Theoretical analysis of Rayleigh–Taylor instability on a spherical droplet in a gas stream

A linear analysis of the Rayleigh–Taylor (R–T) instability on a spherical viscous liquid droplet in a gas stream is presented. Different from the most previous studies in which the external acceleration is usually assumed to be radial, the present study considers a unidirectional acceleration acting on a spherical droplet with arbitrary initial disturbances and therefore can provide insights into the influence of R–T instability on the atomization of spherical droplets. A general recursion relation coupling different spherical modes is derived and two physically prevalent limiting cases are discussed. In the limiting case of inviscid droplet, the critical Bond numbers to excite the instability and the growth rates for a given Bond number are obtained by solving two eigenvalue problems. In the limiting case of large droplet acceleration, different spherical modes are asymptotically decoupled and an explicit dispersion relation is derived. For given Bond number and Ohnesorge numbers, the critical size of stable droplet, the most-unstable mode and its corresponding growth rate are determined theoretically.     

Availability analysis of a repairable duplex system: a z-dependent Sokhotski–Plemelj problem

We analyse the point availability of a repairable duplex system characterized by cold standby and by a priority rule. The system is attended by two (general) heterogeneous repairmen. To describe the random behaviour of the system, we introduce a stochastic process endowed with probability measures satisfying (coupled) partial differential equations. The solution procedure is based on the theory of sectionally holomorphic functions combined with the notion of dual transforms. The unique solution of the equations determines the point availability of the system. Computational results for the point availability are derived by a numerical solution of an appropriate integral equation.     

Modeling and analysis of a prey–predator system with disease in the prey

A three dimensional ecoepidemiological model consisting of susceptible prey, infected prey and predator is proposed and analysed in the present work. The parameter delay is introduced in the model system for considering the time taken by a susceptible prey to become infected. Mathematically we analyze the dynamics of the system such as, boundedness of the solutions, existence of non-negative equilibria, local and global stability of interior equilibrium point. Next we choose delay as a bifurcation parameter to examine the existence of the Hopf bifurcation of the system around its interior equilibrium. Moreover we use the normal form method and center manifold theorem to investigate the direction of the Hopf bifurcation and stability of the bifurcating limit cycle. Some numerical simulations are carried out to support the analytical results.     

Boundary layer analysis in the semiclassical limit of a quantum drift–diffusion model

We study a singularly perturbed elliptic second order system in one space variable as it appears in a stationary quantum drift–diffusion model of a semiconductor. We prove the existence of solutions and their uniqueness as minimizers of a certain functional and determine rigorously the principal part of an asymptotic expansion of a boundary layer of those solutions. We prove analytical estimates of the remainder terms of this asymptotic expansion, and confirm by means of numerical simulations that these remainder estimates are sharp.     

Solution of Contrast Structure Type for a Parabolic Reaction–Diffusion Problem in a Medium with Discontinuous Characteristics

We consider a reaction–diffusion-type equation in a two-dimensional domain containing the interface between media with distinct characteristics along which the reactive term has a discontinuity of the first kind. We assume that the interface between the media, as well as the functions describing the reactions, periodically varies in time. We study the existence of a stable periodic solution of a problem with an internal layer. To prove the existence, stability, and local uniqueness of the solution, we use the asymptotic method of differential inequalities, which we generalized to a new class of problems with discontinuous nonlinearities.     

Simultaneous estimation of the origin–destination matrices and the parameters of a nested logit model in a combined network equilibrium model

This paper deals with the inverse problem of a type of traffic equilibrium models with combined modes. This problem consists of obtaining a parametrization of the equilibrium model from a set of observations of the outputs for the model. The inputs for the model are an origin–destination (O–D) trip matrix for the various alternatives that have been considered, and a set of parameters for a nested logit model used as a demand model.     

Bifurcation analysis of the Gierer–Meinhardt system with a saturation in the activator production

The reaction–diffusion Gierer–Meinhardt system with a saturation in the activator production is considered. Stability of the unique positive constant steady state solution is analysed, and associated Hopf bifurcations and steady state bifurcations are obtained. A global bifurcation diagram of non-trivial periodic orbits and steady state solutions with respect to key system parameters is obtained, which improves the understanding of dynamics of Gierer–Meinhardt system with a saturation in different parameter regimes.     

Coupling input–output analysis with multiobjective linear programming models for the study of economy–energy–environment–social (E3S) trade-offs: a review

Private enterprises, such as Wal-Mart and Home Depot, have implemented effective relief efforts in responding to Hurricane Katrina in 2005. From the perspective of operation research, the factors of this success have been addressed as quick response, pre-position and logistic expertise. However, the waste made by FEMA for stockpiling food and ice in anticipation of a busy hurricane season in 2006 and several other cases indicate otherwise. In this paper, we introduce the private enterprise into a relief supply chain and propose an outsourcing framework to uncover the reason of Wal-Mart’s success and provide explanations to the counter-cases. Our study shows that the effective relief effort carried out by private enterprises in responding to Hurricane Katrina in 2005 attributes to the combination of proactive response method and logistic expertise. Our findings advocate adopting different strategies to deal with different types of relief supplies. Specifically, the proactive insourcing strategy is good enough for a relief supply chain involving only imperishable relief supplies. For perishable goods, the proactive outsourcing strategy can make a relief supply more efficient.     

The Group Structure of the Normalizer of Γ0(N) After Atkin–Lehner

We determine the group structure of the normalizer of Γ₀(N) in SL ₂(?) modulo Γ₀(N). These results correct the Atkin–Lehner statement (Atkin and Lehner, 1970 Atkin , A. O. L. , Lehner , J. ( 1970 ). Hecke operator on Γ₀(N) . Math. Ann. 185 : 134 – 160 .[Crossref], [Web of Science ®] , [Google Scholar], Theorem 8).     

Anisotropic transient thermoelasticity analysis in a two-dimensional decagonal quasicrystal using meshless local Petrov–Galerkin (MLPG) method

The meshless local Petrov–Galerkin (MLPG) method is employed for anisotropic transient thermoelasticity analysis of 2D decagonal quasicrystals (QCs) subjected to transient thermal and mechanical shock loadings. The wave type model and the elasto-hydrodynamic model are applied to derive the phonon and phason governing equations, respectively. The temperature affects only the phonon field. To find the temperature distributions on the assumed 2D domain, the anisotropic heat conduction problem is solved using the MLPG method. Also, the MLPG method is successfully employed to obtain the transient behaviors of both phonon and phason displacements by solving the governing equations in local integral equations (LIEs) forms. Making use a unit step function as the test functions in the local weak-form of governing equations, we derived the local integral equations (LIEs) considered on small subdomains identical with support domains of test functions around each node. The radial basis functions are used for approximation of the spatial variation of field variables. The Laplace-transform technique is utilized to discretize the time variations.     

The motion of a particle on a light viscoelastic bar: asymptotic analysis of its quasilinear parabolic–hyperbolic equation

We study the large longitudinal motion of a nonlinearly viscoelastic bar with one end fixed and the other end attached to a heavy particle. This problem is a precise continuum-mechanical analog of the basic discrete mechanical problem of the motion of a particle on a (massless) spring. This motion is governed by an initial-boundary-value problem for a class of third-order quasilinear parabolic–hyperbolic partial differential equations subject to a nonstandard boundary condition, which is the equation of motion of the particle. The ratio of the mass of the bar to that of the tip mass is taken to be a small parameter ε. We prove that this problem has a unique globally defined solution that admits a valid asymptotic expansion, including an initial-layer expansion, in powers of ε for ε near 0. The validity of the expansion gives a precise meaning to the solution of the reduced problem, obtained by setting ε=0, which curiously is seldom governed by the expected ordinary differential equation. The fundamental constitutive hypothesis that the tension be a uniformly monotone function of the strain rate plays a critical role in a delicate proof that each term of the initial-layer expansion decays exponentially in time. These results depend on new decay estimates for the solution of quasilinear parabolic equations.     

Dynamic analysis of a non-conservative band–wheel system with a moving boundary part 2: Numerical results

The dynamic formulations of a non-conservative band/wheel system with a moving boundary are derived in the companion paper by use of Hamilton’s principle and calculus of variation. In this paper, numerical simulations for the system are obtained in transient amplitudes of the string and positions of the moving boundary by a modified finite difference method (FDM). Since the moving boundary position may not locate exactly at a grid point for any computational time, a special technique of the FDM is proposed to approximate both the transversality condition of a moving boundary and the partial differential equation of the neighboring grid points. The effects of parameters such as radius of the wheel, tension of the string, propagation speeds of the longitudinal and transverse wave and various initial conditions on the transient responses are investigated and compared with those of the fixed boundary problem.