of friction is lowered to a minimum of about 0.1 by these modifications. There is a parallelism between surface energy and coefficient of friction. However, it is found that the surface energy is not the only factor that effects the lubrication, i.e. although the surface energy is similar the coefficient of friction is smaller when (1) the surface is modified by a bilayer rather than by a monolayer, (2) the polymer viscosity is higher, (3) the polymer is liquid rather than solid at room temperature and (4) the reactivity between polymer and monolayer is higher. It has been deduced that a high molecular weight fluorinated polymer, which can be effectively bound to a surface, will be a good lubricant.     

单根多楔带附件驱动系统中各带段横向振动固有频率计算方法的研究

将单根多楔带附件驱动系统中相邻两轮之间的带段简化成纵向运动梁,推导了纵向运动带(梁)横向振动固有频率的计算方程。以一典型的三轮(主动轮、从动轮和张紧轮)-带附件驱动系统为例,分别运用轮-(梁)带耦合模型(将带简化为梁)和单根纵向运动梁(带)模型,计算分析了附件驱动系统中各带段的横向振动频率。结果表明,当带的弯曲刚度较小和带速较低时,可以利用单根纵向运动梁(带)模型计算得到带的横向振动固有频率。该文的计算方法和结论,为单根多楔带附件驱动系统中带横向振动固有频率的计算分析提供了分析模型和计算方法。     

A model for correlated failures in N-version programming

The multi-version programming technique is a method to increase the reliability of safety critical software. In this technique a number of versions are developed and a voting scheme is used before a final result is provided. In the analysis of this type of systems, a common assumption is the independence of the different versions. However, the different versions are usually interdependent and failures are correlated due to the nature of the product design and development. One version may fail simultaneously with another version because of a common cause. In this paper, a model for these dependent failures is developed and studied. Using the developed model, a reliability function can be easily computed. A method is also proposed to estimate the parameters of the model. Finally, as an application of the developed model, an optimal testing resource allocation problem is formulated and a genetic algorithm is presented to solve the problem.     

Crack front perturbations revisited

The problem of the in-plane dynamic perturbation of a crack propagating with a front that is nominally straight is solved, to second order in the perturbation. The method of approach is a streamlined and generalized version of that previously applied to first order by the author and co-workers. It emerges, however, that the analysis at second order requires for its consistency the introduction of a new singular term, of a type not present at first order. The analysis is restricted to the case of Mode I loading, for clarity of exposition. It is carried out at a level of generality that incorporates viscoelastic response as well as propagation in a “vertically stratified” medium including, as a special case, propagation in a slab of finite thickness. For illustration, the general solution is specialized to the case of a stationary crack in an infinite elastic medium and agreement with a solution recently developed by methodology that is specific to the static case is confirmed.     

A hybrid genetic based optimization procedure for aircraft conceptual analysis

The problem to define a methodology for the analysis of aircraft performances, in the phase of conceptual design, is addressed. The proposed approach is based on a numerical optimization procedure where a scalar objective function, the take-off weight, is minimized. Deterministic and stochastic approaches as well as hybridizations between these two search techniques are considered. More precisely, we consider two-stage strategies where the optimum localization is performed by a genetic algorithm, while a gradient-based method is used to terminate the optimization process. Also, another type of hybridization strategy is investigated where a partially converged gradient-based method is incorporated in the genetic algorithm as a new operator. A detailed discussion is made and various different solutions are critically compared. The proposed methodology is consistent and capable of giving fundamental information to the designer for further investigating towards the directions identified by the procedure. A basic example is described, and the use of the methodology to establish the effects of different geometrical and technological parameters is discussed.     

Mirror tilt immunity interferometry with a cat's eye retroreflector

This paper describes the behavior of a cat's eye retroreflector, which is incorporated in a novel way in a double-pass homodyne polarization interferometer. The amount of mirror tilt immunity a cat's eye provides is calculated within the paraxial approximation using 4×4 ABCD matrices. It is found that there is a position of the target mirror in which the tilt immunity is at a maximum. A real cat's eye, which is affected by aberrations, is optimized and examined using Zemax software for optical design. The maximum amount of mirror tilt immunity is numerically calculated and written in terms of defocus and spherical aberration. Finally, for the purposes of comparison, the amplitude of the Lissajous pattern as the target mirror tilts is calculated for both an interferometer with an integrated cat's eye and an interferometer with a cube corner.     

Elastic Instability of Pseudo-Elastic Rubber Balloons

Elastic instability for the inflation and deflation of a thin-walled spherical rubber balloon is examined within the framework of finite pseudo-elasticity. When a spherical rubber balloon is inflated, it is subject to a complex deformation after a pressure maximum has been obtained. One part of the balloon is lightly stretched while the remainder becomes highly stretched. So an aspherical deformation is observed after the initial spherical inflation. A pseudo-elastic strain energy function including a damage variable which may model the loading, unloading and reloading of rubber is used. The balloon is idealized as an elastic membrane and the inflation, deflation and re-inflation of the balloon is described in detail. Instability of solutions is discussed through energy comparison. Furthermore, the effect of temperature is discussed with a thermo-hyperelastic model and the residual strain is analyzed with a pseudo-elastic strain energy function including a residual strain variable.     

Instability analysis in pressurized three-layered fiber-reinforced anisotropic rubber tubes in torsion

Instability analysis of the large deformation of three-layered fiber-reinforced anisotropic rubber tubes subjected to an inner pressure combined with torsion and axial stretch is examined within the framework of finite elasticity. Based on a fiber-reinforced incompressible hyper-elastic material model, the relation between the principal stretch and the inner pressure, torsion and axial stretch is obtained. It is shown that there exists a critical thickness for the tubes. For a thin-walled tube which is thinner than the critical thickness, the tube under-goes a uniform stable inflation when the inner pressure is small. However, the tube may under-go a strikingly non-uniform deformation when the inner pressure is larger than a certain critical value. One portion of the tube may become highly distended as a bubble and it is proved that this deformation is unstable. While a thick-walled tube which is thicker than the critical thickness, always under-goes a uniform inflation. The critical thickness of the tube to take unstable deformation is given based on the deformation curve and its slope. Furthermore, the effect of axial stretch, torsion and the distribution angle or the strength of the fiber on the deformation and the stress of the tube are discussed.     

The effect of the resonant mode structure on flux tunneling in SQUIDs

The problem of macroscopic quantum tunneling in SQUIDs is discussed, taking into account the resonant mode structure of typical devices. These are evaluated for the particular case of a SQUID formed from a conical point intersecting a hemispherical cavity, and it is shown that the conventional representation of a SQUID as a Josephson junction in parallel with an inductor and a capacitor is a good first approximation in most cases, provided the inductance and capacitance used are those of the whole device rather than of the weak link alone. The discussion is extended to another case of practical importance, where such a cavity is connected to an outer hole by a flange, and it is found that if the capacitance of the flange is large, the tunneling behavior is largely independent of the presence of the outer hole, apart from the effects of any dc bias.     

On the Elastic Coupling Through the Flux Lines and Magnetic Interaction

It is defined the magnetic interaction energy between two superconductor pieces situated in a magnetic field by using the elastic coupling through the flux lines. On this basis, it is shown that a force between a superconducting material and a source of magnetic field is always repulsive, the force between a ferromagnetic material and a source of magnetic field is always attractive and a force between a normal metal and a source of time-varying magnetic field is always repulsive.     

De-icing by slot injection

Summary We consider the removal of ice from a plate in a cold cross flow by injection of hot fluid through a slot in the plate. De-icing of this sort is required in a number of diverse industrial scenarios, and is particularly relevant to the aviation industry, where the presence of ice on aircraft wings is a major safety hazard. Thin aerofoil theory is used to determine the flow above the injected fluid layer, and this is coupled to flow and energy equations in the injected layer and the ice. The key non-dimensional parameters and ratios in the problem are identified. The result is a nonlinear singular integro-differential equation which is coupled to a convection/diffusion equation and a Stefan condition. Some special cases are discussed and some asymptotic limits are identified. The problem is then solved numerically, and results for a number of different cases are presented.     

A theoretical model to predict interface slip due to bending

Casting a new concrete layer on the tensile or compressive side of a reinforced concrete element is a common technique that is used to increase the flexural capacity of weak reinforced concrete elements. Until now however, a model has not been presented in the literature to evaluate the slip between the two components. Usually, in common practical design, slip is ignored and the strengthened element is assumed monolithic. This may not be a conservative assumption, as any slip would affect the ultimate resistance of the strengthened element. In the present paper, an analytical procedure is presented that predicts the distribution of slip strain, slip and shear stress along a reinforced or unreinforced interface between an initial beam and a new concrete layer. By following this process, the capacity of a strengthened beam is determined by taken slip into account. In addition, a step-by-step design procedure is presented and then applied to an experimental result. Good agreement if found. Further verification of the analytical procedure is performed by comparison with finite element analysis and very good agreement is found.     

Risk informed resource allocation policy: safety can save costs

During economic doldrums, decision making on investments for safety is even more difficult than it already is when funds are abundant. This paper attempts to offer some guidance. After stating the present challenge to prevention of losses in the process industries, the systematic approach of quantified risk assessment is briefly reviewed and improvements in the methodology are mentioned. In addition, attention is given to the use of a risk matrix to survey a plant and to derive a plan of action. Subsequently, the reduction of risk is reviewed. Measures for prevention, protection, and mitigation are discussed. The organization of safety has become at least as important as technical safety of equipment and standards. It is reflected in the introduction of a safety management system. Furthermore, the design process in a pro-active approach is described and the concept of inherent safety is briefly addressed. The concept of Layer of Protection Analysis is explained and also the reason why it is relevant to provide a cost-benefit analysis. Finally, after comments regarding the cost of accidents, the basics of costing and profitability are summarized and a way is suggested to apply this approach to risk-reducing measures. An example is provided on how a selection can be made from a number of alternatives.     

Vavilov-Cherenkov radiation in active biresonant media

The radiation of a charged particle moving in a dispersive medium with two resonance frequencies is theoretically studied. It is shown that such a medium can amplify the generated electromagnetic waves, provided that the low-frequency resonance is active, the high-frequency resonance is passive, and the particle velocity is within a certain interval. A method of calculation of the amplification effect is described and a particular example is presented.     

An evolutionary algorithm for global optimization based on self-organizing maps

In this article, a new population-based algorithm for real-parameter global optimization is presented, which is denoted as self-organizing centroids optimization (SOC-opt). The proposed method uses a stochastic approach which is based on the sequential learning paradigm for self-organizing maps (SOMs). A modified version of the SOM is proposed where each cell contains an individual, which performs a search for a locally optimal solution and it is affected by the search for a global optimum. The movement of the individuals in the search space is based on a discrete-time dynamic filter, and various choices of this filter are possible to obtain different dynamics of the centroids. In this way, a general framework is defined where well-known algorithms represent a particular case. The proposed algorithm is validated through a set of problems, which include non-separable problems, and compared with state-of-the-art algorithms for global optimization.     

A Scheme for a Sustainable Urban Water Environmental System During the Urbanization Process in China

Urbanization is a potential factor in economic development, which is a main route to social development. As the scale of urbanization expands, the quality of the urban water environment may deteriorate, which can have a negative impact on sustainable urbanization. Therefore, a comprehensive understanding of the functions of the urban water environment is necessary, including its security, resources, ecology, landscape, culture, and economy. Furthermore, a deep analysis is required of the theoretical basis of the urban water environment, which is associated with geographical location, landscape ecology, and a low-carbon economy. In this paper, we expound the main principles for constructing a system for the urban water environment (including sustainable development, ecological priority, and regional differences), and suggest the content of an urban water environmental system. Such a system contains a natural water environment, an economic water environment, and a social water environment. The natural water environment is the base, an effective economic water environment is the focus, and a healthy social water environment is the essence of such a system. The construction of an urban water environment should rely on a comprehensive security system, complete scientific theory, and advanced technology.     

Systematic separation of a multicomponent mixture of solids based on selective crystallization and dissolution

A cascade process for the separation of a multicomponent mixture of solid particles based only on solubility is disclosed. It consists of two subprocesses: One is made up of a dissolver-filter-crystallizer-filter train, and the other is made up of the same plus an evaporator. While the former is a well-established technology, the latter is not a commercial one. Discussion of how and why the subprocesses work for two-component systems is first given. Then, a step-by-step procedure for the design of a cascade process for a multicomponent system is presented. In addition, other issues of relevance to the conceptual design of processes—choice of solvent, choice of operating temperatures, selection of the separation sequence, operability issues—are considered.     

On a marching level-set method for extended discontinuous Galerkin methods for incompressible two-phase flows: Application to two-dimensional settings

In this work a solver for two-dimensional, instationary two-phase flows on the basis of the extended discontinuous Galerkin (extended DG/XDG) method is presented. The XDG method adapts the approximation space conformal to the position of the interface. This allows a subcell accurate representation of the incompressible Navier-Stokes equations in their sharp interface formulation. The interface is described as the zero set of a signed-distance level-set function and discretized by a standard DG method. For the interface, resp. level-set, evolution an extension velocity field is used and a two-staged algorithm is presented for its construction on a narrow-band. On the cut-cells a monolithic elliptic extension velocity method is adapted and a fast-marching procedure on the neighboring cells. The spatial discretization is based on a symmetric interior penalty method and for the temporal discretization a moving interface approach is adapted. A cell agglomeration technique is utilized for handling small cut-cells and topology changes during the interface motion. The method is validated against a wide range of typical two-phase surface tension driven flow phenomena in a 2D setting including capillary waves, an oscillating droplet and the rising bubble benchmark.