Parameter-transformation relations for traveling-wave solutions of kdv-burgers equation

 Burgers suggested that the main properties of free-turbulence in the boundless area without basic flow might be understood with the aid of the following equation, which was much simpler than those of fluid dynamics, 更多还原

Analytical solution of a multidimensional Langevin equation at high friction limits and probability passing over a two-dimensional saddle

The analytical solution of a multidimensional Langevin equation at the overdamping limit is obtained and the probability of particles passing over a two-dimensional saddle point is discussed. These results may break a path for studying further the fusion in superheavy elements synthesis.

A scenario for torus T(2) destruction via a global bifurcation

We show a scenario of a two-frequeney torus breakdown, in which a global bifurcation occurs due to the collision of a quasi-periodic torus T(2) with saddle points, creating a heteroclinic saddle connection. We analyze the geometry of this torus-saddle collision by showing the local dynamics and the invariant manifolds (global dynamics) of the saddle points. Moreover, we present detailed evidences of a heteroclinic saddle-focus orbit responsible for the type-if intermittency induced by this global bifurcation. We also characterize this transition to chaos by measuring the Lyapunov exponents and the scaling laws. (C) 2007 Elsevier Ltd. All rights reserved.

Non-periodic driving of coupled oscillators:a spherical swing

Nonlinearly coupled, damped oscillators at 1:1 frequency ratio, one oscillator being driven coherently for efficient excitation, are exemplified by a spherical swing with some phase-mismatch between drive and response. For certain damping range, excitation is found to succeed if it lags behind, but to produce a chaotic attractor if it leads the response. Although a period-doubhng sequence, for damping increasing, leads to the attractor, this is actually born as a hard (as regards amplitude) bifurcation at a zero growth-rate parametric line; as damping decreases, an unstable fixed point crosses an invariant plane to enter as saddle-focus a phase-space domain of physical solutions. A second hard bifurcation occurs at the zero mismatch line, the saddle-focus leaving that domain. Times on the attractor diverge when approaching either fine, leading to exactly one-dimensional and noninvertible limit maps, which are analytically determined.

Part-time job design : symptom and solution for a changing work environment

Part-time work presents a conundrum. Across industrialised countries, there has been significant growth in part-time work as a solution to resolving the diverse interests of employers, workers and families in managing time and resources. However, there are intrinsic disadvantages associated with part-time work; notably with pay and career prospects, which impact the same stakeholders it is intended to benefit. These disadvantages are particularly evident in professional services organisations, due to strong cultural norms of long work hours, single-focused commitment to work and 24x7 availability. There are indications, both in research and practice, that the design of part-time work arrangements could be improved to address some of the disadvantages associated with part-time work, and to challenge norms and dated assumptions that influence the structure of professional work. This study explored the changes made when professional service workers move from a full-time to part-time arrangement. The study drew on a recently proposed framework for work design, which extended previous models to reflect substantial changes in the contemporary work environment. The framework proved to be a useful perspective from which to explore the design of part-time work, principally because it integrated previously disconnected areas of literature and practice through a broader focus on the context of work. Exploration of the differences between part-time and full-time roles, and comparisons between part-time roles in similar types of work, provided insights into the design of professional part-time work. Analysis revealed that having a better understanding of design characteristics may help explain disadvantages associated with professional part-time work, and that some full-time roles can be more easily adapted to part-time arrangements than others. Importantly, comparisons revealed that even roles that are considered difficult to undertake on a part-time basis can potentially be re-designed to be more effective. Through empirical testing of the framework, a contextualised work design model is presented that may guide further research and the practice of crafting part-time arrangements. The findings also suggest that poor work design may lead to the symptoms associated with professional part-time work, and that improved work design may be a potential solution to these structural constraints.

Analytical Solution of a Walters’ Liquid B Flow Over a Linear Stretching Sheet in a Porous Medium

This chapter represents the analytical solution of two-dimensional linear stretching sheet problem involving a non-Newtonian liquid and suction by (a) invoking the boundary layer approximation and (b) using this result to solve the stretching sheet problem without using boundary layer approximation. The basic boundary layer equations for momentum, which are non-linear partial differential equations, are converted into non-linear ordinary differential equations by means of similarity transformation. The results reveal a new analytical procedure for solving the boundary layer equations arising in a linear stretching sheet problem involving a non-Newtonian liquid (Walters’ liquid B). The present study throws light on the analytical solution of a class of boundary layer equations arising in the stretching sheet problem.

Adams-Type Methods for the Numerical Solution of Stochastic Ordinary Differential Equations

Stochastic differential equations (SDEs) arise fi om physical systems where the parameters describing the system can only be estimated or are subject to noise. There has been much work done recently on developing numerical methods for solving SDEs. This paper will focus on stability issues and variable stepsize implementation techniques for numerically solving SDEs effectively. (C) 2000 Elsevier Science B.V. All rights reserved.

Student focus and prioritization of design parameters in first-year engineering design projects

BACKGROUND Research on engineering design is a core area of concern within engineering education and a fundamental understanding of how engineering students approach and undertake design is necessary in order to develop effective design models and pedagogies. Understanding the factors related to design experiences in education and how they affect student practice can help educators as well as designers to leverage these factors as part of the design process. PURPOSE This study investigated the design practices of first-year engineering students’ and their experiences with a first-year engineering course design project. The research questions that guided the investigation were: 1. From a student perspective, what design parameters or criteria are most important? 2. How does this perspective impact subsequent student design practice throughout the design process? DESIGN/METHOD The authors employed qualitative multi-case study methods (Miles & Huberman, 1994) in order to the answer the research questions. Participant teams were observed and video recorded during team design meetings in which they researched the background for the design problem, brainstormed and sketched possible solutions, as well as built prototypes and final models of their design solutions as part of a course design project. Analysis focused on explanation building (Yin, 2009) and utilized within-case and cross-case analysis (Miles & Huberman, 1994). RESULTS We found that students focused disproportionally on the functional parameter, i.e. the physical implementation of their solution, and the possible/applicable parameter, i.e. a possible and applicable solution that benefited the user, in comparison to other given parameters such as safety and innovativeness. In addition, we found that individual teams focused on the functional and possible/ applicable parameters in early design phases such as brainstorming/ ideation and sketching. When prompted to discuss these non-salient parameters (from the student perspective) in the final design report, student design teams often used a post-hoc justification to support how the final designs fit the parameters that they did not initially consider. CONCLUSIONS This study suggests is that student design teams become fixated on (and consequently prioritize) certain parameters they interpret as important because they feel these parameters were described more explicitly in terms how they were met and assessed. Students fail to consider other parameters, perceived to be less directly assessable, unless prompted to do so. Failure to consider other parameters in the early design phases subsequently affects their approach in design phases as well. Case studies examining students’ study strategies within three Australian Universities illustrate similarities with some student approaches to design.

Novel solutions for a model of wound healing angiogenesis

We prove the existence of novel, shock-fronted travelling wave solutions to a model of wound healing angiogenesis studied in Pettet et al (2000 IMA J. Math. App. Med. 17 395–413) assuming two conjectures hold. In the previous work, the authors showed that for certain parameter values, a heteroclinic orbit in the phase plane representing a smooth travelling wave solution exists. However, upon varying one of the parameters, the heteroclinic orbit was destroyed, or rather cut-off, by a wall of singularities in the phase plane. As a result, they concluded that under this parameter regime no travelling wave solutions existed. Using techniques from geometric singular perturbation theory and canard theory, we show that a travelling wave solution actually still exists for this parameter regime. We construct a heteroclinic orbit passing through the wall of singularities via a folded saddle canard point onto a repelling slow manifold. The orbit leaves this manifold via the fast dynamics and lands on the attracting slow manifold, finally connecting to its end state. This new travelling wave is no longer smooth but exhibits a sharp front or shock. Finally, we identify regions in parameter space where we expect that similar solutions exist. Moreover, we discuss the possibility of more exotic solutions.

Semi-similar solution of an unsteady compressible three-dimensional stagnation point boundary layer flow with massive blowing

A semi-similar solution of an unsteady laminar compressible three-dimensional stagnation point boundary layer flow with massive blowing has been obtained when the free stream velocity varies arbitrarily with time. The resulting partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme with a quasi-linearization technique in the nodal point region and an implicit finite-difference scheme with a parametric differentiation technique in the saddle point region. The results have been obtained for two particular unsteady free stream velocity distributions: (i) an accelerating stream and (ii) a fluctuating stream. Results show that the skin-friction and heat-transfer parameters respond significantly to the time dependent arbitrary free stream velocity. Velocity and enthalpy profiles approach their free stream values faster as time increases. There is a reverse flow in the y-wise velocity profile, and overshoot in the x-wise velocity and enthalpy profiles in the saddle point region, which increase as injection and wall temperature increase. Location of the dividing streamline increases as injection increases, but as the wall temperature and time increase, it decreases.

Solution concepts in two-person multicriteria games

In this paper, we propose new solution concepts for multicriteria games and compare them with existing ones. The general setting is that of two-person finite games in normal form (matrix games) with pure and mixed strategy sets for the players. The notions of efficiency (Pareto optimality), security levels, and response strategies have all been used in defining solutions ranging from equilibrium points to Pareto saddle points. Methods for obtaining strategies that yield Pareto security levels to the players or Pareto saddle points to the game, when they exist, are presented. Finally, we study games with more than two qualitative outcomes such as combat games. Using the notion of guaranteed outcomes, we obtain saddle-point solutions in mixed strategies for a number of cases. Examples illustrating the concepts, methods, and solutions are included.

In-situ measurements of concentration and temperature during transient solidification of aqueous solution of ammonium chloride using laser interferometry

The variation in temperature and concentration plays a crucial role in predicting the final microstructure during solidification of a binary alloy. Most of the experimental techniques used to measure concentration and temperature are intrusive in nature and affect the flow field. In this paper, the main focus is laid on in-situ, non-intrusive, transient measurement of concentration and temperature during the solidification of a binary mixture of aqueous ammonium chloride solution (a metal-analog system) in a top cooled cavity using laser based Mach-Zehnder Interferometric technique. It was found from the interferogram, that the angular deviation of fringe pattern and the total number of fringes exhibit significant sensitivity to refractive index and hence are functions of the local temperature and concentration of the NH4Cl solution inside the cavity. Using the fringe characteristics, calibration curves were established for the range of temperature and concentration levels expected during the solidification process. In the actual solidification experiment, two hypoeutectic solutions (5% and 15% NH4Cl) were chosen. The calibration curves were used to determine the temperature and concentration of the solution inside the cavity during solidification of 5% and 15% NH4Cl solution at different instants of time. The measurement was carried out at a fixed point in the cavity, and the concentration variation with time was recorded as the solid-liquid interface approached the measurement point. The measurement exhibited distinct zones of concentration distribution caused by solute rejection and Rayleigh Benard convection. Further studies involving flow visualization with laser scattering confirmed the Rayleigh Benard convection. Computational modeling was also performed, which corroborated the experimental findings. (C) 2011 Elsevier Ltd. All rights reserved.

Determination of electric field at and near the focus of a cylindrical lens for applications in fluorescence microscopy

We present an explicit computable integral solution of the electric field generated at the focal region of a cylindrical lens. This representation is based on vectorial diffraction theory and further enables the computation of the system point spread function of a cylindrical lens. It is assumed that there is no back-scattering and the contribution from the evanescent field is negligible. Stationary phase approximation along with the Fresnel transmission coefficients are employed for evaluating the polarization dependent electric field components. Studies were carried out to determine the polarization effects and to calculate the system resolution. The effect of s -, p - and randomly polarized light is studied on the fixed sample (electric dipole is fixed in space). Proposed approach allows better understanding of electric field effects at the focus of a cylindrical aplanatic system. This opens up future developments in the field of fluorescence microscopy and optical imaging. (C) 2013 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License.

Dynamic Stability of Electrostatic Torsional Actuators with van Der Waals Effect

electrostatic torsional nano-electro-mechanical systems (NEMS) actuators is analyzed in the paper. The dependence of the critical tilting angle and voltage is investigated on the sizes of structure with the consideration of vdW effects. The pull-in phenomenon without the electrostatic torque is studied, and a critical pull-in gap is derived. A dimensionless equation of motion is presented, and the qualitative analysis of it shows that the equilibrium points of the corresponding autonomous system include center points, stable focus points, and unstable saddle points. The Hopf bifurcation points and fork bifurcation points also exist in the system. The phase portraits connecting these equilibrium points exhibit periodic orbits, heteroclinic orbits, as well as homoclinic orbits.

IPCC WGII Fifth Assessment Report (AR5): Expanding the solution space for adaptation

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