Nonlinear dynamics of complex hysteretic systems: Oscillator in a magnetic field

Complex hysteresis is a well-known phenomenon in many branches of science. The most prominent examples come from materials with a complex microscopic structure such as magnetic materials, shape-memory alloys, or, porous materials. Their hysteretic behavior is characterized by the existence of multiple internal system states for a given external parameter and by a non-local memory. The input-output behavior of such systems is well studied and in a standard phenomenological approach described by the so-called Preisach operator. What is not well understood, are situations, where such a hysteretic system is dynamically coupled to its environment. Since the hysteretic sub-system provides a complicated form of nonlinearity, one expects non-trivial, possibly chaotic behavior of the combined dynamical system. We study such a combined dynamical system with hysteretic nonlinearity. In this original contribution a simple differential-operator equation with hysteretic damping, which describes a magnetic pendulum is considered. We find, for instance, a fractal dependence of the asymptotic behavior as function of the starting values. The sensitivity of the system to perturbations is investigated by several methods, such as the 0–1 test for chaos and sub-Lyapunov exponents. The power spectral density is also calculated and compared with analytical results for simple input-output scenarios.     

A new approach to particle confinement

A new approach to permanent confinement of non-relativistic and relativistic particles inside microscopic regions of space is presented. Motion in suitably chosen energy-dependent potentials turns out to be such that the size of orbits of particles bound in such potentials decreases when energy is supplied to them from external sources and there exists a maximum size of these orbits. The energy spectrum is purely discrete without any continuum. The dynamics of such particles requires the introduction of a space-dependent metric in the Hilbert space of states to ensure conservation of probability.     

Detection and measurement of surface defects by automatic fringe analysis

A novel measurement and inspection system for the detection and measurement of surface defects, such as chips and cracks, has been developed and applied to engineering components such as cylindrical rollers.The position, depth and volume of such a defect can be determined automatically. Measurement of such defects requires that three-dimensional information be made available for computer analysis. This is achieved by using a grating projection technique to provide contour fringes on the object, i.e. to give depth information. The contoured object is viewed by a charge coupled device (CCD) camera, the output of which is digitised and stored in a frame buffer from which it is available to a computer system for digital image processing, analysis and comparison. Calibration tests on defects of known size have confirmed that the system is fast and accurate.     

Scattering of particles with internal degrees of freedom

The scattering of particles with a small number of internal degrees of freedom is considered. Billiard formalism is used to study the scattering of two such structurally complex particles. The main scattering characteristics are found. Various types of scattering modes are revealed. In particular, a mode is detected when the velocity of motion of such particles away from each other is higher than their approach velocity before the collision. The scattering of such particles is shown to occur after a finite number of collisions. A generalized Newton law is proposed for the collision of particles with a small number of degrees of freedom, and the form of the effective coefficient of restitution is found.     

Cawley's counterexample to Dirac's conjecture as a curved spacetime

Cawley's counterexample Lagrangian to Dirac's conjecture on dynamical systems is modified to a line element in curved spacetime, and the energy-momentum tensor corresponding to such a spacetime is found. The spacetime obtained satisfies the Einstein field equations and describes a three-dimensional matterfilled universe. It is further shown that such a universe cannot be filled up with other sources, such as a perfect fluid, a scalar field, or an electromagnetic field, without violating the Einstein field equations.     

The one step fermionic ladder

The one step fermionic ladder refers to two parallel Luttinger Liquids (poles of the ladder) placed such that there is a finite probability of electrons hopping between the two poles at a pair of opposing points along each of the poles. The many-body Green function for such a system is calculated in presence of forward scattering interactions using the powerful non-chiral bosonization technique (NCBT). This technique is based on a non-standard harmonic analysis of the rapidly varying parts of the density fields appropriate for the study of strongly inhomogeneous ladder systems. The closed analytical expression for the correlation function obtained from NCBT is nothing but the series involving the RPA (Random Phase Approximation) diagrams in powers of the forward scattering coupling strength resummed to include only the most singular terms with the source of inhomogeneities treated exactly. Finally the correlation functions are used to study physical phenomena such as Friedel oscillations and the conductance of such systems with the potential difference applied across various ends.     

Modeling interface roughness scattering in a layered seabed for normal-incident chirp sonar signals

Downward looking sonar, such as the chirp sonar, is widely used as a sediment survey tool in shallow water environments. Inversion of geo-acoustic parameters from such sonar data precedes the availability of forward models. An exact numerical model is developed to initiate the simulation of the acoustic field produced by such a sonar in the presence of multiple rough interfaces. The sediment layers are assumed to be fluid layers with non-intercepting rough interfaces.     

Some Remarks on Symmetries and Transformation Groups in General Relativity

The motivation for this paper is the recent interest in the study of symme tries in general relativity and its purpose is to discuss the mathematical foundations required for such a study. The general (formal and informal) ideas of what constitutes a symmetry of space-time are discussed and developed and the idea of a Lie algebra of symmetry vector fields is studied in detail. The relationship between such Lie algebras and the ideas of Lie transformation group theory (Palais' theorems) is stated and a general theorem regarding the orbits of such symmetries is given. Finally some specific symmetries in general relativity are explored and some of their similarities and differences noted.     

Nanoscale radiative heating of a sample with a probe

The purpose of this paper is to show that it is possible to transfer large amount of heat to a sample at a nanometer scale by approaching a probe such as those used in near-field microscopies. We evaluate the different heat exchange processes such as convective and radiative heat transfer. An application to local heating is discussed.     

Stability of homogeneous universes

The stability of a class of homogeneous cosmological models is investigated. It is shown that the perturbation problem for six such universes can be reduced to a system of ordinary differential equations. The time development of the perturbations is such that they remain finite at all times for which the unperturbed metric is non-singular.Work supported in part by the National Science Foundation.     

On a model of an unconstrained hyperfluid

A hyperfluid is a classical continuous medium carrying hypermomentum. We modify the earlier developed variational approach to a hyperfluid in such a way that the Frenkel-type constraints imposed on the hypermomentum current are eliminated. The resulting self-consistent model is different from the Weyssenhoff-type model. The essential point is a conservation of the hypermomentum current such that the final metrical and canonical energy-momentum forms coincide.     

Optimization of global kinetics parameters for heterogeneous propellant combustion using a genetic algorithm

We examine the combustion of heterogeneous propellants for which, necessarily, the chemical kinetics is modelled using simple global schemes. Choosing the parameters for such schemes is a significant challenge, one that, in the past, has usually been met using hand-fitting of experimental data (target data) for global burning properties such as steady burning rates, burn-rate temperature sensitivity, and the like. This is an unsatisfactory strategy in many ways. It is not optimal; and if the target set is large and includes such things as stability criteria, or bounds, difficult to implement. Here we discuss the use of a general optimization strategy which can handle large data sets of a general nature. The key numerical tool is a genetic algorithm that uses MPI on a parallel platform. We use this strategy to determine parameters for HMX/HTPB propellants and AP/HTPB propellants. Only one-dimensional target data are used, corresponding to the burning of pure HMX (AP) or a homogenized blend of fine HMX (AP) and HTPB. The goal is to generate kinetics models that can be used in the numerical simulation of three-dimensional heterogeneous propellant combustion. The results of such simulations will be reported in a sequel.     

Gas–crystal phase transition in a 2D dipolar exciton system

A system of dipolar excitons at temperatures exceeding the expected Bose–Einstein condensation temperature is considered. It is shown that a first-order phase transition with the formation of a phase close to the crystal of such excitons is possible at such temperatures. The phase diagram in the range of low concentrations and temperatures is constructed. The effect of this transition on the luminescence spectrum of the system is analyzed.     

Engineering Optimisation: An Introduction with Metaheuristic Applications,by Xin-She Yang

When a beam of high intensity laser light is scattered by the fluctuations spontaneously existing within a fluid medium a spatial modulation of the dielectric constant may be induced. The role of such a modulation in causing stimulated scattering of the intense laser beam or Bragg reflection of any weak independent probe beam is discussed and theoretically analyesd. It is shown that such Bragg reflection provides a convenient technique for the study of the modulation. Experimental observation and investigation of Bragg reflection from such a modulation is described. A related technique has been used to investigate the development of light induced periodic structures on surfaces.     

Concave grating miniature spectrometer with an expanded spectral band by using two entrance slits

A new miniature spectrometer with two entrance slits is proposed to expand the spectral band. The proposed spectrometer is designed such that the two entrance slits share the same concave grating and detector array. The two slits are located at different positions such that the spectral range of the same light source incident on the detector array varies greatly between the two slits. Only one of the two slits is illuminated at a given time; as such, the two spectral ranges are sequentially measured. Theoretical calculation and experimentation are conducted to verify the proposed design.     

Temperature or strain induced adjustable-chirp characteristics of uniform fibre grating with tapered metal coating

Temperature and strain characteristics of uniform fibre grating with tapered metal coatings have been analysed theoretically, by which adjustable chirp characteristics of such gratings are shown. Electroplating is adopted to fabricate such gratings, and the tapered metal coating is obtained by gradually drawing the fibre grating out of the solution during the process of electroplating. The gradually changing cross-sectional area of the metal coating is calculated by a newly suggested numerical method. By combining the theoretical and numerical simulation analyses, the gratings' characteristics are given at various temperatures and strains. The results obtained using such a method are also testified by experiments.     

Vibro-acoustic control with a distributed sensor network

The purpose of this work is to demonstrate the ability of a distributed control system, based on a smart sensor network, to reduce acoustic radiation from a vibrating structure. The platform from which control is effected consists of a network of smart sensors, each referred to as a node. Each node possesses its own computational capability, sensor, actuator and the ability to communicate with other nodes via a wired or wireless network. The primary focus of this work is to employ existing group management middleware concepts to enable vibro-acoustic control with such a distributed network. Group management middleware is distributed software that provides for the establishment and maintenance of groups of distributed nodes and that provides for the network communication among such groups. The control objective is met by designing distributed feedback compensators that take advantage of node groups in order to effect their control. The node groups are formed based on physical proximity. The global control objective is to minimize the radiated sound power from a rectangular plate. Results of this investigation demonstrate that such a distributed control system can achieve attenuations comparable to those achieved by a centralized controller.     

Modelling of layered resonators for ultrasonic separation

The potential of ultrasonic techniques for the separation and concentration of particles within a fluid has been investigated in some detail in recent years. Devices for effecting such separation typically consist of a piezoceramic transducer driving into a matching layer, fluid layer and reflector layer. This paper uses an equivalent-circuit transducer model, coupled with acoustic impedance transfer relationships to model such cells with regards to both their electrical characteristics and the strength of the resonance produced under different conditions. The model is compared with experimental results from two different cells and is shown to match experimental values well in terms of electrical characteristics and separator performance. The effects of matching layer thickness are also examined using the model. The importance of the adhesive bonding layer is demonstrated, and it is shown that the model can predict the effects of such a layer. The model is also used to demonstrate the effects of coincident resonances in cell layers and to examine the pressure distribution across cells at key frequencies.