The Bardeen-Stephen theory

The experimental situation that prompted the theory is reviewed, the essentials of the Bardeen-Stephen theory are sketched, and several extensions are mentioned, particularly those that are needed to understand the high-temperature copper-oxide superconductors.     

The kosterlitz-thouless transition and vortex dynamics

The physics of the Kosterlitz-Thouless vortex-unbinding transition in two-dimensional superfluids is discussed, and theN ×N Josephson junction array is considered as a prototype system. Dynamical behaviour is considered in two cases: (a) the complex impedance shows structure at a frequency-dependent transition temperature, similar to the dynamic susceptibility of a spin glass; (b) with a perpendicular non-uniform magnetic field, of a particular ‘self-similar’ hierarchical pattern, a scaling argument gives non-exponential relaxational dynamics of a prepared non-equilibrium vortex distribution.     

Roll‐up of a viscous vortex sheet

Abstract

The vortex sheet roll‐up for a viscous fluid flow under an initially periodic perturbation is studied by using a core‐spreading vortex method [2]. The viscous term, usually neglected in prior studies, is considered in the present study. In order to avoid the singularity at the center of point vortices, a convolution decomposition procedure is applied to form the vortex blobs. When calculating the stream function and the velocity field, the computations for the vortex method are usually time‐consuming due to the involvement of a large number of vortex blobs. This is improved by employing an efficient algorithm based on multipole expansions [6] to perform far‐field calculations. With the help of the fast algorithm, the time complexity of the one‐step calculation is directly proportional to the number of vortex blobs.

Numerical results show that the roll‐up of a vortex sheet with the viscous effect is slower than that of an inviscid vortex sheet. During the roll‐up of the vortex sheet, the spread and the flatness of the vorticity distribution are also studied by calculating the second moments and the fourth moments, respectively. Both results indicate the roll‐up of an inviscid vortex sheet is stretched slightly longer than that of a viscous vortex sheet.     

The behaviour of excited plane jets

A plane subsonic jet can be excited to entrain more fluid from its surroundings by subjecting it to antisymmetric periodic disturbances. The essential feature in this phenomenon is the rolling-up motion of an initially flapping jet to form large vortices which are responsible for greater entrainment. Several methods developed to impart oscillations to the flow at the nozzle, such as the acoustic pressure oscillator, the vibration of a single vane in the potential core region, the reciprocating lip system and the twin vane exciter, are described in this article. A minimum threshold in amplitude is necessary for exciting the flow. However, the frequency of oscillation is much less than that predicted by stability considerations.     

Phase diagram of turbulence in superfluid 3He-B

No Heading In superfluid ³He-B mutual-friction damping of vortex-line motion decreases roughly exponentially with temperature. We record as a function of temperature and pressure the transition from regular vortex motion at high temperatures to turbulence at low temperatures. The measurements are performed with non-invasive NMR techniques, by injecting vortex loops into a long column in vortex-free rotation. The results display the phase diagram of turbulence at high flow velocities where the transition from regular to turbulent dynamics is velocity independent. At the three measured pressures 10.2, 29.0, and 34 bar, the transition is centered at 0.52–0.59 T_c and has a narrow width of 0.06 T_c while at zero pressure turbulence is not observed above 0.45 T_c.PACS numbers: 47.37, 67.40, 67.57     

Vortex simulation of turbulent mixing layers

We present here a brief survey of vortex-dynamical simulations of the plane mixing layer using different forms of vortex elements. Points and blobs, which have been widely used in the past, suffer from irregular evolution of the vortex sheet approximating the shear layer, and the rather long time-averaging required to obtain meaningful statistics. A technique recently proposed by the authors, using vortex arcs or sheet elements, has been found to be helpful in avoiding these difficulties. In particular, this technique avoids the singularity in induced velocity associated with point vortex techniques, and is therefore in no need of any form of the “desingularization” that is often introduced in the latter. New results for excited mixing layers using the vortex sheet element model are presented, and are shown to be in good agreement with experimental observations.     

Vorticity and the theory of aerodynamic sound

Lighthill strongly advocated the use of vortex methods in most areas of fluid mechanics with the notable exception of the theory of aerodynamic sound. But it is straightforward to transform his famous `acoustic analogy' to make vorticity rather than Reynolds stress the ultimate `source' of sound in homentropic flows. `Vortex sound' theory becomes especially useful in applications involving acoustically compact flow-structure interactions, where it actually emerges as an extension of Kelvin's theory of `vortex impulse', a notion that Lighthill regarded as important enough to be given special treatment in undergraduate lectures on fluid mechanics. The `impulse source' can be recast in a form more suited for numerical or analytical evaluation, and is closely related to the `compact Green's function'. Convergence difficulties encountered in the casual application of the acoustic analogy to non-compact flow-structure interactions are resolved in a natural manner by the methods of vortex sound theory. New illustrations of these methods are given in this paper by consideration of the unsteady development of lift by a starting airfoil, of the production of sound by a `vortex whistle', and of the infrasound generated when a high-speed train enters the tunnel.     

The value of nonlinear control theory in investigating the underlying dynamics and resilience of a grocery supply chain

In an empirical context, a method to use nonlinear control theory in the dynamic analysis of supply chain resilience is developed and tested. The method utilises block diagram development, transfer function formulation, describing function representation of nonlinearities and simulation. Using both ‘shock’ or step response and ‘filter’ or frequency response lenses, a system dynamics model is created to analyse the resilience performance of a distribution centre replenishment system at a large grocery retailer. Potential risks for the retailer’s resilience performance include the possibility of a mismatch between supply and demand, as well as serving the store inefficiently and causing on-shelf stock-outs. Thus, resilience is determined by investigating the dynamic behaviour of stock and shipment responses. The method allows insights into the nonlinear system control structures that would not be evident using simulation alone, including a better understanding of the influence of control parameters on dynamic behaviour, the identification of inventory offsets potentially leading to ‘drift’, the impact of nonlinearities on supply chain performance and the minimisation of simulation experiments.     

Stochasticity and time delays in gene expression and evolutionary game theory

We discuss effects of stochasticity and time delays in simple models of population dynamics. In social-type models, where individuals react to the information concerning the state of the population at some earlier time, sufficiently large time delays may cause oscillations. In biological-type models, where some changes already take place in the population at an earlier time, oscillations might not be present for any time delay. We illustrate this idea in models of delayed random walks, gene expression, and population dynamics of evolutionary game theory.     

Vortex Motion and Quasiparticle Resistivity in MgB<Subscript>2</Subscript> at Microwave Frequencies

The electrical transport in superconductors at nonzero frequencies is affected by the normal and superfiuid fractions, as well as moving vortices, resulting in intricate expressions for the complex resistivity. In MgB₂, additional complications arise from the two-band nature of this material. We present an accurate study of microwave resistivity data measured in MgB₂ thin films by means of the Corbino disk broadband technique between 2 and 20 GHz. We show that a two-fluid model applies well in a relatively large region of the H–T phase diagram. Excellent agreement is found between the derived superfluid parameters (superfluid density, upper critical field) and theoretical predictions. In the same H–T region we isolate and discuss the vortex motion complex resistivity. To this end, we make use of the expressions given by the model by Coffey and Clem (CC). We show that the frequency dependence of the complex vortex resistivity recovers the CC model. However, the temperature and field dependence of the obtained parameters are at odds with the assumptions of the model. We discuss possible explanations of these oddities by considering collective pinning of vortices.     

The generalized Hartree-Fock theory of nonmagnetic high-temperature superconductors

The Eliashberg equations are generalized to apply to high-temperature superconductors without spin correlations. The generalization assumes any general electronic density of states. Consequently, it treats the Coulomb interaction dynamically, and takes into account the averaged momentum dependence of the self-energy and of the interactions. Unlike in the conventional Eliashberg equation, the bare Coulomb interaction yields a frequency-independent term in the renormalization function. This term breaks the symmetry of the self-energy, and changes the renormalization.     

涡流管分离模型及实验研究

通过对涡流管的热力分析和流动分析，建立其内部过程的数学模型。从速度场的变化推导内部热分离的温度方程。实验系统测量涡流管内部温度场及速度场，理论计算值与实验值吻合。     

西南涡大气科学试验的观测布局理论与实践

我国是气象灾害十分严重的国家。西南涡是一个非常重要的灾害性天气系统,与我国夏半年的暴雨洪涝灾害密切相关,对国民经济、社会发展和人民生命财产安全都有着严重的影响。基于西南涡理论研究与科学试验现状,阐述了西南涡大气科学试验的观测基础对西南涡基本信息、理论研究和业务预报的重要意义。从站点分布、设备技术、观测要素等方面,提出了西南涡大气科学试验观测布局的设计思想与技术原则。在此基础上,系统设计了西南涡大气科学试验的观测布局工程,并于2010年、2011年开展了两次西南涡大气科学试验,检验了观测布局设计思想的正确性,推动了西南涡研究与业务的进展。最后,从西南涡大气科学试验的需求、现状和效果,进一步指出了加强其观测布局理论研究和具体实践,对我国经济发展、防灾减灾的重要意义。     

The thermal conductivity of dense fluids using revised Enskog theory

A predictive method designed to obtain the thermal conductivities of one-component dense fluids is described. This method is based on the revised Enskog theory. Here, an effective state-dependent hard-sphere diameter is used to obtain the hard-sphere diameter needed by the revised Enskog theory in order to deal with actual fluids. In addition, we introduce the contribution of the internal degrees of freedom through the Mason-Monchick procedure. Our predictions for noble gases and hydrocarbons, at high density, are compared with predictions coming from the conformal solution model, with empirical correlation schemes, and with experimental data. A very satisfactory agreement is found.     

Constructor theory of life

Neo-Darwinian evolutionary theory explains how the appearance of purposive design in the adaptations of living organisms can have come about without their intentionally being designed. The explanation relies crucially on the possibility of certain physical processes: mainly, gene replication and natural selection. In this paper, I show that for those processes to be possible without the design of biological adaptations being encoded in the laws of physics, those laws must have certain other properties. The theory of what these properties are is not part of evolution theory proper, yet without it the neo-Darwinian theory does not fully achieve its purpose of explaining the appearance of design. To this end, I apply constructor theory''s new mode of explanation to express exactly within physics the appearance of design, no-design laws, and the logic of self-reproduction and natural selection. I conclude that self-reproduction, replication and natural selection are possible under no-design laws, the only non-trivial condition being that they allow digital information to be physically instantiated. This has an exact characterization in the constructor theory of information. I also show that under no-design laws an accurate replicator requires the existence of a ‘vehicle’ constituting, together with the replicator, a self-reproducer.     

A scenario to the anomalous Hall effect in the mixed state of superconductors

We argue that the motion of vacancies in a pinned vortex lattice may dominate the contribution to the Hall effect in an appropriate parameter regime for a superconductor. Based on this consideration a model is constructed to explain the anomalous Hall effect without any modification of the basic vortex dynamic equation. Quantitative predictions are obtained. Present model can be directly tested by an observation of the vacancy motion.     

Flux Dynamics in Tl2Ba2CaCu2O8 Thin Films

Investigations on flux dynamics of ring-shaped T1₂Ba₂CaCu₂O₈ superconducting thin films have been carried out by measuring the temperature dependent magnetization M(T) during field-cooling (FC) and zero-field-cooling (ZFC) processes. For a given magnetic field, from the magnetization behavior two distinct temperatures, T_kink and T_irr, can be defined. Below T_kink, a clear hysteretic behavior of M(T) is observed leading to a large irreversible signal M = M_FC – M_ZFC. Above T_kink, this irreversible signal, though being very small, is still non-zero until it eventually vanishes at a higher temperature T_irr. Above T_irr, both curves M_FC(T) and M_ZFC(T) merge together and become temperature independent. We attribute the first region ( T< T_kink) to a 3D vortex-glass phase, the second region (T_kink < T < T_irr) to a vortex line liquid state and the third region (T_irr < T < T_c) to a pancake liquid state.     

Decoding the architectural theory

Starting from the illustration of the definition and concept of the architectural theory, the author established his unique understanding about the framework of the architectural theory and the innovation of the architectural theory underlined by Chinese characteristics.     

Pinning of Vortices Nearly Parallel to the Superconducting Plane in κ-(ET)2Cu[N(CN)2]Br and κ-(ET)2Cu(NCS)2

The vortex state under a magnetic field applied nearly parallel to the superconducting plane has been studied by means of an ac susceptibility measurement around 2 MHz in the organic superconductors -(ET)₂Cu[N(CN)₂]Br and -(ET)₂Cu(NCS)₂. The diamagnetic response, due to pinning of the staircase vortices for the inclined field, was suppressed by the increase in the magnetic field. This finding indicates that the parallel vortices become freely movable as a result of either decoupling between layers or depinning of Abrikosov vortices in the layer plane. We found that the suppression of the diamagnetic response was promoted by the parallel field component.     

The Coulomb interaction in the generalized Hartree-Fock theory of superconductivity

The matrix self-energy equations of the generalized Hartree-Fock (GHF) theory of HTSC are reevaluated and rederived, while avoiding some shortcomings of the former derivation. The density of states is given for an interacted and renormalized electronic system. The self-energy equations are essentially different in several respects from the conventional Eliashberg equations. The matrix self-energy is analyzed with respect to its dependence on (p). It is found to depend one very weakly, which results in self-energy equations which depend on a single variable,, as in the conventional theory. However, it is found that the bare Coulomb interaction contributes extra terms to the pairing self-energy and to the renormalization function. In the simplified version of the equations, the effect of these two extra terms is incorporated as a single extra term of the renormalization function.